From c149013fe3a71392398c28cd4b6ce3d343786088 Mon Sep 17 00:00:00 2001 From: Craig Gidney Date: Wed, 4 Oct 2023 13:16:24 -0700 Subject: [PATCH 1/3] copy --- glue/lattice_surgery/base.gltf | 552 +++++++++++++++++++++++++++ glue/lattice_surgery/gltf_gen.py | 214 +++++++++++ glue/lattice_surgery/lasir_gen.py | 12 + glue/lattice_surgery/main.py | 12 + glue/lattice_surgery/old_gltf_gen.py | 521 +++++++++++++++++++++++++ glue/lattice_surgery/sample.gltf | 1 + glue/lattice_surgery/sample.lasir | 1 + glue/lattice_surgery/sample.olsco | 103 +++++ 8 files changed, 1416 insertions(+) create mode 100644 glue/lattice_surgery/base.gltf create mode 100644 glue/lattice_surgery/gltf_gen.py create mode 100644 glue/lattice_surgery/lasir_gen.py create mode 100644 glue/lattice_surgery/main.py create mode 100644 glue/lattice_surgery/old_gltf_gen.py create mode 100644 glue/lattice_surgery/sample.gltf create mode 100644 glue/lattice_surgery/sample.lasir create mode 100644 glue/lattice_surgery/sample.olsco 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"indices": 3, + "material": 4 + } + ] + }, + { + "name": "rectangle-transparent-cyan", + "primitives": [ + { + "attributes": { + "NORMAL": 2, + "POSITION": 1 + }, + "indices": 3, + "material": 4 + } + ] + }, + { + "name": "square-transparent-yellow", + "primitives": [ + { + "attributes": { + "NORMAL": 2, + "POSITION": 0 + }, + "indices": 3, + "material": 5 + } + ] + }, + { + "name": "rectangle-transparent-yellow", + "primitives": [ + { + "attributes": { + "NORMAL": 2, + "POSITION": 1 + }, + "indices": 3, + "material": 5 + } + ] + } + ], + "nodes": [ + { + "children": [ + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13 + ], + "name": "try" + }, + { + "mesh": 0, + "name": "type0", + "rotation": [ + 0, + 0, + 0, + 1 + ] + }, + { + "mesh": 1, + "name": "type1", + "translation": [ + 2, + 0, + 0 + ] + }, + { + "mesh": 2, + "name": "type2", + "translation": [ + 4, + 0, + 0 + ] + }, + { + "mesh": 3, + "name": "type3", + "translation": [ + 6, + 0, + 0 + ] + }, + { + "mesh": 4, + "name": "type4", + "translation": [ + 8, + 0, + 0 + ] + }, + { + "mesh": 5, + "name": "type5", + "translation": [ + 11, + 0, + 0 + ] + }, + { + "mesh": 6, + "name": "type6", + "translation": [ + 14, + 0, + 0 + ] + }, + { + "mesh": 7, + "name": "type7", + "translation": [ + 17, + 0, + 0 + ] + }, + { + "mesh": 8, + "name": "type8", + "translation": [ + 20, + 0, + 0 + ] + }, + { + "mesh": 9, + "name": "type9", + "translation": [ + 14, + 2, + 0 + ] + }, + { + "mesh": 10, + "name": "type10", + "translation": [ + 16, + 2, + 0 + ] + }, + { + "mesh": 11, + "name": "type11", + "translation": [ + 11, + 2, + 0 + ] + }, + { + "mesh": 12, + "name": "type112", + "translation": [ + 8, + 2, + 0 + ] + } + ], + "scene": 0, + "scenes": [ + { + "name": "Scene", + "nodes": [ + 0 + ] + } + ] +} \ No newline at end of file diff --git a/glue/lattice_surgery/gltf_gen.py b/glue/lattice_surgery/gltf_gen.py new file mode 100644 index 000000000..52e159eaf --- /dev/null +++ b/glue/lattice_surgery/gltf_gen.py @@ -0,0 +1,214 @@ +import codecs +import struct +import json + +SQ2 = 0.70710678118 + +def float_to_little_endian_hex(f): + # Pack the float into a binary string using the little-endian format + binary_data = struct.pack('0 and ExistX[x-1][y][z]: + exists['-x'] = 1 + if ExistX[x][y][z]: + exists['+x'] = 1 + if y>0 and ExistY[x][y-1][z]: + exists['-y'] = 1 + if ExistY[x][y][z]: + exists['+y'] = 1 + if z>0 and ExistZ[x][y][z-1]: + exists['-z'] = 1 + if ExistZ[x][y][z]: + exists['+z'] = 1 + + degree = sum([v for (k,v) in exists.items()]) + if degree == 1: + if NodeY[x][y][z]: + if exists['+z']: + gltf['nodes'].append({ + "name":f"InitY({x},{y},{z})", + "mesh": 4, + "translation": [SEP*x, SEP*z, -SEP*y] }) + if exists['-z']: + gltf['nodes'].append({ + "name":f"MeasY({x},{y},{z})", + "mesh": 4, + "rotation": [1, 0, 0, 0], + "translation": [SEP*x, SEP*z+1, -SEP*y-1] }) + else: + pass + elif degree == 2: + if NodeY[x][y][z]: + gltf['nodes'].append({ + "name":f"MeasInitY({x},{y},{z})", + "mesh": 6, + "translation": [SEP*x, SEP*z, -SEP*y] }) + else: + if exists['+z'] and exists['-z']: + if ColorZ[x][y][z]: + gltf['nodes'].append({ + "name":f"PassZ({x},{y},{z})-color1", + "mesh": 5, + "rotation": [0, SQ2, 0, SQ2], + "translation": [SEP*x+1, SEP*z, -SEP*y] }) + else: + gltf['nodes'].append({ + "name":f"PassZ({x},{y},{z})-color0", + "mesh": 5, + "translation": [SEP*x, SEP*z, -SEP*y] }) + + if exists['+y'] and exists['-y']: + if ColorY[x][y][z]: + gltf['nodes'].append({ + "name":f"PassY({x},{y},{z})", + "mesh": 5, + "rotation": [SQ2, 0, 0, SQ2], + "translation": [SEP*x, SEP*z, -SEP*y-1] }) + else: + gltf['nodes'].append({ + "name":f"PassY({x},{y},{z})", + "mesh": 5, + "rotation": [0.5, 0.5, 0.5, 0.5], + "translation": [SEP*x+1, SEP*z, -SEP*y-1] }) + + if exists['+x'] and exists['-x']: + if ColorX[x][y][z]: + gltf['nodes'].append({ + "name":f"PassX({x},{y},{z})", + "mesh": 5, + "rotation": [0, 0, SQ2, SQ2], + "translation": [SEP*x+1, SEP*z, -SEP*y] }) + else: + gltf['nodes'].append({ + "name":f"PassX({x},{y},{z})", + "mesh": 5, + "rotation": [0.5, -0.5, 0.5, 0.5], + "translation": [SEP*x+1, SEP*z, -SEP*y-1] }) + + if exists['-x'] and exists['+y']: + if ColorX[x-1][y][z]: + gltf['nodes'].append({ + "name":f"Turn-X&+Y({x},{y},{z})", + "mesh": 7, + "rotation": [-0.5, -0.5, 0.5, 0.5], + "translation": [SEP*x, SEP*z, -SEP*y] }) + else: + gltf['nodes'].append({ + "name":f"Turn-X&+Y({x},{y},{z})", + "mesh": 8, + "rotation": [-0.5, -0.5, 0.5, 0.5], + "translation": [SEP*x, SEP*z, -SEP*y] }) + + if exists['+x'] and exists['-y']: + if ColorX[x][y][z]: + gltf['nodes'].append({ + "name":f"Turn+X&-Y({x},{y},{z})", + "mesh": 7, + "rotation": [0, 0, -SQ2, SQ2], + "translation": [SEP*x, SEP*z+1, -SEP*y] }) + else: + gltf['nodes'].append({ + "name":f"Turn+X&-Y({x},{y},{z})", + "mesh": 8, + "rotation": [0, 0, -SQ2, SQ2], + "translation": [SEP*x, SEP*z+1, -SEP*y] }) + + if exists['+x'] and exists['+y']: + if ColorX[x][y][z]: + gltf['nodes'].append({ + "name":f"Turn+X&+Y({x},{y},{z})", + "mesh": 7, + "rotation": [-0.5, 0.5, -0.5, 0.5], + "translation": [SEP*x, SEP*z+1, -SEP*y] }) + else: + gltf['nodes'].append({ + "name":f"Turn+X&+Y({x},{y},{z})", + "mesh": 8, + "rotation": [-0.5, 0.5, -0.5, 0.5], + "translation": [SEP*x, SEP*z+1, -SEP*y] }) + + if exists['-x'] and exists['-y']: + if ColorX[x-1][y][z]: + gltf['nodes'].append({ + "name":f"Turn-X&-Y({x},{y},{z})", + "mesh": 7, + "rotation": [0.5, -0.5, -0.5, 0.5], + "translation": [SEP*x, SEP*z+1, -SEP*y-1] }) + else: + gltf['nodes'].append({ + "name":f"Turn-X&-Y({x},{y},{z})", + "mesh": 8, + "rotation": [0.5, -0.5, -0.5, 0.5], + "translation": [SEP*x, SEP*z+1, -SEP*y-1] }) + + if exists['-y'] and exists['+z']: + if ColorY[x][y-1][z]: + gltf['nodes'].append({ + "name":f"Turn-Y&+Z({x},{y},{z})", + "mesh": 7, + "rotation": [1, 0, 0, 0], + "translation": [SEP*x, SEP*z, -SEP*y] }) + else: + gltf['nodes'].append({ + "name":f"Turn-Y&+Z({x},{y},{z})", + "mesh": 8, + "rotation": [1, 0, 0, 0], + "translation": [SEP*x, SEP*z, -SEP*y] }) + + if exists['+y'] and exists['-z']: + if ColorY[x][y][z]: + gltf['nodes'].append({ + "name":f"Turn+Y&-Z({x},{y},{z})", + "mesh": 7, + "translation": [SEP*x, SEP*z+1, -SEP*y-1] }) + else: + gltf['nodes'].append({ + "name":f"Turn+Y&-Z({x},{y},{z})", + "mesh": 8, + "translation": [SEP*x, SEP*z+1, -SEP*y-1] }) + + if exists['+y'] and exists['+z']: + if ColorY[x][y][z]: + gltf['nodes'].append({ + "name":f"Turn+Y&+Z({x},{y},{z})", + "mesh": 7, + "rotation": [0, 1, 0, 0], + "translation": [SEP*x+1, SEP*z, -SEP*y-1] }) + else: + gltf['nodes'].append({ + "name":f"Turn+Y&+Z({x},{y},{z})", + "mesh": 8, + "rotation": [0, 1, 0, 0], + "translation": [SEP*x+1, SEP*z, -SEP*y-1] }) + + if exists['-y'] and exists['-z']: + if ColorY[x][y-1][z]: + gltf['nodes'].append({ + "name":f"Turn-Y&-Z({x},{y},{z})", + "mesh": 7, + "rotation": [SQ2, 0, 0, SQ2], + "translation": [SEP*x, SEP*z, -SEP*y-1] }) + else: + gltf['nodes'].append({ + "name":f"Turn-Y&-Z({x},{y},{z})", + "mesh": 8, + "rotation": [SQ2, 0, 0, SQ2], + "translation": [SEP*x, SEP*z, -SEP*y-1] }) + + if exists['+x'] and exists['+z']: + if ColorX[x][y][z]: + gltf['nodes'].append({ + "name":f"Turn+X&+Z({x},{y},{z})", + "mesh": 8, + "rotation": [0, SQ2, 0, SQ2], + "translation": [SEP*x+1, SEP*z, -SEP*y] }) + else: + gltf['nodes'].append({ + "name":f"Turn+X&+Z({x},{y},{z})", + "mesh": 7, + "rotation": [0, SQ2, 0, SQ2], + "translation": [SEP*x+1, SEP*z, -SEP*y] }) + + if exists['-x'] and exists['+z']: + if ColorX[x-1][y][z]: + gltf['nodes'].append({ + "name":f"Turn-X&+Z({x},{y},{z})", + "mesh": 8, + "rotation": [0, -SQ2, 0, SQ2], + "translation": [SEP*x, SEP*z, -SEP*y-1] }) + else: + gltf['nodes'].append({ + "name":f"Turn-X&+Z({x},{y},{z})", + "mesh": 7, + "rotation": [0, -SQ2, 0, SQ2], + "translation": [SEP*x, SEP*z, -SEP*y-1] }) + + if exists['+x'] and exists['-z']: + if ColorX[x][y][z]: + gltf['nodes'].append({ + "name":f"Turn+X&-Z({x},{y},{z})", + "mesh": 8, + "rotation": [0.5, 0.5, -0.5, 0.5], + "translation": [SEP*x, SEP*z, -SEP*y] }) + else: + gltf['nodes'].append({ + "name":f"Turn+X&-Z({x},{y},{z})", + "mesh": 7, + "rotation": [0.5, 0.5, -0.5, 0.5], + "translation": [SEP*x, SEP*z, -SEP*y] }) + + if exists['-x'] and exists['-z']: + if ColorX[x-1][y][z]: + gltf['nodes'].append({ + "name":f"Turn-X&-Z({x},{y},{z})", + "mesh": 8, + "rotation": [0.5, -0.5, 0.5, 0.5], + "translation": [SEP*x+1, SEP*z, -SEP*y-1] }) + else: + gltf['nodes'].append({ + "name":f"Turn-X&-Z({x},{y},{z})", + "mesh": 7, + "rotation": [0.5, -0.5, 0.5, 0.5], + "translation": [SEP*x+1, SEP*z, -SEP*y-1] }) + + elif degree == 3: + if exists['-y'] and exists['+y'] and exists['+z']: + if ColorY[x][y][z]: + gltf['nodes'].append({ + "name":f"JuncY&+Z({x},{y},{z})", + "mesh": 9, + "translation": [SEP*x, SEP*z, -SEP*y] }) + else: + gltf['nodes'].append({ + "name":f"JuncY&+Z({x},{y},{z})", + "mesh": 10, + "translation": [SEP*x, SEP*z, -SEP*y] }) + + if exists['-y'] and exists['+y'] and exists['-z']: + if ColorY[x][y][z]: + gltf['nodes'].append({ + "name":f"JuncY&-Z({x},{y},{z})", + "mesh": 9, + "rotation": [1, 0, 0, 0], + "translation": [SEP*x, SEP*z+1, -SEP*y-1] }) + else: + gltf['nodes'].append({ + "name":f"JuncY&+Z({x},{y},{z})", + "mesh": 10, + "translation": [SEP*x, SEP*z+1, -SEP*y-1] }) + + if exists['-z'] and exists['+z'] and exists['-y']: + if ColorY[x][y-1][z]: + gltf['nodes'].append({ + "name":f"JuncZ&-Y({x},{y},{z})", + "mesh": 9, + "rotation": [SQ2, 0, 0, SQ2], + "translation": [SEP*x, SEP*z, -SEP*y-1] }) + else: + gltf['nodes'].append({ + "name":f"JuncZ&-Y({x},{y},{z})", + "mesh": 10, + "rotation": [SQ2, 0, 0, SQ2], + "translation": [SEP*x, SEP*z, -SEP*y-1] }) + + if exists['-z'] and exists['+z'] and exists['+y']: + if ColorY[x][y][z]: + gltf['nodes'].append({ + "name":f"JuncZ&+Y({x},{y},{z})", + "mesh": 9, + "rotation": [-SQ2, 0, 0, SQ2], + "translation": [SEP*x, SEP*z+1, -SEP*y] }) + else: + gltf['nodes'].append({ + "name":f"JuncZ&+Y({x},{y},{z})", + "mesh": 10, + "rotation": [-SQ2, 0, 0, SQ2], + "translation": [SEP*x, SEP*z+1, -SEP*y] }) + + if exists['-y'] and exists['+y'] and exists['-x']: + if ColorX[x-1][y][z]: + gltf['nodes'].append({ + "name":f"JuncY&-X({x},{y},{z})", + "mesh": 9, + "rotation": [0, 0, SQ2, SQ2], + "translation": [SEP*x+1, SEP*z, -SEP*y] }) + else: + gltf['nodes'].append({ + "name":f"JuncY&-X({x},{y},{z})", + "mesh": 10, + "rotation": [0, 0, SQ2, SQ2], + "translation": [SEP*x+1, SEP*z, -SEP*y] }) + + if exists['-y'] and exists['+y'] and exists['+x']: + if ColorX[x][y][z]: + gltf['nodes'].append({ + "name":f"JuncY&+X({x},{y},{z})", + "mesh": 9, + "rotation": [0, 0, -SQ2, SQ2], + "translation": [SEP*x, SEP*z+1, -SEP*y] }) + else: + gltf['nodes'].append({ + "name":f"JuncY&+X({x},{y},{z})", + "mesh": 10, + "rotation": [0, 0, -SQ2, SQ2], + "translation": [SEP*x, SEP*z+1, -SEP*y] }) + + if exists['-x'] and exists['+x'] and exists['-y']: + if ColorX[x][y][z]: + gltf['nodes'].append({ + "name":f"JuncX&-Y({x},{y},{z})", + "mesh": 9, + "rotation": [0.5, 0.5, 0.5, 0.5], + "translation": [SEP*x+1, SEP*z, -SEP*y-1] }) + else: + gltf['nodes'].append({ + "name":f"JuncX&-Y({x},{y},{z})", + "mesh": 10, + "rotation": [0.5, 0.5, 0.5, 0.5], + "translation": [SEP*x+1, SEP*z, -SEP*y-1] }) + + if exists['-x'] and exists['+x'] and exists['+y']: + if ColorX[x][y][z]: + gltf['nodes'].append({ + "name":f"JuncX&+Y({x},{y},{z})", + "mesh": 9, + "rotation": [-0.5, 0.5, -0.5, 0.5], + "translation": [SEP*x+1, SEP*z+1, -SEP*y] }) + else: + gltf['nodes'].append({ + "name":f"JuncX&+Y({x},{y},{z})", + "mesh": 10, + "rotation": [-0.5, 0.5, -0.5, 0.5], + "translation": [SEP*x+1, SEP*z+1, -SEP*y] }) + + if exists['-x'] and exists['+x'] and exists['+z']: + if ColorX[x][y][z]: + gltf['nodes'].append({ + "name":f"JuncX&+Z({x},{y},{z})", + "mesh": 10, + "rotation": [0, SQ2, 0, SQ2], + "translation": [SEP*x+1, SEP*z, -SEP*y] }) + else: + gltf['nodes'].append({ + "name":f"JuncX&+Z({x},{y},{z})", + "mesh": 9, + "rotation": [0, SQ2, 0, SQ2], + "translation": [SEP*x+1, SEP*z, -SEP*y] }) + + if exists['-x'] and exists['+x'] and exists['-z']: + if ColorX[x][y][z]: + gltf['nodes'].append({ + "name":f"JuncX&-Z({x},{y},{z})", + "mesh": 10, + "rotation": [SQ2, 0, SQ2, 0], + "translation": [SEP*x+1, SEP*z+1, -SEP*y] }) + else: + gltf['nodes'].append({ + "name":f"JuncX&-Z({x},{y},{z})", + "mesh": 9, + "rotation": [SQ2, 0, SQ2, 0], + "translation": [SEP*x+1, SEP*z+1, -SEP*y] }) + + if exists['-z'] and exists['+z'] and exists['+x']: + if ColorX[x][y][z]: + gltf['nodes'].append({ + "name":f"JuncZ&+X({x},{y},{z})", + "mesh": 10, + "rotation": [0.5, 0.5, -0.5, 0.5], + "translation": [SEP*x, SEP*z, -SEP*y] }) + else: + gltf['nodes'].append({ + "name":f"JuncZ&+X({x},{y},{z})", + "mesh": 9, + "rotation": [0.5, 0.5, -0.5, 0.5], + "translation": [SEP*x, SEP*z, -SEP*y] }) + + if exists['-z'] and exists['+z'] and exists['-x']: + if ColorX[x-1][y][z]: + gltf['nodes'].append({ + "name":f"JuncZ&-X({x},{y},{z})", + "mesh": 10, + "rotation": [0.5, -0.5, 0.5, 0.5], + "translation": [SEP*x+1, SEP*z, -SEP*y-1] }) + else: + gltf['nodes'].append({ + "name":f"JuncZ&-X({x},{y},{z})", + "mesh": 9, + "rotation": [0.5, -0.5, 0.5, 0.5], + "translation": [SEP*x+1, SEP*z, -SEP*y-1] }) + + elif degree == 4: + if exists['-z'] and exists['+z'] and exists['-y'] and exists['+y']: + if ColorY[x][y][z]: + gltf['nodes'].append({ + "name":f"CrossYZ({x},{y},{z})", + "mesh": 11, + "translation": [SEP*x, SEP*z, -SEP*y] }) + else: + gltf['nodes'].append({ + "name":f"CrossYZ({x},{y},{z})", + "mesh": 12, + "translation": [SEP*x, SEP*z, -SEP*y] }) + + if exists['-x'] and exists['+x'] and exists['-y'] and exists['+y']: + if ColorX[x][y][z]: + gltf['nodes'].append({ + "name":f"CrossXY({x},{y},{z})", + "mesh": 11, + "translation": [SEP*x+1, SEP*z, -SEP*y] }) + else: + gltf['nodes'].append({ + "name":f"CrossXY({x},{y},{z})", + "mesh": 12, + "translation": [SEP*x+1, SEP*z, -SEP*y] }) + + if exists['-x'] and exists['+x'] and exists['-z'] and exists['+z']: + if ColorX[x][y][z]: + gltf['nodes'].append({ + "name":f"CrossXZ({x},{y},{z})", + "mesh": 12, + "translation": [SEP*x+1, SEP*z, -SEP*y] }) + else: + gltf['nodes'].append({ + "name":f"CrossXZ({x},{y},{z})", + "mesh": 11, + "translation": [SEP*x+1, SEP*z, -SEP*y] }) + + elif degree >= 5: + raise ValueError('Have 3D corner!') + +gltf['nodes'][0]['children'] = list(range(1, len(gltf['nodes']))) +with open(OLSCO_FILE_NAME.replace('.json', '.gltf'), 'w') as f: + json.dump(gltf, f) \ No newline at end of file diff --git a/glue/lattice_surgery/sample.gltf b/glue/lattice_surgery/sample.gltf new file mode 100644 index 000000000..d6af77309 --- /dev/null +++ b/glue/lattice_surgery/sample.gltf @@ -0,0 +1 @@ +{"accessors": [{"bufferView": 0, "componentType": 5126, "count": 4, "max": [1, 0, 0], "min": [0, 0, -1], "type": "VEC3"}, {"bufferView": 1, "componentType": 5126, "count": 4, "max": [2, 0, 0], "min": [0, 0, -1], "type": "VEC3"}, {"bufferView": 2, "componentType": 5126, "count": 4, "type": "VEC3"}, 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[[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], [[0, 0, 0, 0, 1], [1, 1, 0, 0, 0]]]], "CorrKI": [[[[1, 1, 0, 1, 0], [0, 0, 0, 0, 0]], [[0, 0, 1, 0, 0], [0, 0, 0, 0, 0]], [[1, 1, 0, 0, 0], [0, 0, 0, 0, 0]], [[1, 1, 1, 0, 0], [0, 0, 0, 0, 0]], [[0, 0, 0, 1, 0], [1, 1, 0, 0, 0]]]]} \ No newline at end of file diff --git a/glue/lattice_surgery/sample.olsco b/glue/lattice_surgery/sample.olsco new file mode 100644 index 000000000..c8c4a3013 --- /dev/null +++ b/glue/lattice_surgery/sample.olsco @@ -0,0 +1,103 @@ +{ + "i_bound": 5, + "j_bound": 2, + "k_bound": 5, + "ports": [[0, 0, 4, 5]], + "stabilizer": ["Y"], + "NodeY": [ + [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], + [[1, 0, 0, 0, 1], [0, 0, 0, 0, 0]], + [[0, 0, 0, 1, 0], [0, 0, 0, 0, 0]], + [[0, 0, 0, 0, 1], [0, 0, 0, 0, 0]], + [[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]] + ], + "ExistI": [ + [[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], + [[0, 0, 0, 0, 0], [1, 1, 1, 1, 0]], + [[0, 0, 0, 0, 0], [1, 1, 1, 1, 0]], + [[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], + [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]] + ], + "ColorI": [ + [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], + [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], + [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], + [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], + [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]] + ], + "ExistJ": [ + [[1, 0, 1, 1, 0], [0, 0, 0, 0, 0]], + [[0, 1, 1, 1, 0], [0, 0, 0, 0, 0]], + [[1, 1, 1, 0, 0], [0, 0, 0, 0, 0]], + [[1, 1, 0, 1, 0], [0, 0, 0, 0, 0]], + [[0, 0, 0, 1, 0], [0, 0, 0, 0, 0]] + ], + "ColorJ": [ + [[1, 0, 1, 1, 0], [0, 0, 0, 0, 0]], + [[0, 1, 1, 1, 0], [0, 0, 0, 0, 0]], + [[1, 1, 1, 0, 0], [0, 0, 0, 0, 0]], + [[1, 1, 0, 1, 0], [0, 0, 0, 0, 0]], + [[0, 0, 0, 1, 0], [0, 0, 0, 0, 0]] + ], + "ExistK": [ + [[1, 1, 1, 1, 0], [0, 0, 0, 0, 0]], + [[1, 1, 1, 1, 0], [0, 0, 0, 0, 0]], + [[1, 1, 1, 0, 0], [0, 0, 0, 0, 0]], + [[1, 1, 1, 1, 0], [0, 0, 0, 0, 0]], + [[0, 0, 0, 1, 0], [1, 1, 0, 0, 0]] + ], + "CorrIK": [ + [ + [[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], + [[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], + [[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], + [[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], + [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]] + ] + ], + "CorrIJ": [ + [ + [[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], + [[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], + [[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], + [[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], + [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]] + ] + ], + "CorrJK": [ + [ + [[1, 0, 1, 1, 0], [0, 0, 0, 0, 0]], + [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], + [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], + [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], + [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]] + ] + ], + "CorrJI": [ + [ + [[1, 0, 1, 1, 0], [0, 0, 0, 0, 0]], + [[0, 0, 1, 1, 0], [0, 0, 0, 0, 0]], + [[1, 0, 1, 0, 0], [0, 0, 0, 0, 0]], + [[1, 0, 0, 1, 0], [0, 0, 0, 0, 0]], + [[0, 0, 0, 1, 0], [0, 0, 0, 0, 0]] + ] + ], + "CorrKJ": [ + [ + [[1, 1, 1, 1, 0], [0, 0, 0, 0, 0]], + [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], + [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], + [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], + [[0, 0, 0, 0, 1], [1, 1, 0, 0, 0]] + ] + ], + "CorrKI": [ + [ + [[1, 1, 0, 1, 0], [0, 0, 0, 0, 0]], + [[0, 0, 1, 0, 0], [0, 0, 0, 0, 0]], + [[1, 1, 0, 0, 0], [0, 0, 0, 0, 0]], + [[1, 1, 1, 0, 0], [0, 0, 0, 0, 0]], + [[0, 0, 0, 1, 0], [1, 1, 0, 0, 0]] + ] + ] +} \ No newline at end of file From 5d7debed4ea6597db7a91eb1fe0d93d96a9712f5 Mon Sep 17 00:00:00 2001 From: Craig Gidney Date: Wed, 4 Oct 2023 14:08:46 -0700 Subject: [PATCH 2/3] CL --- glue/lattice_surgery/.gitignore | 9 + glue/lattice_surgery/README.md | 11 + glue/lattice_surgery/base.gltf | 552 ----- glue/lattice_surgery/docs/demo.ipynb | 848 ++++++++ glue/lattice_surgery/gltf_gen.py | 214 -- glue/lattice_surgery/lasir_gen.py | 12 - glue/lattice_surgery/main.py | 12 - glue/lattice_surgery/old_gltf_gen.py | 521 ----- glue/lattice_surgery/olssco/__init__.py | 2 + .../olssco/lattice_surgery_compiler.py | 460 +++++ .../olssco/rewrite_passes/__init__.py | 0 .../olssco/rewrite_passes/attach_fixups.py | 64 + .../olssco/rewrite_passes/color_z.py | 176 ++ .../rewrite_passes/remove_unconnected.py | 134 ++ .../olssco/sat_lattice_surgery_solver.py | 1805 +++++++++++++++++ glue/lattice_surgery/olssco/tools/__init__.py | 0 .../olssco/tools/verify_stabilizers.py | 40 + .../olssco/translators/__init__.py | 1 + .../olssco/translators/gltf_generator.py | 1582 +++++++++++++++ .../olssco/translators/networkx_generator.py | 250 +++ .../olssco/translators/textfig_generator.py | 184 ++ .../olssco/translators/zigxag_generator.py | 301 +++ .../olssco/translators/zx_grid_graph.py | 157 ++ .../paper/graph_state_olssco.py | 111 + glue/lattice_surgery/paper/graphs8.json | 106 + glue/lattice_surgery/paper/graphs_large.json | 889 ++++++++ .../paper/rand_graph_baseline_opt.py | 103 + .../paper/rand_graph_olsco_hier.py | 193 ++ glue/lattice_surgery/sample.gltf | 1 - glue/lattice_surgery/sample.lasir | 1 - glue/lattice_surgery/sample.olsco | 103 - glue/lattice_surgery/setup.py | 27 + glue/lattice_surgery/stimzx/__init__.py | 14 + .../stimzx/_external_stabilizer.py | 90 + .../stimzx/_external_stabilizer_test.py | 7 + .../stimzx/_text_diagram_parsing.py | 178 ++ .../stimzx/_text_diagram_parsing_test.py | 149 ++ .../stimzx/_zx_graph_solver.py | 196 ++ .../stimzx/_zx_graph_solver_test.py | 137 ++ 39 files changed, 8224 insertions(+), 1416 deletions(-) create mode 100644 glue/lattice_surgery/.gitignore create mode 100644 glue/lattice_surgery/README.md delete mode 100644 glue/lattice_surgery/base.gltf create mode 100644 glue/lattice_surgery/docs/demo.ipynb delete mode 100644 glue/lattice_surgery/gltf_gen.py delete mode 100644 glue/lattice_surgery/lasir_gen.py delete mode 100644 glue/lattice_surgery/main.py delete mode 100644 glue/lattice_surgery/old_gltf_gen.py create mode 100644 glue/lattice_surgery/olssco/__init__.py create mode 100644 glue/lattice_surgery/olssco/lattice_surgery_compiler.py create mode 100644 glue/lattice_surgery/olssco/rewrite_passes/__init__.py create mode 100644 glue/lattice_surgery/olssco/rewrite_passes/attach_fixups.py create mode 100644 glue/lattice_surgery/olssco/rewrite_passes/color_z.py create mode 100644 glue/lattice_surgery/olssco/rewrite_passes/remove_unconnected.py create mode 100644 glue/lattice_surgery/olssco/sat_lattice_surgery_solver.py create mode 100644 glue/lattice_surgery/olssco/tools/__init__.py create mode 100644 glue/lattice_surgery/olssco/tools/verify_stabilizers.py create mode 100644 glue/lattice_surgery/olssco/translators/__init__.py create mode 100644 glue/lattice_surgery/olssco/translators/gltf_generator.py create mode 100644 glue/lattice_surgery/olssco/translators/networkx_generator.py create mode 100644 glue/lattice_surgery/olssco/translators/textfig_generator.py create mode 100644 glue/lattice_surgery/olssco/translators/zigxag_generator.py create mode 100644 glue/lattice_surgery/olssco/translators/zx_grid_graph.py create mode 100644 glue/lattice_surgery/paper/graph_state_olssco.py create mode 100644 glue/lattice_surgery/paper/graphs8.json create mode 100644 glue/lattice_surgery/paper/graphs_large.json create mode 100644 glue/lattice_surgery/paper/rand_graph_baseline_opt.py create mode 100644 glue/lattice_surgery/paper/rand_graph_olsco_hier.py delete mode 100644 glue/lattice_surgery/sample.gltf delete mode 100644 glue/lattice_surgery/sample.lasir delete mode 100644 glue/lattice_surgery/sample.olsco create mode 100644 glue/lattice_surgery/setup.py create mode 100644 glue/lattice_surgery/stimzx/__init__.py create mode 100644 glue/lattice_surgery/stimzx/_external_stabilizer.py create mode 100644 glue/lattice_surgery/stimzx/_external_stabilizer_test.py create mode 100644 glue/lattice_surgery/stimzx/_text_diagram_parsing.py create mode 100644 glue/lattice_surgery/stimzx/_text_diagram_parsing_test.py create mode 100644 glue/lattice_surgery/stimzx/_zx_graph_solver.py create mode 100644 glue/lattice_surgery/stimzx/_zx_graph_solver_test.py diff --git a/glue/lattice_surgery/.gitignore b/glue/lattice_surgery/.gitignore new file mode 100644 index 000000000..fb6b59ce3 --- /dev/null +++ b/glue/lattice_surgery/.gitignore @@ -0,0 +1,9 @@ +__pycache__/ +.vscode/ +/tmp/ +.idea/ +*.zip +new_run/ +*.egg-info +/build/ +.ipynb_checkpoints/ diff --git a/glue/lattice_surgery/README.md b/glue/lattice_surgery/README.md new file mode 100644 index 000000000..4b3fa6dcc --- /dev/null +++ b/glue/lattice_surgery/README.md @@ -0,0 +1,11 @@ +# Optimal Lattice Surgery Subroutine Compiler (OLSSCo) + +## installation +In this directory `pip install .` This will also install a few packages that we need: 3 packaes from pypi `z3-solver`, `networkx`, and `stim`; 1 package from included files `stimzx` [(source)](https://github.com/quantumlib/Stim/tree/0fdddef863cfe777f3f2086a092ba99785725c07/glue/zx). + +We have a dependency [kissat](https://github.com/arminbiere/kissat) which is a SAT solver, not a Python package. +It is recommended to install it and find out the directory of the executable `kissat` because we will need it later. +Our compiler can be used without Kissat, in which case it just uses `z3-solver`, but on certain cases Kissat can offer big runtime improvements. + +## how to use +See the [demo notebook in the docs directory](docs/demo.ipynb) \ No newline at end of file diff --git a/glue/lattice_surgery/base.gltf b/glue/lattice_surgery/base.gltf deleted file mode 100644 index aa76e405b..000000000 --- a/glue/lattice_surgery/base.gltf +++ /dev/null @@ -1,552 +0,0 @@ -{ - "accessors": [ - { - "bufferView": 0, - "componentType": 5126, - "count": 4, - "max": [ - 1, - 0, - 0 - ], - "min": [ - 0, - 0, - -1 - ], - "type": "VEC3" - }, - { - "bufferView": 1, - "componentType": 5126, - "count": 4, - "max": [ - 2, - 0, - 0 - ], - "min": [ - 0, - 0, - -1 - ], - "type": "VEC3" - }, - { - "bufferView": 2, - "componentType": 5126, - "count": 4, - "type": "VEC3" - }, - { - "bufferView": 3, - "componentType": 5123, - "count": 6, - "type": "SCALAR" - }, - { - "bufferView": 4, - 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"cell_type": "markdown", + "metadata": {}, + "source": [ + "## Prerequisites" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "This Jupyter notebook aims at giving a minimal demo on how to use this compiler.\n", + "The reader needs to know how lattice surgery works to fully understand this notebook.\n", + "The most direct reference is [our paper]() (link TBA) which, in itself, also provides more pointers to background knowledge references.\n", + "There are two we would like to mention here.\n", + "- [arXiv:1704.08670](https://arxiv.org/abs/1704.08670) links merging and spliting operations in lattice surgery to ZX calculus.\n", + "We leverage this connection a lot in our software.\n", + "- [arXiv:1808.02892](https://arxiv.org/abs/1808.02892) is helpful because it works through some examples of composing lattice surgery operations to perform quantum computation." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Introduction" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "In what follows, we are assuming a surface code quantum memory with nearest-neighbor connectivity among the qubits (in both the physical and the logical sense).\n", + "We perform fault-tolerant quantum computing with lattice surgery between patches of physical qubits.\n", + "Some of these patches correspond to logical qubits whereas others can be temporary ancilla during computation.\n", + "\n", + "Since the logical qubits are in a 2D grid, and there is the time dimension, the compilation problem is laying out operations in a 3D grid to realize certain computation.\n", + "We consider only a bounded spacetime and what *can* be realized within the bounds is called a *lattice surgery subroutine* (LSS), because it should be considered as a subroutine in the whole quantum algorithm.\n", + "\n", + "Because of the connection between lattice surgery and ZX calculus, an LSS can be seen as a ZX diagram with nodes at points in a 3D grid and edges only between nearest neighbors, as seen on the right in the figure below.\n", + "If you have worked with ZX calculus, you would know that this ZX diagram is a CNOT.\n", + "However, it seems that there are two \"unnecessary\" identity nodes in the middle.\n", + "This is because there are other constraints when it comes to realizing the CNOT in a surface code memory.\n", + "Our representation of an LSS, the 'pipe diagram' below, does account for these extra constraints." + ] + }, + { + "attachments": { + "e1d30228-b8e9-4608-942a-e09fe765c155.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![Screenshot from 2023-09-14 05-14-00.png](attachment:e1d30228-b8e9-4608-942a-e09fe765c155.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Pipe diagrams" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "We use a 3D coordinate system with basis I, J, and K.\n", + "We avoid using X, Y, and Z because these letters are also used in ZX calculus for different purposes.\n", + "K is the time dimension while I and J are the space dimensions.\n", + "\n", + "If we want the pipe diagram to look like exactly what happens on chip, we need to draw them in scale, e.g, shown on the right below.\n", + "There are four patches of surface codes, and only three are used in the computation.\n", + "These three are identified by their coordinates in the I-J plane: (1,0), (1,1), and (0,1) from left to right in the picture.\n", + "Between the patches, there are some 'gaps' which are lines on physical qubits.\n", + "We can perform merging and splitting of patches with these gaps.\n", + "Since the gap is narrow compared to the patches, but what happens there are really what decides the computation.\n", + "Thus, to see these merging and splitting more clearly, we often stretch the gaps in the pipe diagram, resulting in something like the picture on the left below.\n", + "\n", + "The unit in all three dimension is the code distance.\n", + "So, a patch going through a full QEC cycle will become a cube.\n", + "These cubes are sitting at integer points in the I-J-K grid.\n", + "Nontrivial logical operations are done by connecting these cubes with pipes.\n", + "For example, two cubes connected in the I-J plane correspond to performing merging and splitting of two patches; a cube that has a vertical connection below but not above is a logical measurement; etc.\n", + "At this point, we see that the problem of compiling LSS is laying out these cubes and pipes in a limited spacetime." + ] + }, + { + "attachments": { + "dac9ce3a-5960-445f-a5d9-f13e0ac44c80.png": { + "image/png": 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rwFWR5wvmq3jSuIM6NogwkUsaujp9YRN/WmpcZOQ+QWiaxunTp/d7GBky7Cta59GlhN3dInt7efb2BodRjmmp57VEyhKwG+ztLiNY7OOlMh3SbiFMX8rlS52XbuE0yux6DnW+ui7V5D2HWhRYoXbCz+EeojKc9b6LuOsaEk3KdqCYtXqZtZATn5Swa+a4kp/nUn6Bp+cPcM0q4ggdV+gk2brVHIn5DHi7GiY+Ni4eGj4qBruMOrQuJZIqcAlYQIhbQu84DQJilBJkNR1R9xhGpqG1D7oaVR51HwjARtDUjvBZ85U8oR/HFcoi0r73pLqPdX8LXZbo3FmTR0bu+4A/+ZMP8Rd/8RcsLS2zvLzE8rJ6rtfrwytnyHAdQkp1JtrzNOp1i729AuWyheOMo20qH2cpfYTYBYyA1E8MqafT8nlOpHXLTq1jwaN1uYLSxFq7owuBnB08t3jHpNuNLA3JJJVVe/o1nre3QfOZp9mmwGfsW/jG6iE44Ee2Eca8U+e7q49zh3eZKhabzPGUOMhV5jkj1tmmQAOTBgYuGg0ETXYAgRCt/BiS0bZOOu9Kyuh5bpYm+uiy4cfbBl2vYfOofop/MF/BBf1gT6kIiL0JlLHkNUzZQGbk/uxCPp9jeXmF7e1tzp8/j++rH+bc3By2Pb0vO0OGSUJKtYfuODr1ukW5nKNSUUfXup3ihu/DhmWlbB1W0hDCQVFrlAtUuO1wmyYSK34iTmhnFzG9bqH2Wosogq+j9lhzCLSgVy1UbxJHqWSwiqhjcoUFvimO8mlxG+fdFe5qPE0jBeEqh7Emx9jimNxS16Q64neNea6wxLawuITNFXGEKkXqXKVEjjJ5mqKXNtKQvYfvPz7wvUaWpdDeB5WPQujDynxgQ6zwBfMFfMr4Npqifw5XxF5B2YcsfGMRX9/K9tyfbXjnO3+Cd77zJwDwfZ+dnR22t3f42Z/9ub7z8BkyXG9oRYyr1y3qdZNq1aZSsfG8sBNY0qmyNb15KEJv7Vw2Ue5JCwn2daPa1CJGEBc6ZfiIw1im2xGvjtq/r9E5VuWgpnGdti9dbOCUuL7D15roXBLLfIMjPCRO8bhYx8VAx4uoGY/ejY4wdCQH2eMge213/xqPs0eeXVHgAitcEUuURJ4yOcoiRw2bPQrUsIJIawn24GVp4nvk6ctkzPV0bbronNEOc7/5Er5u3IIX+Q237u0qQiyqbHW6h68bTNNtMiP3fYamaaysrLCysoLrpvuhZhgOmVRNyzAUzaZOrW5Rrdg0mga1qh2KGBewQWooxzhFCkqrEaJIvx97DGK4pHWOuVeHGuDcHokkYjngZI9sORiDGYyjhZamX6Hl2z+4TxeN86zwVXGcr3KCp8Qajb4wK+mQeGtAQE465GhyUO5yK5ch0PB3KLAj5iiRY0vMUyZHSeTZEItsiTnK5CmLHE4PxejALT3dzE57H19LD5fVsHjQfDEPGbdzUVvvkWjdmA0kOwjmEGIF0LHlFkVRQYjpnojo+uSziTDDsw2O4wwXyhALzxPUahaVSo5qVQWXaTTVtKGmr1EJ3UXKHYQo0PFHztEfH2w0nEd5wB9NKJ/mXQyWVQzUa85v7ba2oqLZgeQWsBeUW7RsFarsC9zEOXGAhznGebFCbQr7s8mIXr2n1nUNyQoVVqSKy9+ijTomO6LIHnlqWOyKAlfFItdYYEfM8YxYoobBnTH9DhpT0nI54L9BddOO55y2zoPGi/kX4zbqIsraKkGWAR9EDkSx7a3gCw90OfW4JZnmniFDhj40Gibb2wVqNUXojqPFJmpJjpbO6qMOni2gpqB04WWT4DIquUiY3GW7rWRUnnbZMow4WtScR4V98VGE35qENZRp/284xTfEC7jCEhVhU2/XjPIvSD++NE59aeRzOKzLHdZRIVV9KahjBk56JlVh4aKzSrmvbmJCj/j6RtXQRymvYfGYfpJPmy/hjHYEL077ltuopdwCIrQok4DUBZ4x/SiFGblnyJABUHHFq1Wbzc0ijYYVEHqyM9DxaHlH7yFEKxiohQpVmja8LInH4nIQl2Uk29ECCaKfJRlNWpned9IKgOIDj3KYv+VFPCHWqFAckAp0NAurkC7C7/ZUHzrOUKCeuKN+ce0IJHma5FsbEz2f9+S09+Qa+jh91zH5rPlC7jdezLZYaBN717ckHdSmjAnMQ5v8ZVvSFC450WRSVqo4ZOSeIcNzGK1ELTs7BXZ387iuFgpsEoPEXF9Cyg3UzvJaqOJ4i4VkAymgaLO/Vtpe0st31MthJFLF4usc45PcziMcpikMJCLxR+Tjc9XZZiFy9z4YjZTcVm/yq41neN5SHk9abDsOG40GJdflahAjP63JOq0FYNQ2+8rbH+8wik/Z7oCyTbHIX1mv5Zv6aVz0noVXq7aHSkprAYWIxZkieF1zMXU3pStkemTkniHDcxS+D8e2K5y+cpmH5UG+6R+kiomHwA2CmyRjGdn21xGiBNSQsoEQJxFinv6pczyTe6dq3JSsUpNIaeBHNh+wQyIT73CkJRUPgYPBQ+Ikf8NLOM8KqT4H2TrTfhWBS9GJsIBIiSV9nLrPb1U3eJO3iR+8Z1toFO0cR+1OsNWy53Kt2aTiuey6LluOQ1P6SCkRAvwIK8ek9q/TynTK02f7S0vyHhpP6Mf5G+M1XGydXe+L8yNRZyI2EGKN8KKyT176OJqgoWlTJ9+M3DNkeI5C02DdLPFm/VHeyjdpoHNZzvOov8o35EHOyUV2ZJ46JjUMGgRaZRsSKZVznNot9lFay2rgCZxmKp/kHqSkSecIWlyP6VsdT66Jzg4FHuYo94k7OcuBAbUiPg/poT7jMurdrQX/b3Rq+T7znsvRWpkfrFzjFlFFBy4KwSUpMSTcJAR2YGSXBKFUdYNivkMHjvTZdV3KrkvF89h2HKqeiyslnvRxpcSV3Yb6sbTxMWQmva/ewh4Fvmrcyt+br6ImeqPOB5YZ6SKoAU2EOBYpE/4udRxyWgPM6R95nji5u9Uq9aefpn72HNXHH6f2raeoX7hAebPK/8kfYJpw5IjJgQM6hw6ZrK8brK8bHD5ssLZmcPRoFsTluYzG1Ws0Nzepb2xwsbKKeeImbr7ZJJfLMuJNA5tankvGPCfcXSw8ToodTurbvIEncKTGebnIWbnEWbnMObnEJgXKWOwiKEsdRS5VhFhivFCaCcgtBepImgN3iUfP8Z5GXnnJGzzDAo9wmAfErXyLgz2LpCEty5brXev0/By0AqUEWrzwfRbcJs9rVPiu2g5vklUWdYkIxc07IQQ1KSlLuIKkGRgv8kKQDywvDsrhL4/ggGlxwOx8p56UlFyXiuey4zqUXZem79OQPg3fx/UV4btDPpWJaO9DkvYMa2NQmYPOee0g9xt38ZDx/AGN1FBOoi5CHIyXC+236zQpijKaNn29OlEPztY21Scep3HhIvUzT1M9c4bGuXNI10M2m0jPQzoOvusiveidBAOooG7EnZ3Bqe50HXRdtJ8No/W/wLIEa2s6Bw+qxcDBgyZra2qhsLqqc/jw/qZPfK6i8cwGjc1rNC5dprm1RWPjKs7uDo2r13C2t2luboHvIz1X3TdSqnvF99X903qE2ryHn+Cf+REATBNMU2CaYFkC0xTceafJyZMmd95pcuqUydGjmSEqLeqaQUUzQp7Unb1iQ/icZptTYhs4Qw2Ti3KBy3Kecwgu+HlK4hhbMs8mkioyMOVPAuOZ7htoNJPkdE/gPD8a4Qua6Gwwz6Mc5ouc4nFxKN0ZdSnpWERcIAdivltGwBwuL6ps89L6Ht/rVTiu+ZEfWZvIBawh2g5u21JyTcp2nvN5wBYC3/dVatNg73heCBZNk0XT4Ag5JOD6PiXPY891qHs+Nd+j4nk0fB8nIP5m0E6yzy1F+YSi1oXLy+R5TD/BP5jfwRVxgDAxdwRbi609BCsIkeQ7bf2ufDytiablE9QZD4lmw8sfupuNv/zvI5uzQH08S2yyQ3SmtDA8DzyvM9304sKFlsEt+kf/G7+xxlvfujjaQDPEQnoen/2+H0A6ahHnNxoqdK6f5KebHiWW2q8dBxyn+564dMlDTUfBqliHXE5g24Lv/E6b970vYSCU5zA8XeAaGjT7tdxek2uOJjeJa9wkrvEqoCl0NjnHM3KOiyywIee4wjxXmeOKnKcUmUBzFIxC9BYSo+c9pfP2Hoa4Oh6Cr3KMb3KU82KFb7FGtXcfdhAEIEuhCzqIpR4hiRBVfti+yJutHV5RaXBS82CIgSucPKflt7eMYFl0ohY0pcq11zrMNRfUO+/7ivyFsgcIYEloLJsay6YiOF9Kmr5P1VekXvU8yp5Lw1fafcXzqHoujhxkVQmNMZHMaNp7VPnD+k3cZ76cLbGA7Etj2wq0VAmuLYEwImTi4WvgGtNP5wsJyd06tD5cKMCghfAS24nIfVzs7GSR3qYB6bo4m1ud/6fcXz0ylng8PA8qFUmlIrHt6Z8jfTagpFls6nl6l9Lt55iUm0qz91inxEFR4oVcpiF1dsizQ54tqZ4fl2tsMMcFucQuk9BWglFEZTDrgo5iuuEkMqSnxGiR+me5mafEGpcJE3JS34Iy6jiVpWRFfzY9TVR5rXWFH7M3+G5zk1Naa3HdS0bxCM/TQtAORCMASwgOAgdDhA+K1jSpUp1owJaUbAG6BA9JCbhZCBZ1HVvvJEn1gv15x/ep+T5138PxJRXPZc91qfoeFTcZ4fe9uwjz/DiLhsvaATa1VhihXrgob3hQSx4jQrEf/D0bwqNoNJhmNrh2X4mEFiejBc9RGi40AWxvZ+Q+DfjN5nChMdD7oyuR5L6L/hHNzWXkngQN3aBmqGlgmOY+SEYClvA4SJk1yiAU2b3UP0cNk5KwucYcF+QiT8g1zrLCDvkEe8+DMEij16gj2vHdB9ZOEY62t1dQ7/NhjvJJbuMMq2yIhcgRDRqzypVeAzGPoABYfUephKjxausSP2Vf4TuMEjdpTbS0Yfcjem/xUy8thf+XwEEBCNG+nqeTLc9HsAJclJIrwQJgGxWl76QQ2JqGrWmdZDpS4vqSppS40qfpS+rSY9dxqXpe22vfkf7UHOZ6ZeqY1EQrdmAvGkAJReqt5U2SXkXXAkAXPrbenPoxOEhI7uba2kQ6WwgiF00b9fq0dcrnJnzXnWl/FRZGrru+PhvT140OoUk8XeCgYeD3kXg3wXeHIR0sq7S8ZVFjiRqHgJvY5EUY1IRJHYNNinxDHuIMqzwlD4xpxu8nzQrKQSytK2bS2aOCxZc4xWe4mUsssSPyeKlSgUikrKHSzsyj4gEY9Cdnd3i+eZlfyp3nteYeh4WDnVhJT67Fx5F6+7Xsvp5DtL+xllwxJL+G2jTblJIdX+3pA6wJWBUCQxMYCFpJfnxpsGZa+IFTXtOXlAPtvuJ57LoOJVe56w3T3pO8897yhrACn4ieZY6sAQ0Qi3RSA/V+UkN6kWoPxNc0HN1IfU+OglSae8oFbh+W2RyjdhQinB2Acnk6e8DPdcgZk3udfpNkUiwvZ971yeDzZWlgS4NDokkeRTHh0+mDNPjI55AZP1xXx6cgmhSC7G+H2eH5XMZHwxEaWxR5WB7hCdZ4WB5mb2Qzvur1s8C30539PXb+Sji5SdSRti9xio9zJ2fFCi76CBYIiZRPovTf44AIRezrfJorxhX+XeFJ/pW5Rx6fdFFLk8/Wg4i81VIS7b4gOtdzwJxUr9dD169Iyb9ISV1KPBTRHxVCBWoVAinUSfGCJlnUDY5YBOSvFpY7rsOu67LpNNlxHKq+10/4I3wau6LIrujOCKAsKk0Eq8QvE6N5qFdG+D4mNTzDun7I3Tp8aCKdzUXEFJ4GtrZmS0KThGVdv0cBZSgJyyxsI1XmhwvFYGUl09yTQAiNvGZwUmicRmla54BrEnZR2tciarJVU1j03maL1BORv+oZgcQQPuBjAUWaHBfbvAlw0HiGeZ6UB3lErvOIPMweOTwEXsIAOy7zeJhInLHuV4kyOzvofEUc5694CRf6IsJ1Ww76R9YK9OMDZwGJELf2dyYkJj5F/Srv1OwgmQAAIABJREFUzp/jF+xdDmv1EX9w6dQxEfWPjKeuRNeF+jS00EiOCcGxkCzAE77PF3yfNSFYEIIdKblDCMLBWzWhPtc1y2LVsrg5WPw70mfPVUF4dl23fVxPSmVn8om4VyPgo+G3/DSkBC4gxCq0twcHkXhvq/1yOjUW/AvoxvQ95SEhuetzcyrixZhe0cUZ7bmXyzemWb7ZbGLb1y+5T3vPPYwSC/hjhGFYWso096QQJmBIcBWJ30pnqqqgkrC0fvk2Khlri1p1lEMVJCf2JL9OA5+j7HJU7PJa8QQegitykUdZ51uscVEuskeOGibNIMCO36cPHQL5JFLEZwaMNu924KCzR45HOcR94g6+RRLn4u5GOoF+tlF7t6cj4up75LQm6/oWP2Rf5uftbU7qoTjwI5tNR6sYtnSL0Pc7XHtvLWxkpHzctVs1jVuCFYDa/4YzUhFzI5CbI3Dyk53FZQ4whcaKabESnMmXQNP3g8A7Hnuey47j0PS9wLkPXNl9PE8CFXJUhYWUVVSgoHX6os0lMsVHy0nAMQRF7TryltdME2NpCXdra7jwAOSoDxeaACqVG9Ms35wheY4C35mdRaTG3Fj1Fxczck+KDa3AtshxKnCPkqHJvACcpvP/DirbmocyUlpSRTjTgoeNmlTCRD5Ua5IDygJoSI6wwxF2+B4ewxeCDeZ5mhU2mOe8XGaTIiVy7JGngoWkQP9xuOGQqJjvl1nkPCt8ntM8xqG+3OTDWlGkrqKXKYpaQYgc3cTgk9eq3GRs8QrrMm+zr/GdmkcuKmlMcmf4iIqjETyo7eJwv0P35oNXrVQzUcOOI/3WPzkheH6Pt/4l3+eKlMGmjno+JARzwRl9F3UvzgGWprFu2+26npQ0fJ+S61ILCL/meTSlT8PzcaSPq+k0cFB397Dz6yOQvKYhZ2iZTXy32keOjE3u+fYxgulidzfzlp8G4gIUTaTtnv/3BiTCGAYhMs09DaqGTV23oDlc216kY6T0pdJFt+kQug3tM9AmHQeraK09Oen0Gz0l6+yxHmRDb+3ZX2KJ83KZyywCEgt3YDu9cNB5ijW+wRG+xjEus6jOqKfc65ZyD0USDaCIEP2hZg1R5WZzi1dbV3izdY1X6E4QMCams5E09/GtmEkd7gjJ9RJ8r0xU/WHkfyTIf9667kjJNSRl1Nn8GsqP3RcCR0oaUmILQR61WCjoOvngiF7bQuB77Lkul1ydXXeJujAQYhnaGwlDvniRZL9ddagJn6Ix/WxwLSQmd3NtdezOZqW57+3dmJr79Q45Q8tCJZHmHv2jWl7WMM3sKFxSGIbE0TvHxuK07c5zZ+pdhvZp7gbKmFlHTY0uat/eRH1T+eAx6U0zicDA5yAlDlLiLnEeB51dcixQT9Sfi8ZjrPM1jvEwRzkXG/d9sGe0lNuItsHXRIjDkXI3m5d5o32J15ubvEJvBkFkRMSHM+anNXL1+GXYINP8MPneOlGOfIPM9+HXphC0vcGCI3r1gOSbKJuJDJ6bwZayKQQm6p61EVhCZ89Y4hPyJJ/zV2lIG9G1vZOEvJNp8ZrwyGkl/JTxO0ZFYnK3Dg6KnZsMeSpjt5EU1apPoZBpb5OE78xyz3306HLZMbh00HWdiyJPSeosio51ZjDB9z9b0P7WJEpv3aZzzrwMXIPg8JNy1uudgCZF/CYeq1T6Fiq98BA8ymE+J2/iKVY5PzTIVjRNSbmNopQcYCBE1DFOyZq+zZvtS/yI9QwvMaqsiE7ZSEhdbfRPOM6jPlzWS9zh151n2Vcnbl8+biEQN6acUMfzlgEpBL6UVIGSUEsuHXXPbUhJBckZb5H/4byYL3prlGSSVEPdBC4i5aJJXgqBY5qpDkuOg5lq7oUZkruc1CyRoQ2vMpttFRjPUz4j93QQQmdbt2kIDRVrLNqMnoTgw88a0IrOLVFnzls7zi33sl0EBSQFGBiyaPLavkINk/vkHXyV4xEOecPgI2UJZZ9YCB65CGc5yYq2x5tz53i7tckdepV17ca0LiY5Dhf9WiYi89i+ZNQiYXC/ABqCIv3bQztIPuQs85nmIs+wjpfUDJ9IS4+QkT4GZXyrcP2Ru7E8+h5oCzkGJ4yZJGo1n2Ix09wniebmeD4XaVCiN5Z2cpw8mZF7Gggh0E0fNNlJFc4wgg/vpg4nelDm+VaIEIki+CKgCahLuIBaAOgompwneQCaUclfAnvkUhK7RMoGKvhMAWWDMIM0t61WFc0URI3X5c7y0/Yz3KXXWBUeevic2FijJ5oVh1YYr88uRzuZjGiT7KmH6XJQG/EEH20R6NX+y9LgA83D3OPcSdm/jKZpwffZQIhixGiikIbkQeCz6l9B02eX2CyFWX4yUeqK7FJJFFZ0PNRqN+bK+HqGV5ud5p5Fp5strlgL1DQL6SsHtEEkPUibT1q35XDXmoDCznegzPcbqH18EzgCI5+fGERjWrBMGThZd13ykfIplOvgMUBEaOpg0OC1uaf4pfxFXqU3sJEhUo/qYEyCJ20TY/bZaiHoe9BxuRblhn3fB2nfvf+3+5FJCL77de+1j3kaf9g8zTfd5+NgI0TLD8ylO55hEvIOv5MhEJKmKbFndAwO0mjuS6NrUmEc4NqEyT36w63VMrv8pNEc87REGjTGSDKyvJyRe1ps6fPUNTOxyR3UhBs+NkeUzID6XTICtFDhweDRwkXgPGr6bQVqbelYyjt/NLLS8RGxow+utIPPXAB8hLgl8l0op8Emd9jneG/hDK83nRRDitJbUyJ1E+P3GTZCSDokHwU1U4u2ib6/bHhnrT6i5UM+EISIXUr2EHzcK/JHjbv4ln8oZKlpzTMOUlZ7TjW0Rtbbfu+/URsKva0IHF1DRB1xnBJSkPtkCPkAm5zj5om0NQid9KAZJgVnZza5AWC80LPF4ux+QM8WGIaDL/rjxodfJyL8BPV6X8dpkeErR4IHKG/8bZRRvIHaqz+Aol+NbotAXHsttGLdRUlL6YFo+fw3gGOB6b3b2CvwWRYNXmju8bOFR/gRsxrf4eCCMcWnOOclaDqpFj3IJJ/EdC9Fh+Cj5TpH8HwJ56XBn7mr/HnzeWzLNbo3e7ygthWY5AehW5uPn2X6FwSakCxYNZhYGuThmOmeO8D8jJLHZOQ+eczSoa4yhkNdFlc+PQxD55KW44QsYYuO6bSFWGIPzayjEXvoegLlW6IM4uGA2CVUFD0PgYEkh9oJl6j9+wLBdB7RtobEbE/wwc6t9FGpPZsgGyCWEKI3Mp0i9QNahRebm7zZusqP2lusioSBnga+zwnOXTNeGIxD8K3X7dHI0duQKE/5r/kF/sQ5yr3O82hEKgyt78ugc1Az6X57eMTDZCUFvU58rMTJIzG56zkbrVDAqw6f4Af9RpeZjWm3Ws323CcNt6xyA8xi2RT9Q0yG+fmM3NPCMCzO6wXuEjoWbkINvvNLH0Tew4h92P00rHyezn68h4qitwd4Uk1w4Z1Ujf69+znqaAQxyOUetIKeit7gMy34zIka32Fu8r32Fd5mbXNSS0DqzxF9o8uBLULD7jzLSHLu/X8Ugt+T8EmvwJ87t/GgexSXXI9kFKLu+kntuUPVNGcUvkYhVfBu+9hRao8/MdY9mqV9vXHR3Jx0Vj+FqG9qHIe6hYWM3EeBa+r4CTVxIsqiXseXxfw+g/5HJXydzvE7UDSt8np1/q+hSF5HGUkPUEKXm8FxKFDn1KOTZRmizOutq7zOusYbzC1u06/zJFWJXRHGd7CLazGq5WEm+l5T/VA52Xl9UWr8v+5B7nZOsO0fhb7DZ+GWWnvurfj/vYghb9Er03exCzm5h2fmrl9ytw4epPb4E2N1OD+j5DGNRkbuk4ZXmU2cgjLzyBGTIhpGRu6jYsPM0dQ0pDec2LuuRRDyYO29/7eZ5NeajPC7qUSjO7COi0qGI4JHBbDZQ+MYneAz/ZO0Liq8wrzGu3OXeamxOxqppyLazjsaG/tJ8IHTZTSZdzvXDdPIBy0SWq8/5/t8xDnJJ9zb2JPDFITtnn322A2jUA+DEK/xH/AuYlmzyQbXQipyN9eTZEQa0gaziXJWr2dm+UnD3ZvNwmyc6HRHjmSe8qPimjlPU3Q+v0EauXqWQ8qjyvrN+IMwOdJXMOhO4Knc5Tw8MYdoZwDr1NBFnZeYG7zLvsqrzV3u0McMoT15/pxwvxNeWJCM4KOGmMYcX0fyGa/IHzafx+e9wzTbXhcD3N7kDkIsBnItV8xB6IwuKqlvtKySc3WHvDY7ZzpIa5afALnPKnlMuXxjkvv1nM/dLc2K3Ec/dnloLbPYjArNku3jRsOInd5rPdr7qMQebmugzEAEhDGgndZlA3Cpx24TGHKLQ9432XHKbGkmG0LnoDamZSgxf05Bg0/c3GRXISLiGFscwUM/qYdf9z43pORv3WU+0LyVJ/3DNLtoLV6bVt4Zp1CbNa08h4MXBP3tJiP5km2P4SI8GtKZ5Q9H70OlgT2jKHU3WtrXRkN9Lrbdmz/4+oBXm03SH4C9RJp79I/q6InZro6fTdB1jTMUWZc1tODjHbZnPsx8P0g+TjYKabTztDJrbGPg0ZfzUICFxzG3yqpb4ss1wf2GhtB0jlg2zzdNbtF1lscl+6GYsLq/T1r8YO1bdN0hSR3qLviC/+Ss83fO7VTkSmDkH+Yw1ypXrpVSNoE9hFjrkQvLxiHZYmDRqKCyL8wOqchdnx9/7WFNxSzf/wHv7NxYaV+v/1zusxvfOOleM7P86LCsAk9oc7yUTczQBBe3X96npUc44w1aBMT9D0QSULqFQNBADJGFL+lDWhYonW4ByYKrMoc3mw3uBXY0jbxhcsQ0eZll8TzdwA4ClZiAHhe0ZGCXEyDTVE3MztoV1uBjJAaOpzXTuxK+JS1+vXGSz7g34dK7dz6IcIM7RKwErx2kLCNEVHK03rGIiKajxtuz527sUR9ju3EUpCJ3Y2F0D+YWcjMyy2cOdZPFNHO596I8RgTDjNzHg5HzCRvXEhN7l1w30pj4ezEpzX6QzAlcTGSMTdEg7G3dOv6no4LPHvN9aDbwmw3+uqIC69xu2xiazktMk5sMA1NoWEIwJ0Q63W3aC4CxxzBaI8O08kFyAtiS8Gkvz/sap3jauxUhBoUsGkTyrW9cB5JaTNOZ41uyVSs3oovw6EhH7ivjrzymo7n3Y2/3Oj+icoPBr8/OLD/OMbilpcxTfhxsm/k2gY1L7LKvjejXxF1PsGc+CHKI9t5qZxHRn6mrPXe7tDLlxfejxG8OHjQaNIF/rEFDCJZNk3Xd4PmmyZqmk9c08kJQFKKt5Scj0SkS+oz7H0TwDCi74MOfuov8f80X8LSfZJt4EBm36E9HiAL9S4v4sScnedCp0bDyYwTUHg3pyH1+fM1dx2eB7YT7qqNjZzfT3CcJvzHDjH4MCwMZjywT4Hi4YCziCRFKmRxN0LHEHnEsLlIu4vUgjKaZR9fqvZpDQ3RFqevAw8SLSNI5bDwmylULKZHNJlWa3FcDNI11w2RR01g1DOY1nSVNY1nTWdEEZiJnrmcH2kQesf4K78C3jiw+7lt8wDnI3zs3UZWrpCHYaOJ2Qv/3p+lN1vZwuQX3WzM/BgdpyX1xoXOuYQwssDt1cs+ywk0WvjM7S0hzjPjLc3PPnclxGhC2FpppUxJ7CrlhM0i7PLHn/OAWB4W2dWmFm+1XXlxyeCFjeuJxhyBQwXKOAvg+stngKvA04AiNFV0npxvM6xoLusFBXecmLcpRb/LH1Lqa3id9aNgxt6bU+EevwAedE3zWPY3Tt7mRTOPul08yz/STdzSdx49BFzV0fbb77ZCS3EF5zDcvXR56Hwy6V1bZ4IJa104Ntd3aVNt/rmGWZvnqyMk9M7P8uLBtg6fJcTuVxKQcpb3L4MUgc35U/WGIjWw3QpstGR0PFbB2nd6J2cXC63IvhN7ZbZjJvhcCFRctLwHp4/k+O47DFcDSNCxN5wFdo6DprBkGLzRN1jWNuXZq2Skx8dC1w5QWF6L/iFzLe/6KhP/uLvPnzk085q3jYhL+jvqpPI02bwXyEnUcbhCiST66l27ZRn7Wh+AURiD3IzQvXR6r01WeGat+EuzVZxno79kP6c1Ocx/HLG/bmeY+Dgzd4hFtmdv8TjTCpBp4kgVAWpN82NQ/qMY45n2V073RKQ3dQj4mfsQ0OYoG377eU6g88QO7ge/j+j5VV2W+q2qCpzUNV9M5YpqcMEyO6wZHNA1TTJHkBzY7hX4DJ/SWUdiTkq9JnT9xDnOvcytX5Tz9YWQZwOHDSH4DIVZDMgaD6LrTXxorgZJdMMowRuyOUZGa3PM3naL80ENjdbrA3lj1k2B3NzPLTxJefXZ77s0RXU9sG/L5THMfB0IIfMsFN+SQxmjEntSMH/X/MExyr14D1miwEykfZ3yNJ7jYxY0cLgeKwuYDCelLHN8HXLadJptC8JCuo2k6nq7zXbbNcU1nbdJn7RMRPMOE0ncrwJeSz/g6/6F5in9xb6ZKge7vIQEJd8m2W+9clXuho28tcg/LTy6QTf5GIXfr8OGxO11ie+w2kqBa9SkUssl+ErgRHOqOH099O2eIQMUykaETq8O07T7ylpPZd4/qYyy5iHP4oMjdohpbW8aWDO8zzj1p2PaGghqwSRAYVUo0KZG+j8RBA+6tVbkILBgmBcPg2w2T77IsikIg+gjxxsD/cHP8VuOlXPZX8NGIJs+0++zhOgJQ24xSesAuQvTuiU+I5AVIc3+ijqaeDe2JkPts0r76/o1zQ1/vmNWee4U5Rk0ac/PN2VbMJPC4fQg4H0xZUcfiop+jSb1f+09rmu/IJjcHD9w27im0gKMs8wgCL3Iu7z78NKixuN2DZGQeVdb/+Qk6NLIkpdIJnSY4TT4L/D9AUde5w7S407R4lWkiBOgIDEATwyOjJxvs5OZXT0rqaPyus8D7Gy+gwWqoNFpT73dxiy7thwzFlPcCLT4ucFaatiNk/TqN3NwYCaxHR2py14uj74d2Op3N/m2lIpkb3TcrQwhuZTbBh8YKPXs0C2AzCUjbxKc3IChdr5MQe1ebEWWptOE2x0UT/LhWgB2c2DY8lLtV9F3X7TSY1PSe5noa2UPBA88Dr8Yn6zX+CrB0nTtNi9tMk1O6gSkEVnDWPhcXRS+MyI99Mqb5poQv+wb/wVnnk86L8SMDyqTRpJPIz4XkWscgE7TfWr21xQbLr3mXMfX9mZdSk7uxNP7egc2MtMCKxwhvMUMEnO3ZWFt2u1bs6XDwYEbuk4BheGxKi1XRiNTekxJ70j33RNQQz59pqsaiwSaKwnvNwIKr5KihUwiizydpb7Kknsw7P+r6keCB51HxatxXr1EVgmXdYNUwuN00OaTp2JpgXmgsBqQfiVjDyegOdtsSPu8V+UPnMPe7t+APjeEXIuFEPB9nvm/5ZOkIsZRAvr9Z9TENXhRIrYph7E++i9TMpxXGNzCY7eAB00WzmZnlJwWvOhvNfXeMuPInTmTkPglYVp5vijyvCcJzDiTiRMSe7Ehc1MXoX3A6Z7ZB1Vvyi5TbloreCX5DmNSkRr4/tUxfg5Mg9ejrPRaCEdowUIf9kBJch7Lr8E/1GiUhOGCYHNR1jukGS7rGoqazrmksC4ERJvuBBD9oNN3wpOSKNPhLd4k/cU5w3j+ExCK9Zh7uO3md7lHG0WAaa0H0eFzTQDLCNsgEkN4sP6fM8uMchphVTvdKJSP3ScEtlWfSzzjkPjeXOU9OApqms2dZ0ByibY+hsUdp/WkxSQ1+iXqI3LuxgU0txg8kfvtgeJ/jmuDTtBF1LYeKqL4mJdJpsunAU4CuaSxpOou6zhHDwNY0bjFMloVQgXXGPAnnSck3pMHdzmE+6tzMZbmI7FscpKHDUYjeA9laLvlDaqVtv/MeLEuSZNdjGkhvlk+RGS7uHpiVWd5xbrzjcNdrPne3PJtc7uNkhMvnszPuk8KuZSFDa/BBjnHJiL2jeY5C7FGa7LDaA0t7qq/ETvCCKjZuV/KY4Q1OR4MfzUKQ5JoAisED38f1fK44DlcFaELjW7pOXteZ13VWDYOjus66pjPXp5UO/l5cCZ/0c/xu4yRf9I5Tpcgo3vDxv/RkiwPRPm4rISb08MD2xfA+QFIw6oiewDuzQnqzvG2jz83hlUfX5MwZOtTdKGg01Ex6vZJ7c2s2xxdLY4Qlzs64Tw5PW6vABSCGvHvM2l1lEe0l0djH+bWmqRsle4L+6OK9dYZRd/tqBL+lJfW4sllp9gao3IxSgvSo+B4lBzaE4KzQ+IwmMHWdvG5wVDe40zA5pesBocSb6D/oHuCPmyd53FtHiqRz3Xgm+P46NcLfdidt0OgaehyaOvtE7SN6m+VOnaTy8DdG7lTHo0CJKtMNy1cu3ziae7M5u3Pko8ArV4YLTQD1MQ6NZHHlJweZU5NfN3kHjnUJiV3GyMTJDx1TCtlE9UIkbKMPmIBNohg7yXjSknfc9bAFZFQLQSrZntMJrfhtSImUHpoPrutSFk3OCMHnhaCE4LRls67rvMI0Oa3rbdo84/v8R2eZe5ovYlMWUKF6kmrLEaNNZevuJm0p94BlhCCwO6T3zo8LbRQuMWQNadkpxzo5jETu1tGjY5E7wCEu8RS3jdXGMHjejaO5X+/wZnTO3UmcV7kfmVl+cjAtjW1MlnqOiCXSyiPk1P/RjnVx7Q1HMqIbhFadJj6SbQKXsx44tLyrR99GmOz1tHVGkg0RfPh7E3Sisiuyl6ygYrD5NZezwOeFwA9C5i6bRT7u3c6n3FM0sWlRavQIEv6GW6nk0tZDovIItDzkNyMC2PTKp+mjIz/n72Ab++fkOxK520ePjt3xCps8NXYrg5FlhpscnO3ZmOWHa+7RP7BDhzR0PSP3SUGYOb4mC7xG7AI9e+dBlo9BpB73HLn3HoFRCT51/XZ1H5VYNH48wxY5ve0OS545OtHPSHvvutgfzCgMjY6hOweckhI8F+m53NuwuN84TFPk2i3F82RUDzHCsuefPrG4Tlpe+RIpa0GM+eEm9vhPL0a7FyV0XSBuJM29cMstY3d8kPGSzyRBqZSR+6Tg7u7OpJ/miJr7gQPZMbhJQtMMHF0HP4a8A35JYmofVD9KPikmVk+AKV0E0Zkk6yziYSFJfhx02pr4JI7GDboetTBJWr/3fw9t5O8qusXx9t2FmKOzFOld0CXoq+9S9MKgYdr4mhuV7mYmGInczYOjBxppYRbx5ev1zCw/CfjN2RxdBCJyNSfD7bdnoWcnCSnUvntUjHnZo8UN2lcfRv7DfqHJfsFjnnsPWrBxIs/x+OjIAYSSZE9/OmSfzA9gXFJP027UtU2KOBOluCRadlwd6HZxW5xgX92LCdPw0MT+cdBI7sV6XplOxzE2HOLSGLV7ET2Svb24oBMZ0sCrRWs008CoDnVZAJvJwkdwzlaL+DBJJ9HKB8l1yYjOtbhHUoxavyVnCTgioo97OhTxQnpQ0j6GyQy6Hkeco9RJ2vdwYo/fKR8MvV030QmyxBj/bhEi6XwTqpNQvqg30MX+WY9H0ty1wmgpOcOYhebeaGSa+yQgne6IgmPGsIhFiYXI3NlJcOJEFmZ4ohCCumFPRCvvfpax8nGY1L02qB0dWIpNNSwgNsTNkH7GDGoz6Tqx1xOa4eOS9wwaoy9a3vGTQTIbygAp6aKIvbfeZKPjSUMgR0nSMyGMRu655OQeRwT6DM66Z3vuk4FXm42n/Dhn3A8dysh90tBMnxo6ebwI0o4PahN1rSXZJ5PA8SwpxmlGgyC96OT7HIWck5eNZ5pHjmdyT3JdYiTWd0dG7D54VGH4ew4rLr3vZPSz7rps4hnGvpL7aGb5uRsjM1xmlp8MvPpszPJbHBy5rm1nnvKThmcVeErmugi681oqYg6V0fN6KLGTnJAHme7TGUvjHzsMjsKYxuzfJZPE2TuibpqyQWOKbEuqRVVvWTIDd7x5PmocmrCCw2/7ZUntHpUQdkIP9ohPY6CXf+cx718lr7v75ikPI2vu42e50WOTMEwOmVl+MvCd2ST6SZbuNRoZuU8WQgh83aRq5sGt9BDzBDT2mPqTwKjtHeDqWG0OlIk4XZCmfjzZx9eKJfXUfURdS07WGnnaemTbwWy/fq+7KIe6FpLsuSczw4fh0Aje8v7NSyNp7kIIrDHPumtM32Seae6TgZyyt3zr9t9UmagTSPYjI/fJQwqJq7uDiV2Ey7qfu2tEy6Ql4mHae+L2Wppr6GHIuEWs4Co2bnD/xfWfZMyTKlOfa1xJRJ0YTT1cJ1E7seMZ9BmIvgj0yT65qJbGg5T1zjaQqAWadfIxiITfumdaSF3fV8195GDcuRPHx+p4FnvutVqmuU8CXnU2ZvkyS8OFYmCPHtguQwwcobNpLdAikhadhIk5/tEtP4gQpRjWFin6DT0iCLz96HmvEliLbUlwSeRxYhYPScYc9z4HtRO+2v83rF5QNuD9Ro4xph0irwtkiO6i2tgBykj8gQSadJkUg1T8WQZcQCD9y3RCzw779uIQXc+09j+o1sjknr9VBbIZdfizMMvfSLHlr2fMyiy/zdrIdTPNffLwNJ2Sme8iVUKv2//37b3Lfhl6ZbrbSfMYjOj7IEmbBwa0fjlQR9KOp09ODCkPlfQupuLaTlOW9npc2aB2+v+XwXmDpBiD6IciR8dzfy/dWBKfWZfMiRKmmF18kCiMrrkfPzFmx5JciohP8Yi/ZXwfGo2M4MeF35hNUptR48qfPq2jaRm5TxpCgGaAI7sjjEVP4NFEHifTN3WLXunhj/i/QEKko4jDsce1NLaZJ0mssaTE31/e+77S1B1eNqxO2ra6IWKuKx15PBtt53OZxC9ciAJCtFzNRnEMT/INO7i2ia/vb2CtmZjl476UNa6M2n1i3Gimefs6tC/PitxdRvsxnDqVRaebBoSAqm5xMVh0haezvucBe+9xz+GgRzWEAAAgAElEQVQ2J6/BR2NQe8q7INm9nnZMXXKi/+qwNpKW90GkrzPaAiF6lq8ANTTkRPaeI0aQutlQQB2RLitpvE0oDBeNOpZloen7ezx3ZHI3VjqezaN+bUeCfNHTRLV6Y2juzeb1m8/d2bm+48qfOpWdcZ8GhNBomjabuh6plQ/SxpMSe3eHfS+GYugioGefezBckDsxZXqqhcVQ0k8wrtEsAMPLRtXiR+nfQcNvWTwmHpluXExKKWiNxwEqzGkOti73LdVrCyPPitoENMxVNsZuYxhulEA2jcb+7s8MgleZTS73JqMdsbzllozcpwWpCaRptBXaNKSdVGY/bGtRfSo/oLh7PX6UacffkR8to92o5cMWCWnKouX7k9nUsXHb59xHx3CteZTocim+uSHNS+kB2whRxNB9dM1PMabpYGTNfRJn3ZfYGruNYajXbwxyv57hNfoj1E3jth1slo/v8dixjNynhbpmsWOovcmhpN02AYuBslFkPy7SaO9x/epAPiYzHIG/d9Qj7diGyUy6XA4wzbfqDmozjXwvPKExteh0sX4ag2AAIlCqJ3UH+qhzATkgT9OwcffZJA/jaO7W+Jr7ZJPHRGO/AtlIKff1jOMkMSuzfGNEzf3AgZHXqBmGwNFUIJs4Qu7Sg2T3tZE097YyO7uIZq1edGBB1CLpvc4iEp3ucKWD20smN15Gu8RafEQ3kzLNd5d1dzSPiS1mTXSSeGVAD5Ul3wIdPJPvIoSNCogjMDUHXex/jJWRZ0Vhj783fHgG5D7rPfcvfOGL/Ot//S5e+crX8P3f/4N84AN/1N5Pv1Hh7iU5MjIeahSCyTM9TPPZsYi6HqHpPpqhJqpeQu76v4/YRV8d6JWJaHBEPh+ouROtvfd2ZwFHYyZ8GSKFYX0lHWOcj0GadtKWJymLa3NQX3HQsdEw98FC3f9OpdxC+e63aG8Se+4l1J1TDNp1cP0tPDm7TJpxGN0sb5qYB5PHAo/6bsUMotTNcs/90Ucf5b3vfR8vf/nLec97fppiscDdd3+Ef/NvfmNmY5gGvPr0E8dscnjkupaVkfu0oGk6u8YcF6QdSegyuBhNdP3xvPoesXUT1g+NiYSyg9voT4olgDpLePSbmNO331OvvegYHAxmaDtJyiMOmydtN0mdTlk4uE1rF37032hkzVTNtUbbBDyEACnPI0SyBGiRBlgpQZaDH0DrSJ0HVDFEg32OXwOMYZYHyJ8+hbOhnOJGMaJpqWukxyzJ/e/+7qN85CN3czBY9LzjHW/nXe/6KT71qU/z5JNPcsstt8xsLJOEH0PukzSc7o4RV97MTsJNDUJo1PUcJS0HshE50fe+jpPpk5XxJBEawVCJSeKK3I0hDqUHjTKSoXVCbzFJ++PKzK5MsEWVKs2QxH6yngeBQillHTFynHuJpAI4CBbb16CKkD6eNo8n6qNrzhPCWP3nTp0aq/NZaO6zxOtf/7o2sQPkcjne9rYfAeDq1Wv7NayxIJpNOHtu6v1c48gItSrAWXx/+qGMn8sQukQzuwOI9oY0jSPwyOtBwbQoO1Z7ThDm1qTbvyT9tD9Y6x0sPzhT+bD2hsm0yyK6SdL2wDYTI+knozDZpUCB6H32NO9CImUDdXxkHoQW1G0AOpbUmdNq6DeyQx3AF7e32QIWgdMj1J988phd4BpqX6UBHObJJ2swRszyNLjrrrv6ri0vK4309OlTMxnDOMg98QTL//wplv75k5jXrqHV62i1Gt+GWu96oYcDXAkel4EtYBzj/bWhZnkXeAJlWrsZ9SO1gDV0fXaa3XMRdd2goncmxd78670EPlBzl/3Xhn97E9TehzS1yi5nY8rSE1l0G5GIcCScqhaf0FowiNST1Klj4MbqkGHJ6Wv0yunNCF6vJBtP7zaGbKJmuvlQpLsKim8OoHEVS2uiaeOfJhsXY5H7+q23cPK+fwA6E3s5eAAswEBja4ocTgE84CKdgIZN4CTKAOGjVmY3Ef5Gdndnc0Y7Do8++hivfOUrOXRoWMaz2UHf3WXx/gdZfPAB8t96CmN7B71SRmvGewJrwSNsAV8Cbg/976JI3wlel1BLrY3gMch20Z/u9XJQYyV4ADw/ouYZLOvmAS1nGBd1PUfFKCDZ7CKE1Jp7BLHTIz8Iaab/UUl4qT3qaC+hzvPwHtKOIbnuOL7MqOXJ6nWkKtg0E9HMrM32w8akxhM+n6+IvQEUEKK12C0H15QC6eomDcNK4Yc/PYxF7nMnT7VpNof6OGzgQHCtAVRRX9cmasLPAy3DdTS5l1EEngtqLEFX5LKjdAL/D78R9jP8bL1e5957P85/+S+/vy/9i2aT4le/ysLnvkDhkUewL13G2N3FKJWm0p8RPFpuKiuopVcLLeNVM/S8BVzCYosG6nufQy0j1qCtzcd/z8eP86w5cni9QmggNNlHzi0M1ty7A5tEyU6S1BJhADcfaSe06jeS72CyPMFx9LUTcwxwaqTf8zmMsyCIszX4wkCm2v2dJsl7dHaikx5VC96ZdFDcFCb2OoqjFmlxkqb56Pr1sd08FrmfOH2KpwaUhyn5WPDsoz6iJmAggQeAF4SGYgC3jTOsLtTr+0fuf/zHH+Td7/4pTp06OVx4TJiXrzD/0EPMf+khck+fxdrYwNzcRHj7f96yBQHoaHyWF/JJXsD93MF5VjnPGpJrMEJWuJtu2v+9rWc7NE2wo9vsorNA51hcas19iOwkkN6A3y29HHscU3CBPKfYTj2mROOJ2eqYRNsDZYIPbBTTvCobNoIcjHTOPby4mk7IrMQjkS5KDZkPiL2lpngoZaTz/izNJac3UVbk/cVYM6Nd7H4DSX5YAvVx0JbdZbDxfjzsF7k/+OCDuK7LW9/6lr6yZ57ZoFTaY2lpmZWVZTQt+cpWK5UoPPoYc1/7GoVHH8e+eAH7wkX06iQy7E0ej3OYT/BC/okX8gSH+QbHcbtuu9YPdy6q+lDcdlvmKj9tCKGxrRfYEyYL0kupuYeuR+zz/v/svXmwJMl93/fJOvo+Xr9zzp2ZndnZxZ4QwGMJUCJoQCFZoiCLNE0rZEsUbSsUcpiXSJOggqYYDusI27IYlGWGqCAlWVKIFBkIOcKSeIIgCZMglyBx7wAL7Dn3O+ad3a+PSv+RVa+vqq6sq1/PTH0jeuZ1V1ZmVlVWfvP3y9+hL7mnrAoPqE558HSZNrwyuCVM33MizzBaRJ4suI1OuZPjAU0Fnx9O6cPj3oZeEkzshcfmeouh1jfKvLED1BCipNo/0UnXRupzYRgII168jrSRiNxFQh8kATS4o5VVNy5Og/NeffVVPv7x3+QjH/lh3+O/+Iu/yM/8zD8DwDAM6vU61ep4+kHR61F8+20qX/gilVdfpfTGW5TeepPirdtZdz829ijxCZ7hYzzPZ7jMH/AkmyeuItng2rWc3LOGEALDFghTIF2BJ4jQpyX3aYVtlpJ7dIwzW58+0EZMkbvgHZaQvK1X7YwLenj34qOQuoIpqhgUtJXg4Yirtu+7/upuRjjNaJhS7jJO7H2QB0B5RCMxtNFwTJuBVUhGrCkhUR+MFByMN7idKbnv78/XTeq1177Cz/3cv+Vv/a2PjO0Ff/GLX+T69euYpslzzz3Ht33bt7Kzs8P29jZb9+6xs+3G2f/DP+LyX/kuWjduYPQX18XLQfB7XOP3uManucxv8S6+whmck1W6zss3Wibe9H7hgn4gpRzxcWQU6BjWifStR+5y+neBb5ja8SVA0NhJ2efdZ4/bpgdyB8TkonQYmGUmInQvvOj09Ua5+khkP9aU/n5/eBsGcUTt8DP8Wp511iFSghAlpNwCaiFtSGDfVcMrKyIpJXCEoAhiUu0usZ0jluQ9hLEI5nQpkHuPZEH81rnNl5N0IgTd7vyMG27c+BI/9EMf4du+7S/wi7/4UQAcZ8Dt23e4efMmP/R930Pp9Td4+eYtvnF3l9Lrb3Dh9ddZRtkhvAKcuXmT9s2b7KDua5ehgZoBsbzB08BbrPBpVxr/VV7kD7hKJ1Wb0FkTejDOnt1IsQ85gnBol+hYBeiFE/ukrB627z5dfvh35qaSPgRvCekraWoZhkU0UpsF6VdhaPl0ysXdgx/FALWznapWZuaAmFDfT/XGQwflyxUEB+Xr45yUk9IB2oDlQ+we+iDamObp77dDQnI3LZtNiBQ4dHKorrPLqFojWk3haLcFg8EA08x2H+T111/nr//1v8H+/j4/8RM/OXX8f7Ft/tOP/2bg+TXgAyFtHAGvjnwvonZ8Cih7Tb1giuE4oMgXOc8XuMiv8CIf51neYdU9uliW6eYixHl8HGAK+oaKTDH6Dk//P07qvuWmjLiCJcV5q+stJC3ZZtN3WNl6/YmhYIh7nakSekjSnqiLggPgEEdDmZ8FJrVAIwsz2QUR1CeJ6rnnqeUR+yFKtR+8zSgNAyeFhGppIRm5mwa98+fg5jABTNRxrUzpHKYME1JDiYODA5rN9Pd+e70ee3fuUr17l7WbN/n5r/0a1j//BS7fvctUiIReeDapMFQY9ysfxdso00TPTnMV5W9eZNRRw+caMHibFd5gg1/hRX6N5/lDnqSf2fPwg5d8IToyXrPlcGGaBjtGiY40KAknQDU/vb8+fpyp46lM+7MENh2MkJot3UWybz3HMSofR7zrVR2cy159DHe8NKT8yS6kB+leycj8IuoEG/l1UFJ+EyG8yaUNdBGiNeM8wBAI67SDzg6ReN+/cvXqGLlHhYpsl+XKrkC73U5M7kf7+1ibm8j7m9z+rd9m4zOf5eznP8/LKfUyKS66Hz98AUX6XeA+grOs80We4qN8LR/l63HmSuR+uAU8FevMCI4GORLAMCy2zQptYVGiG0rsoXvyI3vvOtAumnAqsYRBWVR9j/Wpzk0GnW4nXGxKbT9ewz1Opz0VzyJ6qLJAxGV9AUhvopCuMZ3fxNFFSey1k+hzUipfdiWxz55sbDGgaqogN4uAxORevHoVfvO3Yp+vAt5kuS9us7d3SNIAcf/nt/0XtLa3eRH440CdeQW1jQcH2ESwRZlfpc6/4Sq/w/uBF4E3gesxatV9u+K8hXFY+gGGke+5zwNCCBwbpCGRrm5+aBjnT+xMfA+T2E9DeTsJiWRP7vsO4V7Kk3bS603buG66XHz1PCg9h0fuQ4o/rW20ydHnfbz+HKOk9ioeLUrZBnoI4ePy5gdDsBDp4FwkJnfjXPxUnR7GY1ilj+Pj5JLpC/U6je1t+sCvu7/dAj6DinT+QeBllBq8DJqOFunhEDjA4lXK/DNW+Xn+OEd8HcN4gIsGHUv52S+Kad7ENJ9NrUc5ZmOvVOW2aVF3epiMG8JpS+yjSMn4XaZUj1sbVoD/zvGEEZaO9JtOj+JVmoj8Y8S6nzx+RJHOiQvZZKn5kOCwlaEAKV0zP3HSny6whzKe84j9CLX3vowWsUsHU3TpW4VUssSngcTkfvWFF7gT8ZzJISpwIr4H0QZGKmlffZo8x9B6/S33A/Bp1K7NU8C3okKwWijr9zSG9AC1zryDxc9h89O8j9f5IGqZMaPDC4t4fb169bS3Ex4vtO0WBaPIW7SRqGmvSXRiT3Mhn75QIKnhHxzDoRCtvYgEP09JXqv8iXZm9oUEHRkIkwGmfz70xIYSmjipelQzOJw3vOhzSu1uq34Jz5e9MZIcZjYMHKpyD7EA2eA8JO7J2pmNKXKPumg1cDJVzO/tJa/dGtmzD7u+l0b+/hW37CbwOZQc/eeBPxOx/S7wH4D/g0t8nD+F0hXEwYBF2RNKiuvXF8Of9HGBVRBUDME6akwfA68hWHbNlSpoSuyjEICcrbuLQ3pJiLIeGJpUn4Sy00TGM66DpAZ28eqK3mLAPU7I/2KE6lSAIq/CTYb5S9zf5AFq2aovgwsG2MYBpumXbe50kFwtn4JFk2ALtdeRDY6PTz+Q/ypDV7cbKCM3gUqVcht4FkX473XLfA745yzxL/gge3yAY5rIsfCJcTEgPae508VTTy3OKvlxgGHAnlVmjQcYSEqoHIxtBJtIbuEl4VUTi9/MEEwKCaPCa54eVkQASziBJSOTWop+74GVxqxX+xwBUmPvY/JonQo1UWU7gj2Nv/ldPGb3zlLZ3LoIUUHKA8BytQm7CNFguIkqgQdAaSQ5jN6WoSMEh6ZJZYGSWCWfHVMh95vAE4nrCUIa8eWtxqygB9EwGm35EsPMab8O/Brw9/hBdngeTlaYacYA6DFuCrgIgzGeJ8P16zm5zxtvF1Z5Qtyj6Mahlaip8YL79y5KFjp2f/OcXGc9qVm8EUcNnuRtF8CZGcljYtW9APvv4+fGKO9qWKIsKoKXSBEx5pMeYb46KdpDGcvVUPvodZD7IGyGWkwvcI3p5n0Pw7jtgDCgWFysbcLEs6NIwdHYYCtxHbOwt5c8srFIsIjRfQ29tWKXKuM59dJGnGeWpqX8ZJk4qqwB7373S+HFcqQKp2AghUA6k6p3NcqbDPfht1EewhWGY7vArEknhWhsCRYKnv20g9qLnd5vdTjGoBhnEzHk0qKTYPgZqe/BA1HMn9s4dFLfcI1jkNdHBa4BZAdwkKKKOCF2iSJ/EKJKNM8d1R8DSd1arHDhicVuYZjsJqyjQXw/eR3s7ycn90Eh39+dL2a/vEKAnUJugxzRcGhadNDbU19GGZyWURL9jvv/Lira4pRkOIF57rWPXk+fHvga1Rm86fq6p/0Z74n+GXp1zr5u3fJSRLu/XTr0pH7gn2g6xNk9H6/LAlGgQJ8qFqYQjOcmPXb/13R5C2rQzM7SIg4Sk7thCLZK045fYQ9q9PgS2xFajK5GbreTq56Llen0tg8/Ht6ryIPXnA7uC5s9BA9Qknln7OjQuWj0lxJDzxIbpSTtjZzf9qljFrSM9GJCACY9hOj6HDV4S0tlO6PyE6RD81EQ53z/stM32K/uPiZ9MY8X1aeXYvRPC0GRq84tLss2Nq2R6HMdlLlyaeS36O2bdOnZiyUAJpfchaBw5XKiOjYyltz7/YeLxJzkj2UGFvFeRF/x5jHlTweOpSRxz7RzB7iLMkOaBYkaeQ2UcWkdpaI3GO7T3xUnytHke7UJhofBwDXCmj7yFrVkUrqII81HRxqSvO85YvhHWN1tbI6Ten1Hfo5+PRJccrb4+t5nKMvuSETOHlLuoZaf8beXBQ415z6GtThx5SEFcgeoPJsskMgG2yQfzsE4PExeh72ULHxttB2i0RciTWM6yPI+x0f0mdgwcnI/DZimwZYoU0ERdAulzBSooE63EehkUTDc8+2ROorAjlDxIvw9zWcjqUreQ1EOqEu/SUPQTi08VbLxm9bCIJYkf6Ken30NDoa2oJL+2zy8qhW5x9f3P8vK4D7H2AxO+rSNMi5OKnFLimIPc4F83CENa3mg8lS8uOAeVPKYASl1ZwqHh4tl6PDwIUtjukPivFymuQWcj3xejmSw7SJfoc4VuYcllDucRBmhlVCRue8wzKnV0qjTk3c8X3kHFbb0bSRVxs0tIxH4iBFblPOKQlLD4WBGmURL5FQj6ukjrcUPMNP/3XvDHVHBOW23W9mj4bzDmcEmAkkfCxWbbgdojbi8JYAQdOwCtQVyg4OU2HTluWc5IJ6MKfFSxvY1uhPv5vV6yW96oVqbCm1xSu/oI4bbjEfWA53nXKtFsdPIkRaEMDBKEjnyMqh96mH64aL7ZuyhshUOUARdD6nbcM+XAgoSqggGSF5DqevXCA6mHPgexnhJbSwqohZwNCWyymjySKNK7ToCAhANvxnK8vXkl4jzcMJpW8oByDuYVLCRdLE4FhZS3EdtEA2JPSkvi8LiGQGlQu6XL1/is0w/C93xq1bm2QWaScPP3XjkLLMXZZXZJU5f3vWuR+15PDxoF4tK4TLxWnlf1e6loIVkCWU8dxe4h5Lmlxg+8cknf0IDQhkfmwiuufSxD3wZFe6qyZBmQzeiIrjHCaDPgB3ZCai4HTqn6c828xMP0tjDD/5BBJXS6IVIfSYSAFIi2MIWLRrO59kDhLDpyS2kvOb6svv3J3p7kjVrH4f0YqGkgVTIvVwuK/NlJzpBCzzDmn5m9N5uJ6/ZtJPfqlzSTwuC8+fzrZbTwp3CMg5vomRyBf9xrUa8jQpo4+VEeBulim+gpHWLgIlo4oWpu58ByoDPy7y95P7vGejpIvhddDDxN9RxUt86TDYrZDWfzCbzoHPGr8UQNUxRCQzmO12x8P0zOgbAAYglSk6Xy84OALewaYs1hKiMNTAutQf0JwhujLFj216YhDEe0hupMcndg8kgM3I/PExec7HqHx43W8JO25juUYHkxRfzVK+nhphaLBO1p34ZtQnn+ch4xnQCZWA3bbc8/paZeKmiFcnvo3J6tdx6TIZRwaV/FTNh0afBAZs+xzqszjx3VhNTx076dLrL/jhEHlbMQU8XOz5jRVPf+9+1AZIDVzIvIDimRI8GcBsHlc9Qdwmo1x+Bg7TnnQc0HOmSe5LTCQs0E5+4ut3k5C4XzFgiPqI+pyyN6aKiAxwhxB0++MEPJawrR1wUi4IHwmZDqnc2Di2ZwEX37y6cRLrwpPgy7o5oCO8tuYdbKKI/GKnD87GPOuINwA6gpn7akSPnwOuB1UdsN0rxHmoDw5EypjubhzBiHT3DQS3zLPySbh9gcBxrDprdn8bgHkZh8cg9NSuAt22bLvganenATDUEbQ81ZdwEPsPSUgpZ4UqPRrKVLG0b0sHkiOmjPKE/635fxrafm2+XcozBtku8aiyFlgsig8nfC8AZlDRuMYwEfg9F1rra0RbKh76GUsz2UYR/F6aiaM4iKhPperNPo5uR9bec8BtP8zPRkLbfWzz3OvWw1P2XU8Z2M04J+O7fg+lTHJQhiGCYhEwyoMeh65zZFnV6ojRxXlSM9Mc9uSjvLZwbHKRI7s+cP08BdXs/j1KVDdAbFAKwYpO75GSPhVdR2dQd1JRxHniRw8MgG9v54/Tl/3gGbNnBT83poKb3V1DhTZrAC3ircdtepP4/fhDCoGMr5Xn4+633rCSK2JuoEVFiqFp/R8I9hO8uuF/7Xj1eoBzb7cVNAVsQsJs+hI1gxbffuzPPjqSSH4WY+mNu0F4URKpD0AeXUoOvSQR+0Wlp8ogX5raO8KLiSQkcgBsC1xBljMmd8US3XPWlUygM21wgpLbcqL34PO0vfekkcYSHz7nfL4Scb7ATscWvMnSQWUOt15/xLZnGnrtZCV6xZ6NZy2q/fdEM0VYmvn8OpWy9AHyNT3mBtXiL5McO/aIxGTd2BoZviO57UnA/3purrNiV77uNGiFhilDBeARxEzAFHEu4j+e2N16PxDPyHZ2sHSQ7QAWRQfTItLbdtU6fUzs9BG0M18gupD+jf2v3TY78dYwS8CoTIWR3sSmyzDE9YCAKEDvEbDDM0mJOSKn1qvzkk76/P496QXsoaf4BSp6e3Lkqc2tGCMsOKm6VAK64NV5GV/HQ6+U26kPEif2VNV5BTcNXgecIW6jkkvvp435pDcnbgcejSn5BMKRSskqG+rgOao/+GBUjw28X3M/FzavHFlCS6vwDVNCdFUYXAhLHjXovMVHvTBkogej6dji21D7ZyQm/vUxmLk0STdL2iUFdxjbB8iQ7QX184SVvASsIHEwkfaHGzaiYl9YssmweEjdtdZZIjdxLVy4HHvOsYJfdjzKLUntqJdR+2xI73D454xZK/dVEOcwI4OnYfevpxMMMwyMjLkZ5ZbMzpnuCG3wL/5yf4kdweO/I8fC6cnI/ffRKlfBCY9BPFTqKUXtlFShHUETSYJiB+3VUcBudxMGCYbAcG0X4LVS8Mk+4OAsIuq60bqEU/KUMPLJn9TJ7gSTtFkafVYcihzPSp6ZxJ6XsINlEiLOK2JWDO9J5CyHWQRROOnUE7AqTAUY6uyAj58qitVAbnR7Sk9yfuh54bHKoemqwyyiJ/gC4xj5fVKEGgA3GHWKS37qdnT6tVvzLNQrz82LsLZzHZDpocp8/yS/wDJ9i6cTGokwUYgd4+ulHZaH18MIwehxSoMp0ghU/0lC/RSMtGVBUuPWYDIPiHANfQFHJGYbR8Fw35Om+CfeY+4Nn+TFAch/YZIAi9JElg1D/3KbM2ZE9iSRSuwz8orcYik3QmnFn4tQ/uveu1YeIUE9/AGIXgzOccIWUwKFL7CWQEsONTLBPkY6okZaZ2UnXpUPbsvB3lD5dpDZL2kvNWL7utvu5jg0ZRvjZ33do6QS6joko01Z42cUzzoiLCnu8j//Ii3ySDd7CnLDWdyK94ars2lr6+2Y5oqFYLHODEu+ZIHc9A7tkOmG/hUIReNb9ZR+laveS05j4q+6n65UYKNHiKgU+TXUipS2AwW1KY+QeF8HEng18m8hISWAjKJ7MY6MyfXJRTboG1OLEvwKUHucIMMFNyytwWBm8rRzjhEVJFBFJwuF6GDltqf82xWJQqOLTRaoikFEo4HSmXwcdnAlM+5qOwmN/P5lRnVmOqoacJ6Lco+yJ0aTHe/hN3stvcpUvuG4q0+hGjimmcO1aLrmfNgzDYtsuQW8vtKzU/hb+uw68SHaHKKLvoFTtfZQ6fmz0BJBbgT4VjulMLAuEaHLLOM8LbtSzWTq25Jw5m3kjaQXiNxOrDUsUKIhRrdxoaZFgWu8DhwgqDJ+kRD3lPkov7C0iJA25jY1KRHSMEdyfCBgtXWYXy1ocb6xRpDpLigT70jUOMBiM5NpNF0dHi+7fPS+EBQvyEH2//Tp/xNfx6zzHKxROXFOCJ4B7MbO6XbmSk/siQJYEo/ldUxMAY7LS5GlVhh7PB6g9dS98rYGKlme71UxuARToU6XDtqdNFALDuIJtv8zOYI1O93N0URoBh2GO+1gI9ZM7XYPgOK07yBkxR0drjEKsPdSSrczoskq6EVYEVRCjT0EipdIsHTLgKHDu8zO/1MN+wWIx5fa0yX1GWEqdIWpmSO6J3c/vdwUAACAASURBVOGK6UamSu+VPV1Tjit8gffwm7zE71CdmSRzGvc5N/JN/zquX380bRIeNtwtrIK4q6FC1/kW/rv/Mb03qYYi8x7KeM5k6LHuhcU1RuoycDC9SB3CxLJewrb/FKZ5lYLzearueV2UzNhjmP0u/Rks+myRmlQfq0XBsezTljqWzLrEOgC5h/JYGGZzk/TBW2aJ4HmhTYUjMdS+zp5t9Bcfi5gNzsPcyF0HNl16Y7m90yOuBw+Skbthhj/E019jhyGd+7nMXV7kd3iZX2WNO1qt+t2X+6HRD6ZhWVCrLe4L9Tih50Vt9JF8p6H5ZqSsHh49rvzX1Z66RBnh9XG9dwT0pHKJKwEWA0p0EWIJ234/tv0+hFgDwKCBgZIfy6iFQRcv5KoKddNCMzlsRtcbGVMvaTzPBuH+NWBA30dSFif/zKrFr9ARSlovn3gtKGLfB2oIH2IXQM2V3KXwnlZA9Zr9mYxCvlqItw09D6RK7vZyi969e7HPt0jDZ80Pgm432etgLGB4wXmiwj7P8Cnexy9zhRup1Hn7JLq4DtRbVSgsotPJ4wnTkhxgUQ0NjDT97qUjtXuIvqwWDL12iihidgQcShUTsUyPJWOFYuEvYFl/zM0k5hKYMb7H6hkFg1oseCP0dZT6XyeX/STiaiji1R3ehG7LXrmOMDlKRC8jLcoOKjd8+cSXXUoHyV2EWPUldlB77iuuMn4gCghR8C0XuT8jKwNhL66gkSpjla9d4+jV4Ik/bHha2vvB0bG7m6xukYEr3KJL+gXaXOFV3scv8TyvpF7/g5AMW34olXJyXxSYhRKvUeEl9tIZzKf0MoymnC0iqCLZpU9Z3uIF+Spvyyc5dMldgJtxbHZdDsolD5T6fxu1iFhBLQTiXareTU50G7W0MOEYYNGfoSbXhvT0K5WJOAP3EWIJQTBhC6Auu652xsFxbQCSzyDDG9SxSwvpBgcpk3vp8uVE59tjbjXpTuJJ99wNw8Ah3LZ7voSdPtFZFly5UuDDH65y6V9/L/3b76RyPX735e6J5K5/HSmbPuRIAMMscGAUAnMRyZF/p38PKh/9WBii1GuhAuU0GPCs8/vUO3/EvvEPuWl+I58qfi87xtMcUw3tj0ApgSWK1Fsolf3dkTLnY11UvGBAupCqCSYj5UWvx0L6EW+UKUseoZZGyyCGbnWSXRBNBMVpPfkEDFRw2geY9DE1tgWCMdlUtX8Xy06iDcgW6ZL7E1HUrNMwM4l7rp5I0j33UqnEAel74s9vMeCNzOnBKAScOWPyJ/9khb/6VxvU68ok6JP/qneiZky7jw4iVoatXC2/OBACCqXBMKLxSGCUWMQec6AN/d6nW4i8YDgJbiMwGWAxoOV8iZbzJZ7v/Qw7xnVesb6FQ4bpZCdH5KQC1ztecz8SZbm/iZLoV1GBeLyySWIFpOseN31P9dXzBeSEhkN/m1si6YDcQRgqSI26YomyaCgrYg/s0dAVDqCLwYEoITxyTwk15w4Fey3FGtNFquReff75RETQYptbPJFml07Q6+WucApD7UitJvj6ry/xgz/YYnV1eij0D8LyZ0XD6NgIjV41daZCuZyT+6LAQXC3sAxHUZM+zYDPBHIa2nr1Nkx3puV8iW/s/gMOUMTcQlnHqxzw4Zo9r7alkf/3UBJ9DU4iP5j4k+GwN3MQCyaaiN5a3He1j+AAjJHoc0jXWl4MreUDq1c9rcpNLJQWoSBKSvpPSWoHaBdr1JhfUOKoSJXcC+vhq5hZQ3KJ7ZFS6SJpfPlKpaItuS/uXnof2y5z8aLFj/7oMi+8MDuv1uAgmmtbFMiYUfieeSZ3g1sYCEGnMG0qNtTozvZDD/w9wgs0y/AsrppfoozrnBnGZavu/3uoHBlFhu52A/Qi4oGagJcZWu/fZ8T/3v0/uK50Z5ogTUYcFb0QFgaF6FZUsgccgfCWTd5VenvvS9p02hrcxga6mDgUSTvypywWQrcFThOpm4CLYgF5PB1vWgeNGXnhYvbm5K92O7nkHu+qwhHvFY06qPYpFrf4xCf+hFbpwUSkwbSmEa+eIblHu44nnni8vRYWDaY1oIfAnhwdKQ2YLA3P9KqZrqs/cthLcS1RxGygAuY0URb4o3HUwpoqoTJmSuA2w+A4bbcOL9lNEDLzbY9B8AILIayTc7QIWXaBQxANRqMFSHpA391n148iUHB2sIEOA/bpnajpvR4mRd3YR9BKpa4skLodv1EMy7IcjA0Nn+m4ODpK/rI//973cAx8mXHDmDShgnmmZaTRBb6I8uStUCr5p+X1g3N8HF4oAZyYQ++JJ/K48osEaZe4PZIRPY6xnC90uCDDYyd75T4WWH5dE6jMdDWUdm+AksT3UPvr/ZB2J9s+hyJ6b5HQdevy9umHEvGciCVCM16Kbzlmdi+ZeQfkMcp4rsh4GKAuanlTRIwukyL0pyMs9kVp4pyQ/mjAWGA3OMiC3Mul2MNtnbtkNVg7neSSuymUGcdTKLVcF7XCfh39oK56SHIPOihC33HreRdq/R+NFPt74THDk0B/z3283Pp6Tu6LAiEEA7PAtqEWo77qdb/fNSFnDBE9o7P4EExOjuKk3aBJ0+tTBUXyXkAcE2UG9g6KnE9mopAuCpTEvoYi+SpKcndQb/c74KavSdO5K6xHs+uQqIXMEXLaql+Mlho9puLFK2IfGtlK2XH32QvjxK6J4XZGASmCcoP49Wei2z6XLWWfQaH0eKnlDQ1fpSAFz3DPPX30eunugpvu56z7vYtaod8FLqNe8Pnuu7/OUG54Br8XsVjUH4h9n/32dFXzo3bE+shDzy4YDJCWmLFnNXvUZPGOzDI6i9LeCYlPVKM7ar349RK15FZudnATtc/eBVpu3WH9MlALhRKKCnso/d4xahuggKCR9X3WVM9LxoWd4Pvl1iOPUFczSpZ9BG2Uf3txZi1BaLpuHIYoYInwUEvT1xXcZtXZxTQXl9jhlMg9CC12EAyQqURnHr/xSSPUgYrAF4QCaqW+ghvOEpV2sgmjGaEDEXVHS63f32QYLuMyYS9AlEVmf39fv3AMvM21yOcUi2BZi/1CPW4YCJOjYhXZ9beXGbqpRXv/TkqfkvW8gVKDS1zLdgHSJbaos5O3n15y6zPB3QtWkvyxgFWpvxnnBcopo0h0gJoF7rl/e4FyMnlTNAhebSEIvXTOso26Ix6xeyudIxAVVJCaeFdy3jlwA9QKBrHqGN0oGUeBXQrWYgsaqZN78cIF2l9+Lfb5Nn26GaRe6HTmJ0d7O5BXwM08rNRnPZSKLdmQeMut7ZzbQhiGAzOK5C77/hsNaUnvu6xEPqdSWew9rscRA8PkwJ4Ro2vGgInmc61XNK71vN9ZQ/vs0aoEBpIjlFQe3K7/MY/oQbnR4bbzwD22RLT5wdMgKgt+da23UdsANeAC6ey9jl2fD8FP7q4PYFya8Jt65CFqVmxOSB4PgBIi4Uxp0TuZf/sxFwjiZCvh5Bf1b8kGw3Dzwy8m0if3S8pPPex9DDpepENX25FEH2lYy1v1RiRyE6gXzwteAZz4A3QYRq4KxxZKF9BEmdnEe2yRJPeM99y32NAoNd7hSmVxX6THFUKoGPMzozeekAGk4aYW/ZgILeF3VJHCxDEBAwlfBZ7XqjUY3v0qASWh6nlHKo1BHfWmez2fNfK99g235HngvPvrDVSinA5KsPBsBhK/SZ6hoRztgcIAg45QqnQfe0TX0K6j1O5ihbHnI11bITFqmO23d693BX0Eu6KMI6yUNBnuJkvFziL9X6pIndwr16KrW0eRTvKY6ceY1M8dQFjJn+bSyN9tlPuM8sVkQpZ9gHrNR81zkiFKXPbebjC5pyG934kRrCgPYLN4EEJwaJa4I8ucE+2xY9PSns/vEwg8Jkgl5nmUdg38FywOggPNNyCKe5oALo5opr+CssA/ZhhfwwroUxCeZrgVsIPKobbE0NDPIiHR+0jxDqYroE3XrIjdtYwXE25ksg04IFY1+jR7f1zInmvVY2CI6AbFwRgAXWpGHwszgmHw/JG+5J4wBG0hI2/yNPbcjXL0cKmzMJGEkG2UzajBHg7r4EuA8QeTEWFWyNoVLk8a82hACIOuVeaBsDnHkNxnS9H+R5O8oeEkGr12b0978kwpoOMSWibrDQFCwjXUXrpAqdn7KJI3GUay072TnvawgdJI3EOJDVW3/lk726H31ofgDWEE1NcD9hFimTHClV7SXB0LpbBeCmrOHdfGwcAQFdfnPikc1N2zMEwbxGJHPc2A3IeEFEfCK5I0P24wAWxv91lejn/JHrlHVc3rll12Pybn3YhKSTF+L6LEZR8cpRt6dhJ3uBT5nOVmdlkDc8SHYUoMWxKqdDuRvmMa2MVWGUVTx3sIkpKH++bJPAFmHnerFgyJuYda/Hfcv/soUh538prdqo3aCmxxIj+fOIJ1UQuaWNL8CMFbmJQ9yX1UMJfHQNeH2D0T5AbDBDFJIFlz7mGhXPI2U9EGO6g7b6rIe9YxUmSVojwdpG6hZNVqCE2Leb8BlF1Odzg4SJgZrrC4GYB0YBgRyP1wNrknkaEdBP1Q2+DpFp64kq7mJEc66Bo2h9bwnQ8lLR9EMq6LhPjSdZlJ4lQwgLqIuc6IgMn6bZRK3dug82TdTRQ1HkXsUZGhQCHdujqorcItt/5INbrPxsCgMGGvL10CF6LKWPQ5eYTkEKiCMEermdlGGIryASbQx+CAInGe1piNkhygQuOWKNgSw5QL7eMOGZA7gBlBfT15e2pk54K1v5NMK2BVa+GFMkWywRRJcu+Eq+Xj9mYQU2F04cKCW7A8pugbNsd2UJCQIcan1wRjedJAS7PFqCU8v3S/5osn/fC/jqyJv44ylKszzA9/jCLlHYZ+5rragzLDoDtemFvP6mdW9BE/74SekByMeZWrjOpqqTRCOfLY/b2KSgaTHll6IqIjTDrC8+aQI58IkA5q+VTCMAwqtS5WYbFV8pARuRuVIblHfVxLJMkwNbu1/XZ6uxBRrut01nfTrUbZcw+T3JNgENO45dKlPK78IkIYAsMN6BE0bU4Z1438kUh9HXJWFvv4BkPvlyiW25GhUa2B8qEpI6mhSNpAEfx9RqLhacLTDjRQCwfPLO4IeBsvPPbsPjsMOKbr9r+PlAcMlw0uZB/oIqgiRLwgNbNQlj23Oxa24ZfuKwrRtwEbRIFq9Zh6/RjDmJ9rdVxkMlsmiS+/wv0UezKO3d1ke7azgtikiawsMKNI7o6me0GcbVAnJrmfP59L7osIwxDsm0W2sWhpxAEDkrtcjFiVTyM9S/YgK/pmUIfSxoxqR73MPct+LzytZwh4hIqa2URJ5lFmlrJbh0cSKyiaexul0Vhllk++WlYodXwBKA59wqWD2u23oknsETq/JDs4qGA64ZpCHz/2k7a6QAdEi2KxT7PRwbYHi66RBzIid7M2I6hFCNLPDDfEzs7DYZDlvx+dfDRF8RMfHB0lbi8I/dDgFP79PHcul9wXEUIY7JlVHsgiLTFN7rMpL4FRmu+p/oFVosLzBw+qQ0x+iarpjVJ4Zv3TBzyi94j5Mkpl/wZKGi+gl7rag7ekLqPk7yWU2nvH/X8FxhzfjrHYETWkPHR7Uh4J9uL6iSNQavpsWPKi3AW8WAVR7vY40Ut5D8E5DAPqtWNKpd5DQeyQEblbzel17SyMjt1V7sVsNfyOOwm3SYQ1fruysppPDv97ESVCXRS1fNRriyO5N5sPyRv1GEIIgWVJTNthUnD3HRca/u5hx0+OnQw+6X88Sd0z0GMiz7qnnpfhJnw69U+VEeMHdM0EBYqcK6h4lq4cypsosm4xDGoz+Yb5eZJ7ZUyG13+IymyxhNqucBCukVwPIZrjNXtSu1gL7G+0A/4wULqDbQwGwo6+jSolkjsIoYJtVcpdms32Q0PskBG5Fy5eGPseZfJfi03u4XjwIJnkPknuMG/SToblZX1SdbrZeS3ESfea+7gvNnqWTd8sQL8dXngK029REsk2rT18P8IbPRbcl2SzQhrzSVAdBYaS+xHKAA+UxbzD0P0vyttWBbxk0m8Am8IA0fIhdi9fuz+xpw9B32gSmeYEIA8Q1AGLYqHH6urBQ7HPPopMyL104UJ4oQA02I1xlt5Q3N5+ONTyiwDZyyaYEMBdoo+PWi2PK7/IaFtl2lYJjofvbzSpfUiI8cg5nWX2aA0GSp0tGd9b9lT2+n3TPx6Kk1gBySAZD6K1536aqGv1VPtRdWyXgSIlbLE2lqxFyjawdyIJ+yGt5bslOyeOeGVRiB7ARnqCTRkhJK3WEba9+Nbxk8hkxixeOB/5HDHyv0020dF2dxP6uZeSBZaJP3jTGfbNpv7j7ke0lo/Swwczo1D511Sr5ZL7QkOAYxizrbM11fEaVWR2fBQGSrIdtQLyzg8cjQmJV+v0DCz0G6gkMxZKzX6AUt/vud8nEeU+S9lBygcQIyolEPlSlwdvUUBpIjYj+gsIeqirL4MQNBodqtXsBJ0skQm5l65Ox5ePZqUZRbWnX3Onk83qa7FoJ7g3ZoRl+KAdR72qh3tED1EcZWGSY/4wTYMDo0DblfXicZyIz40i3MskTt0qptpUU74T57hEPd2XVJW6GfnYe/7uSiGtTCiOUAucA3Rd64Rrvw9SdoFjhFhFpBJ9LhwVuUMBdR8eyChtOpzE6RMm1WqXleXDSC7Ei4RMul1YW43mVD2BYiRy10dSgzqjFN/Fz8NpLgSaTX12HxxGt5bXvba9GPGjNzZyN7hFhmGYbFsV9rBiG9GpY8GjKJS0MpBoR/fdJx2mwuW5aH2JbGgX81J12rEYRrBbYhiS9gDlP+9tVwTVL4VH7F3Ai+0e3OE0n5qUA7cfBkdGlIRbXbcnBQr2gOXWEab5cO2zjyITchemiVmN7g7nPeCitlo+2pCYZ0739JDesI+03kq6EpqBu4GSe/C1rqw8pMvnxwRCCKQF0vR5hvNUxycgeL82vGhtkxjAmOlv8D64XqCe+Bi/1iyM8WyUFXwFRfgVlL/7tvuZdH6UCBw5cEuZocQ+EwmmP4HA8g1g4wN5jMpKZyMMwdJSm0JBM2bDgiKzGdOsT4dq1X1OyZPH+COpWt6wg/2zF0M1P7sXy8t6j7u3Ez/WgM592ORM5HovnnsYF2aPF9pWga4xYbyk+djGi6X/NsXdiy8yDO/qQaAILbuIHP7w7WPExUzSuEEeuXsZ5uoMfeiHix0HSXvkjPnNjgJoucFnO4AQOtpWlcYVUQRh0Wy2qdWOHyq3Nz9kR+4J4rDrkXv0O9/vJySIKJvWM3BaY8a29VruHySL7z+rFQeDHtG3Ny5cSr4lkiNbHNlNji3/vBLR/coTEFaK6vmJoKknGKD2oiHcel0n4mSimSmD7YgwWKhFj40i+4uo/fq3gS36rh9+zQ1eI0c+00ji2+5XZEWqJ6M87XWWdR0QA6BMpdKjUe9gGPKhJ/fMQn6ZjXqs8wRQ9bXPTI5uQqNHMXfLinRHl647WVRL+SjohWaD88fZs/me+6LDMCXCUNPl6MiNT1wifkAY1988aUCZWQplgQ6xj5b2bzFWUBufzkg3iE5Q6TTa8TvuBcrxot+9ho0UNYTvnQtrQX/OExP/e1+WXHK/h0GXsAA2ymRQiDVM06Fe61AoPBzhZcOQGVtZDf+9Dp17VgtPTxAL3W4yyd2wZxNT5ChIqSK8RsvSa3VwkJzcg1oKDj0b3DfLihaAJ8fpwDRh17DpjkwrMmTIhb+R8Q3sZIhEqzMbeP7ek7CBVqzpJPqbH4mUT0GKn8QgBkEP4Ur4IljSD29fYc9YQsWun1VyH8EyQkjq9Q61WveRIHbIkNzt9fXY54ZHqYt393u9xQ9E0A2Nux4fjYam5H6wn9n00I+hLFpayo3pHgaYps0do8ahZuiTLEPEpmVg58xoK2xUBvdRaJRJgAyt6MMwQLArvNx0aUBOfGZAgJD9oWG2KCNE8FhUvvcVEAblco9mo/PQRaGbhcxmzdKlS7HPbWZkqpLUWt4oh+/7JiXFDl5e7PTpVXfPPY4bnB/8WvNPijMbuouSHKcLIQywjJMHP06w0ZCqgZ0PwScNdmNKCM9gf4oQ0a5XBzp1CARC6Ako8ZdcMjAiQsnZw3Zd4ZTlVhC5e3NcEdse0Gy0KRQerQim2Unuq8G+zGEPtTkzBG38F72/YJ4N6dG3Xk31uqbkvrsbodZo8JfcZ7eUS+4PD/oFC8f0eV4TjzgVqXwOx4PirJuM5HSP0YZuwJ5EZU5BvywQlGdaKmhVoolJqV5SdTYpuYr5ezJIU+sF1lnBNCTNZodK5eGMQjcLmc2axXPRQ9B6aLGZYk+G6HYljhN/Daubpz753nv6u/czvPimMOikF/53snc9oofwLZcfkU2wxwD7Vp2esGOTd5gpWGzintQmaMJvz12ieDO7DbQUoUnwaSmjDQSVVNXymnAvsyj3Kbhx9HZMvwQ1Xsw9tTSr149d6/i59HKuyE5yPxOcICAMK2wRbJeZDI9r8hhdYzqA/t7QoDFtWt2NEZ0uN6Z7eCAtKzhakohDIikQ+8nx6C5pBooOJmcN6fNb2shcss8AEuhq2FxktVwfXXAJscTkfr2UB0hpAxaWNWBpqf1QR6GbhezIfWkJo+zv8wrhDzerQDZHRwmM6jIakfOQSysV/Ufde5CuzcPo9d3n7Iyj/mcnsM3MMWdYFhwKKzgG+YzHLae+6U+6WiVjGNcJVLhVbzaSkwdjQjcfeyqYo3p+gMOePJhbe5PwtlHagCnGo6QqAzrAjbOxsX6AbT+6wl6myoggdzgdTIegTWOAikSSuxkhtvx8XqdsWrl/NG5Ql86dd+vmXMQzX+f4+Ksp9CDHPGBZBW4Uqtz1mVr01fHxfMGTIkhXqIKh+B/zeznC+3oakuL8CN7JWKcxdSUjP9RkGwNHPTMxamR17BasIIRgbfWQSuXRcXvzQ8bkHi+QDUCFbFZ/W1vZpJNddJRK+o9abm3hAG8CN1Puxz6tkW+z3qxtVEDLS2xsLLRdco4RCCEoltapCZObqPEzYEKFLRh79OOK9+jErnN8zHJfjHcgTEfQQfV/tMxYDe6X2fUM1cOnom73ue4o0G3LAY5C2ph5NCHZrss2JpK7QOfEeFc5NQo3t3ul0qPR6DzSxA4Zk/sXHWemcn3Wva0wKj0mfQol4L3Ah/nIRz7At3zLs3ziE/EWHnarFV4oBrIeZ1EG8qDdxgAuAWdRtqVfAW4n7QOwi06Wpi+j4l2tAwYbG4+gtcujjJKBbQjOAy3U2LmLGkc9RtKGnozJYFrMzDLeFbt1SKuJv/HcVBS+qXds2j973jL7VHsx3AKjtWdwKII1tknnuVlSu4IaXQ9EGSEqSOkg5SFq9JWwbYflVvuR8mcPQmbhZwEuVGsMgFuotIFR5K909tyvAE8BVTx/R8eBO3eKfM/3XGV9vceHP7zFX/trd7StJUUElhRk+TJHs6iPYnHudDonJjEGKqTkNdRr00HJ0wZwIUIPPEzvuY/iNRShP+V+V30+c+ahsEvO4WLPruK470kZ9TQ7qEQrAjWegmK2jyJzlzeNF1Ti7w4n3N8dn2NBrevOBZkbyQn0Lj4GlAd6prSihbKoIYR5kk8eljAMh9ZSm2Kp/8hL7ZCx5C6WWxSAc25DX4WpqPFB97h0ktM96lOoAu8D/hxKWm/gH8hAcO9egX/6T8/yzd/8Aj/4g5c5PAy/HVazkZmUneV4izKYe23/hZWBmpSfAM6jjFZuAu9o1tvH4hjPyGW0Q7sovcAV1PMaRZu1tfhJiHLMH13LnrJML6GWbVXUHLDt/t/JKJqa/vHgDnhlSvjPIF2YDpQdUN1pyIkz24yguYjWdwMpYr6vCSdAQ/YxcRBAVxQAgRAdhGgABo36MbXaMeZjILVDxpK7XFo6kV5LwJPAPkryK6MUr0GoRt5zfxqVm6hJ1FFyeGjxsY+1+MQnmrzrXUd8z/fc5MUX/aO0iSgO42QtvesjiuRuOOEGMQL1DM+jVK0PUNKZDYGK956vcvN14AzquU3DNA9ZW7sS2p8ciwPTlLzT3OD8/j2q3fbYsYr7OUTtYztAF4GDZGmk3NyC3ARIsaPfKkxPlJ5F9i4+I3eiuijv/1zniswk+GzElDCVfFnuUZE9BLAlu0i5ixAFwKZU6lGvHz+ybm9+yJTcrfXpIAJ19/MAlQP4Mv4EWOOA8EHSAJ5B6QaSX0q3a/DpT9f4ru96mmvXjvhLf+keH/rQA8rlYe+SpLJND9GD3ETJVjs4agce83tWNpxMzD3UAq7nlh21UOieBLCRKJm/yHAE+Pe71cr32x9G3Fi9zN3qMmcOtjh7cJ/aCMlLhlt0Dookj4E7qLkhiflkrKl7guQm6zDxD2TTg9DNwyyIPVV6SpngBQYGlWBXyAxRd7Y54FhphgxPQ1jBsgY0Gx1Kj4k63kOm5F48d+7EAWFy6Cy5n21UkIhlxlVfLbYCarVR6tuLjFNHUoz38LXXyvz4j1/iH/2jc3zrt27x7d++yfJyH6OkCCrK6xCl7NHMoJbxUSxG23OfhVnX4+V4BqW29NSvdaBPEbWs66O7Y7+ykgeweRjRNW3u1VbYLdW4U1th/XCbMwdb1I8Px5TBBlARUJCCY/f3++7vS0yrw5NSUBypf9Lcz/vbYUYgGyGQYflgI/QrKiKp22e80FHV9hKBIaJHoQyTV/Rmry5Vd1nhmGcQooEQUKt1H6lsb7rIlNzFarhltBevbBv1sjRQ5FAbU8sLt+STKFLwm/CzUbdsbdn89E+f4Wd/dp0/+2d3+OZNK9ObNsiodsPQG9ntdhsRYVKahQLqqS2jiP4L9FHTtl9YSH/kceUfbhxbRe5VC+yUG7yxdI61w22efPAO9c4RhvvOCsAWYEmlnrdQe9lvoAjem0UyM7DTYTkfFAmOL6+s5wWhCd8jtZi1gW7y2tuA/uEaMgAAIABJREFUEzDVpMqtPpU5uNs+QmCIVcCgUOjTeoSj0M1CpuReO3eeA81GllFDawf1kKpsonZ1L6Ak9dEd+vk/qH7f4N/9uxXqXOFlfhvITnoPryl6WV3JfX9/XytvW9TrKQAGBaYN5oJqV2g0Fj9Nb44QCEHPtOkZFoeFMjcbG5zbv8fTm29S7Sl1vedKZsjhorCFUnvfQRHpUkD1J+fHgcbe+Ki1vJz4PVTMmEHwUfucqdo+JfX8ASDlIO40lQgF6SBcU85jUUYIWF05wrIezzkkU7HozJmNE2913efXQq3US7zBh3iVCheYbXp3unhYND2W5jJub29POylr1GvfoRj5rKWlBUvllyM+hEAKg65V4I3WBX7pqffzuxde5E5tlYEwhtIu4oQ4q8AGitw/j/KpcBjPs64jsU+VGflx/Hi49bwHy+3XzHbAN3hMVGk9bWL37ydjfY1jST/s67iPf5J5UvfcGl1sHCTQFxYrK0dUq73HTh3vIVNyLxQKOLV4e8glBvznfIS/zYt8A/+CIvsp9y4ejgKsuueD+MvhQkHv3MHhpLNilFZmYydGRrj19ej533M8PLjVWOd3Lr7I7158iZuNDdpWEceYJpgy8Cxqmb+Dstw4QG33RLasj2jJbjIdoQ7U9qGXPSO0npEX5bTV8Hp9jceIBzDlBjlO9BOtp0S8QkgqloW0ChyJMsXqgNZSsGHw44DMNzQLS7OUaeMYfc411P5Ng/v8Ff47/g5P8Rz/EZPTzbvbRz++/CROcwFZqei13ttJN2nMKPYJTiQ0xHg/19Zyg7pHHVIY3Kut8Klz7+IzZ5/mdn2N/WKFvjDHqECg5oUVFKk+ADZRqnu/oNLxiH3aJU4AW0wbz1luP7QJWOj5lc/uX3rlZ9alQfB+7bUBOSEqT9cySfbBPfftwdSPDuVSn6Mzq7x15ir3GutsrB8+thK7h+xDCS234B0V5iTKjk4NtUL36KDKDv8Df54Dlvkn/Gte4/042grk9OBn8LYovuyzoC25h1jK+0H3+u8SPb3b2lpuUPe4YGBY3Kqvc6e6wnJ7l439LVaOdmh29jHl+L5pCWWNc4DKzi0Y+s3XiEPswb8YKAv+JcYnTOm2qbv8zMrILkr5SPV6BB/BwLYjom+9KUy2oVuHgW0PaDR2GdQtbooLmM0+lvl47rOPInNyL0aQ3GGcKPyGVI1tvo8/zTEVfoJ/z5t8Lc4cwx0easVGD0b8hUAyC5WlJb0pqJ9yutdR7EZ2XZScP3/6oSxzzBeOYbJZXWarskSzs8/6wTZrh1s0O/sUBv2x96fmfgYokvc+VYL95adl87AyahExSRex98JDCH7h1PaaCxKAA1HFVyHsZ5E4c0qbVO77FzZNaDYGVKsOQqh2B2Y+Z8AcyN2YIPeoFuZBKHLE/8gHAPi7/DZv8x6k9ho6PmTATsbDIL3roLu9E+u8sOuXwCEbGrWMYodGI04E+xyPAqQweFBusluqc6e+SrOzz8bBFquH2xT749tzJorkiygiHqBU6QYjAainOErfir3GOGUlJuAAwsxyDklU90R/g+qa1KWmpxmXExUqXU25tEej0cc0cw3fJDInd+vs2Yyz+8JH+EYA/j4f5w1ezrSt/Riq5UlEXwgkf0V0/cUH7fhGKLOuSyn7z0Sqr1YzaDR0XOdyPMqQwmCvVGe/WGW7skSzvc6Z/Xts7G9ScMa9KWyUx42nLj9CxUKs47rSnQzSaO5po8pmr8y0Dbx+fUnLZl13XNTE5DJoAmmxvZRYlkOr1XV92B/zDXYfZE7u9upKZHIPI7+g4z/EN3GfK/wsP8PrvC9iq8mxGNJ7skHutDuZvCY9YLan8jTq9cfb2jXHOKQwOCxUOLJLbFWXeGfpHGf27nFp5+ZUChQTpZYvoKRuB7VvXiY48MwsNAlKPzWjvxHqXxRin1lWQz1vYePdlTEhOyLCThGGw+rqPqUSkTJ1Pk7IXJdhr01HI8vyUazxOj/AB/mfeJE1Xku9/gNWU6ln3sOx2dR71P2d7UTtBF2XktzD1PLjOHMmvmdCjkcXUhhu5LtlPnfmOr/89J/gxtqTdM3pxEQWyviuhLKyN4GvCuUvP1XvjDYNnzKC4AlUi1CFvj/5aL2nKkCEWPxHTfcVre3hn/XaLvX64LG3iJ+F7Ml9Pb4aO669o4HDWW7wY7zID/ENnOXzsfswibB9/fTHWjo16r4EZrebycKjS4HZdsXTrS4v5/toOWZACBzD5NgqcGPtSX792vv48uoV5Ss/QkKe0tZASe5XgJIQvC4Et1HuW35+7KOoMz1CBUojNemGF8XITgqh9XJGJfVwJ7ME9c/o865UNjuZSe1SYlkGa2vdXGIPQeazZ3NtjTjKVc+1ZdbxMJgMuMSn+BG+lr/JN3GBP3SP+PlZ6n2cFG+Z3zUcaIVnjVKjQrOpaWwYwxVOpxfdGAFslpdzH/ccmhCCrlXgi+tX+f+ufA031p5ku9Lk2LR9naxaKJJvCcFdVIjbDt720Tg8l7epJlG+9jsTZeP2PwhZ+7tHV9u786FPl9OcH8fgtmWaPS6c38LMLeJDkTm5t1pLtEvT6lUdck5rXWYy4Cq/yw/zfr6XD3GJV2LXNfDNSR4fk9foZGTxX9AMCWA7Sl+S9N5Pnt/WCmAzjtzHPUdkCMFhocKX157klYsvcWP9KlvVFsfm9AsgUYZyl1D78PdQ6Yq77scrM/r/JPzK6iDQgl6nXNR6Uyw/dcZElw9EKZHUPgtCOKysbGLbWZtoPxqYy+xpLy+HF4qBqAsEgwHX+S1+kD/Bd/OnucwnT61f6dc0u2y1qveonY5frK/kOJpJ7v59X1nxk6Ny5NDDsVXkjeWLfOr8C9xYf5KbjQ0OCpUxlT0AQtBAkXwTpabfR0nknh4r6O3pu59UjdZ0ykWtN3F5iQw6Y+T1bcfQ0Om2X6+3qdfzcNS6mAu5Wyv+5J4GCcapw8DhGX6DH+AD/Lf8RTZ4VfvcXoLws0GYx86RbuKYjmmw5/6dpvS+E+m+HQD3eOmlywl7kCMHHNtF3ly+yKfPP8cXNq7z1eUn2C3VcUYlZfdvE+UXX0FJ5Eeo9LOH+JNhAbR1edr72jH2krMjdtXr0PJul6UICh2UAEJQLndoLbUxjNw6XhdzIXfZPM1kK8EkZSB5Dx/lx3g3f5n/hiXeybzNbGoIL6srua+ZFgZqD/JBxF74wTt/N1Byn2xhEzWtrlOr5ftqOdLDwDC5W1/ly2tP8rmzz/Da6hX2ijUcbwyOkEYJWEep600Uxd0Q17krxoMq2eiRe2TyjfDipU/s4+Z4+oZ2II3Kyd9x4HeabfdZah5j2zmxR8FcyH3lmafZDTg261GVQCtNTBqP+2X+FX+Ha3w738sybwaWS5I4ZhayHrK6+dydTocaKtzMEopqN1GSSxIcBgYD9dAHXkcpRpcxDFhdzQ3qcqQMIeibFjvlJq+vPMFnz72LVzeusVltjaWR9VBAhbJV70KNXxYv8XHxbu6wgkQRf9gSNJ6rm977mp4bnb99fdSFQ9rzmDAktdoxlcoAw8iJPQrmIhqtX7jAJnALWGU6RGEQKqi9rzR2WXQDzHyAn+ID/BQf42/wMb6bLS5n3qb/memWrVQ099y748spz6u/A7yFUllGC0WDm1XLzyXS6/sWityvnBxZX8+N6XJkCCHomTY7lSX2SnVuNTZodva5svUWK4fTsR5sQMget0WDTSp8xTzP0+VNLvTeonXs5zWvkGgvPmQCSS+QTbRofbNgssQgNaldUi53aTY6GEYehS4q5kLu9uoqVdQK+B7K17Q+cjxoDFuoKf80Ir99M/+Yb+Yf8zH+Br/Od7PtkryDkVl/shq6ulI7gNPzN2IrAU+gYg/cRql8quhH+zokaGvmFkoBOj4UNzZyqT3HfDAwTAaFMh27xFZ1mZWjba7ef4PW0XgSpTVX/9g3TJyWzYP1BnvOMzS3Kzy5+SYrTn8qa5wu/MsGzzSLEv1uEkKk994Wi8cst/awbSNXx8fAXMh91KBuHUXYb6MUsGFe3bqPNC3CnazHI/nf4K/zS/wwg4h6hKj9ijaE9UobxjGDwQDTDH/xnBA/dwM46/69h4rb3UQRfVBvJPBgSnJvo3b2r/ieubqaS+455gxXZX+3vs7d2hqNzj6Xt99iY+8+1qBPnSNAsrzc4cyGSjTrGDY761f5ZOs8xZ0OT+3c42L/bQw50NrzDDdU8yzVNIza4tSvGkHLaC4E+8QPPDY+A0hMc0CzeUSlki/y42I+kvvyeJpUC7iIGgjvoPZ3LWYPxDTIO0kdH+CneD8/yyf5Do5QWwanH0c+DA6wRbt9D9O8qnWGHPQDj03evwbDxdkN4BzKb3hy+aOWC54yX6Ks4fvAk4Ft5fvtOU4VQrBXbvCZc8+x1Nrl0vY7GEddVpoesY/DsksM1kt8tlXltZ0znNv9HJf6XYqDHtNhdBT05g/XqC3i5BVdWtdowC8a0AgOAScw1l8UscWiUlHZ3mZHtcwxC/Mh95VlhBDIiaQDBnABJcN1UIQ5OQSCqWYaWUnvHmyOeQ//AhP4LPAMejcwGzV+2MvSQxmoXSeK3WSYn3vQtTzt/n+IUtufQ72WBp5RZAMV5+vzwIuE9T8PYJNjISAEDypL7Jab1I/2OVOdJvZR2LZNf93mzZWv487uXS7sbbLWOaDWP6IQU0F+cpbmRBJfDT+jAb+fJ36bHVomZGUwgmLRZm2tj2HkxJ4Ec5tB7bXghCtepqY3GAaN8JD26iONnZsi8ALq5n2FsEGdXrt6cFBy9ABF7PrGdADOcbIgNlVUMBAb9Tzvg+s3X0bpacKJHfLQszkWC1II9qr6oaGFaXHcOseXLrzEJzee40vNM9wu1jgQFQ1/9xluaCGvTvL9dZ8GNCvdI0r42aF1vhi5XsPosLb2Ve24HDmCMbdbaK+u0bt3f+Y4eRL1iO/ByQ7t6FDTWbhmLb2PwgSuueW+DDyVQrvJsI3SdTw98pv+smJwNFsqGa1R5x57SvebrMLJRw+6+edz5FhUCCEUSbWWeL1e4XZnn8bhMSsHu6y3d6mfhIsCvzcq8B0LeAHTM5wbaSBCpZ0YfRhrVQharSPK5TwKXRqY2wxauHBeu+wayjhjE/9EDkmRhRT9FEpW/krCevYCrcpH4XcFf4gybZt2OatW9a54cJRV/vSoGbQFrVZuHZvj0YFlFejXVthcW+e1s1f5zJkn+WztSXYML0ROREy8HulbxEd//3aFF/JHH8NW+jQaBywtydwyPiXMT3KfoZafhEC5ypWAL9OiQYdKrNxyyeC3QPazBvXKmcBVVEzqe4zLz0H1JYOnM7gIvJugF1L3XelubWq37FWpcz1HY+Su15m1tVwtn+PRg2FYyArsllbYr7XY61RoPHjA+aMHLDv7J+X0wtSqgtm5xQkQ+g10RClW6FyAQqFLs5n7s6eJOe65rwHhj230uA1UafIj/CT/L/+Z1vm6ZeJC54a1UOr6XZgR6y4uvKvzdrOvo/az/a5a/Vap6N2R3oOgOILJcBwjqt/SUv6C53h0YRgmlCz2mme4df4ar5z/Y/x+4wqbhqVlw+MhyzC1CkJ7Qo0bVd606iwvmxSLudSeJuYnubdasc6rcEibKv8P38Hv8X6+k/+Ly3w1cX90pei45UyUkrzGMP7aRoT6gnGM0gusgSZp2rbeGm5wqLfnPgqd6+lQjVRjtSoolfI99xyPOoTyIrJtnEaBrfo1NnvnKW4fc337Dufl2zPPjmJFn2zO0ZPgmywRRV70vOuXlu5Qq2WTjfJxxtxmUGuE3KNI79WRqOZ3uMDf53/mn/A9HITs4y7K+s8EVlCmZHvA3US1vY4yW7lIOLEP70BRMwvj4PAgVq/C7vXBiTe83lPJA9jkeLwglDbbMBDFKt2zy3zqqSf5tdbXccO4QF8YJ9uBUxHgw03vY8Wfn/xoSfBCoPuOC7e1em2feu0wz/aWAeYmuVurK+GFfFDhCJM+A7erEoNP8TKv8jzfxK/w5/n52H3KWnofhZdKsoYi+Q5+pm9B8GT/S8QJ6mCaei9Nd2srct062I8Yjf7cuXy/PcfjjUKhRP98kdfP1rm10+Dyg1usddsUBz0snIz93YOOCYQItqLfkVE0fxK70KfRkBQKud9bFpibiGTW9X1EYXz9V/fJKXdEjf/AX+Bv87/ymuvPPasOnXZ0YKNSocaFgVLXr6EM7+4z66U6RgV4raCU+rqkN35VpZLeVfZ34++5z2phh7VItWxs5JJ7jhwgEIZFd+UiN554iVdWn+Xtyhke2CW6rnd4ELKKJ+95pfu98Afoq9YNAxr1NtVqFv5QOWCee+4j8eUh2t5znT0e4C/53+EC/xs/zvv5db6FX6DFTrKOBiBtKd9AGd6Bom8DRd9DbLq/ei6E8VVWhYLeuU67ncgmIOjcQxpE6X+eNCZHjnEIu8TxWokvLDUoH+1yZv8ezaMereNDKoxLzNknivEIXiJGTu5pCh8CqFb7NJsdhMil9qwwtztrFAoY1SrOoX5mcI8sltjh7ZF0oH74BP8Jf8DLfJif55v4FUx3lyrtwDcGRFif6rXr0fcWcI89VCS3s8SLqzxNoratd2Z3azrVZZzWJ+/ljlbwmmG/c7V8jhz+sO0S/WaJN2srmEcDVva3aB5ts9a+SZN5EPsoBNI1tBPArtCxl5cUCge0WgOsPAxdppir/rN06Ymx77qyXAU9Q68OFX6e7+Tv8nf4Ms9E7F04BIpuZ+dNiyZjj5ZdAbpsoyLumwGlosO29SL09/f2UmhtGgdE85RoNHK1fI4cs2CaFtSL3NtY5yvnnuKLZ57mS7UVDiKkXE0n5oYytJPAMeFShBCSlZUOxWIUh78ccTDXpZO1vDz1m47UvBRJ1S54h8v87/xt3s+v8WH+LU0epCq9P2zDslDQe+Flb7gISEs9P8CkHTFCnW5EvRw5HneYpgUVi93SRQ7rK9w7PKa1d4dzh3doBKSdzSSJlZA4Rnh0zdWVfarVPD/7PDBXcrfX9e3DPQjG3eGi4BN8kFd4H3+Zn+Ilfv9EVZ8EnvSuU073JZpdNq4eYIhaTa8nTrc7VVtSgj/SIvbxfi/Vkz+nHDkeJwjDZFCqc1Co0643uNc7R2v7HdZ3JWflnZNy6RP7SQ9AzHbPrVb3WVrqYxg5sc8DcyX30hMXfX8PI5HaWIKFWZgeNMeU+Wm+jzO8w3/P32eV+zPPTnPwx6lPznenZLztQbo6CQF0KEc+r7msaSSQI0eOMRgGyEKBrt3iXrnJnbUOX7p3gUu7b3MpYZSNMIgZ77ppmKyvHWMY+ZbbvDDXO22t6seXH0VZK6787NXgHS7wo/wk/4bvpJ9wTZPFutOr82AscUxyqR3097DlhOQetQd+OCLMBXK6hXzPPUeOZBBCgGFilKp0n1jhxrvexcdWnuC2XaYnTJwQV7o4sIw6fiFwBA3OntvTjpSZIx3Ml9wb0XzdPZRSTBrzcf4038s/40blZd/jaRN3OvQ8H0yq5T0k6VcnYsTpVsvAtk/7TuTI8WjBsIoMzr2Lz175Gn5n9TluFVY5NszU7IccQEq/5YJkqfUapeJR3JwyOWJiruRuziD3Wc+9zv6Mo9ExwOI3rv8Q7/7l/5BqvYsKbck9ZbU8hKnlp5/62bP56j5HjqxgFCt0z5zljy49xStrV3mrusyO1eCYZDnUD4DBlE2TpFQ8ol4zcnX8KWDO5F6Pdd5syV0/nvEoDg8l9vIyX/O7n+CJv/n9arNqpMYwZL8Inb/MLwfBLnNxW9gNCD4UhPPncx/3HDmyRqlUp7N+hS9dejd/cObdvNa4wt3iKgfEsztSsT9Gz3QoFI5ZXu5TKuXW8aeBuZK77eMKN4qgx19LWXIHODhwg9xYFht/8Tt49y/9e1b+3LdEqkN3uGY7rMNrr9c1I9Qd+6vl9VuaRjtSRji4fDkPbJEjx7xgmja0ytw8f4Evnn2WL61e4p1ykyNhRiL5LjAYmSFMY0CzcUS12s/V8aeEuZK7UalgFKKrf4Il9/ijZlIDbbdaPPljP8qz/+r/prCxkTpxR+tpum9Dsaiplu+lH+d53EBwFP7X2Grl6rscOeYNw7Lo18tsbTzFV849w2c3nudGaZVD9Ej+AHBcOhECqlVJvU6ujj9FzPXOC8PA3tiYXcbnNwNJk8nQqMkI0Alwpa4+fZ0XPvoLPPED34+hmyv11KB3D8plvXI6e+5R73rUjHBnzuRq+Rw5TgvCMOlXlniwfIab56/zmXNPc6O+xmbI9tohroW+lNh2n1arQx5d9nQx92VV8cKFWOdFi1IXBsFgELweNQoFNv7L7+DFj/4CK3/2z0wdn6TAxVDPB8OyNMm9rxemNsp1+JN7cA21Wq7Dy5HjtGGaICt19lvnuHn+WT57+Sn+oP4cW8Kf5A9FHTAwTIfl1jbF4iDfZz9lzJ3c7XXd9J/jaIylfU0+aIIk91EU1te5+uM/xvWf/AnKV6+e/L4YsqX+PahUwsse3wsO7pMEB6F+7uNoNPIJIUeORYFhmEi7RL/WYPviWV658iy/vfwC90x7wnzOBAS1aptGw8r32RcAc1ecFJ+4GBq5ze948ySLetJRo86P4vW19A0v0/ia93L33/wcN//JP4X2tA1A2ilh00OPUil8OdLfjZal3nsKYddyRDQPiWo136PLkWPRIIQA08SsVuhUK/zRapPy5i7X926xPNihgsC2DtnY6CIiJK/JkR3mPpMWzp2LdV6LrRRaHy4MHCcaxRq2zdn/+r/ixY/+Aq2Xvz6lXmRbQ7N5yN/7ewbXrj0RWnZwFC9Q0KyeOBgcTKnlZ/ddR8uQI0eO04VRrHJ8/hyfvPS1/P7yNY5KTc6dO8QwcmJfFMyd3L0odWFT+OTxKgcaZ+lDRy3vh8LqKh/4h/+A4g98P7ul8UQJi0RL733vPv/yX67yoQ9d0irf3dxMvQ+HEaX2/7+98wyI4uoa8AMsZSnSxd5QQYrEFrsSYsSu0WCPLVE/e8HeNRqV2Es0EhUrBgtGDShKogIqKhaEiBqxYkWpAoKw3w/eHVnZhV1AMWaeXzJz586dueOee849BcQ9dxGRfxOGhjLSKlQnq6YdBgYFF44R+bB8cOGubaxZ3LOc4se6KwqNghzqCkMikeDSuxdf/HWC7NatyMyzwVRc57r0QtO1FnwHXd3XfP99POvX16J8efUTyLxJLLrDoqoR5U89W/DYy5XTRkdHFO4iIiIixeWD77nrmLzV5jTZezcgo0THUVTNPS8SXV2aLv+Ju9eucW/eAgzu3S+29v6mGGkgbWwSWb26LDVr2hbe+N37JqeWWA13OZpmp6tUSYyd+RAcOuRd2kMQERFRgYWFZuHDqvjwwt1IUXNXV6AYFrGm+9u7KFKSadSrOTtTbf9eLvruIW3DRgzS0t+Tc52qpcMbWrR4xrJl9ZEUMbj0zavUIo7pLe9eq2iWL3zZU6mSuF/3IahQoeBcEyIiIv9+SkG4G2vUXi4wiq65qxYqycnZlClTcgLF6etu+CQlUe7CRWyiotFWMylM0TcIZOjpZbFmTTYNG35e5F4Asl6+TRJUUh79hW8xKGJrK2ruIiIiIiXBh99zN9BHYqmZuRZA73+lCUqS1NSSC0o7c+YsPXr05Ndft3DTzg4b719IsbRUW4PXvJWMMmV24eOTTcOGtTQe77tkxb+bAbBo5B1lfk/5gq8UNXcRERGRkqFUgor1K1VU+Fsdz/kyaBaHrU7Pz56pl5GtIOLjXzBjxizGjh3P8+fP6dWrJyNHjqBGXWfaHAtAf+7sYm0oKCeL7t3DSE72p3//ASxc+CMvXxZPOGfGKyaxKY7vgPzat9np1OvNzEyMcRcREREpCUrl11TvHeGuDgbvQXN/8qTowj0nJwc/v718801PgoKOY29vz/btW5k82RPjPBEB9Tp3omXoKZ40b1ZgfwWLv7dnjYxecPSoFePGdWbAgP5IJBIOHvydr7/uwbZtO8jMLLiymyYU1zlQ04pw1taicBcREREpCUpJc6+c75g62rsxyRrcpXDR9OpV0czyMTExDBgwGC+vZQBMmTKJ7du3Ym9vr7S9roEBnVcup8qObTw3K7onZLt2zzl61B4rKxOMjIwYO3YMfn57aNfOnbS0dNauXYeHR2/+/PMvjfuuNX8uekVMDawMLdTfc5dKtQgKshSLxoiIiIiUEKUk3ItWPMaSZ2q2VE/nfPNGM+GemvoKL69lDBgwmJiYGNzd27Jvnx89e3oUWtpQW1ub8nXsaRd4BNP5c5QuU5SPWguJJJU1a96wYIELUqlipbpKlSqycOECtm79FScnR+Li4pgyZRrDh4/g5s1baj+bUa1a1D90EEfvX9CzKVvImNQjBfNCe7C01CYw0AoLC1Gwi4iIiJQUpSLcDWordwArTJBYlEgK2twsaBs22NCrl/pFTY4dC6JHDw/8/PZibW3Nhg3rWbToB6ysNHMOlOjqYt+xI43+OESSe9tC27u4PMHfvwLNmlUrcAHh5OTE1q2bWbBgHjY2ZYmIuKTxfry2RIJpvc+of/AAdl5L0JZKgaILeNW13HNp2lSPQ4esMDYWzfEiIiIiJYmWTCYT1Ndnz57y4MG9D3LjjHv3uPXdMLITFR3lCtKldzGYk7gX0rNqUaStDQMHmjJgQBlMTNTTFB8+fMiiRYu5cOEiOjo69O/fj6FDvyuRVIsymYynUdFcnDIN6+e5Dm2rcOUWo4E0RozIon9/O/T1dTXqNyMjg23btrNjxy4yMjIwMjJkyJAh9OnTCz099ZPkvElJJT4oiHur15KdlqZxeNwMdvBKhYDv1MmAefMKFv4lQeXK1ShbtmzhDUVEREQ+IUpNuAPkZGRw/4dFJB4LUjiuSogE0BV/+hTQo2rB7uysz9SpFtjb66tsk5fMzEx8fLbj47ONzMxMXFzK7zGBAAAgAElEQVTqMnPmDGrUqK7W9ZqQlZXFLf+DxK9ey4bXTUm09mDp0krUrVuuWP0+ffqMTZu8OXz4CDk5OVSsWJFx48bg5vaFZuNLSuKx7x4e/LpFo+vGcUjp8b59pUycqFkp2KIiCncREZH/IqUq3OU83/Mbj1atQfYm13tdlXAPoxU+jCygp/zCvUwZbTw9LXB3N0IiUc/AfOHCRRYtWszDhw8xNTVl3LgxdO7cKbfs4Xvk+cOH/HXiMu17fImJiWYJYAri5s1bLF++goiISwA0aFAfT8+J1FaxPaKK10+fErdzF499fyu0bQKWzGOrwjEdHRg71ph+/YpWX6AoiMJdRETkv8hHIdwBXl27xt3ps8h68gRQLuAjqcdapqroIb/g7dTJmNGjzbGyUs8EHx//ghUrVhIUdBwtLS26dOnMmDGjMTN7/+bjD0Fw8J+sWbOOuLg4tLW16dKlM7NmzdC4n9fPn3N70WISQsNUtnlEFZayTvhbRwemTTPh669LbtGiDqJwFxER+S+iM2/evHnyP169ekVyclKpDETPxgbLLp3JuB3L6/v3lbZJwJKztFZyRlGw29rqsmiRBd2762NqWvgec05ODnv37mPy5Klcvx5DpUqVWLlyOT17enxSZQxr1KhOnz690Nc3ICrqGteuRfHHH4FYW1tRvXp1pZYJT8/JXL8eQ8OGDQSHPomREdbt3DFv1ozXz56R8TAu33WPqMoF3IBcB8Y5c8rQqdOHFewApqZmGBl9OEuBiIiIyMfAR+WmrGNsTI2Vyyk/aiRaOvm1banSXG9vBZK+vhZDh5qyZEk2K1YMZ82adUraKxIbe4ehQ4fj5bWMzMxMhg0bip+fLy4udYvzKB81Awd+i7//fjp27EBcXBzTps1g8ODviIqKUmh3+PARTp06ze3bt5UWpDFxcsRxzSoc1qzEqHZthXNJWABgZqbF2rVmuLtL398DiSgwc+ZMJBLJJ7UwLSlevXqFRCJBIpEQFBRU+AWlSFhYmDDWp0+flvZwio27uzsSiYRx48YpPT5q1KhSGtmnyUcl3OXYDB5IzQ3rkZibKxzXz5el7q1gb9pUysGDFRk+3BwbGyuSk5PYu3cfly5dVnqPjIwM1qxZR58+/bh6NZJGjRri5+fLsGHfa+RR/m/FwsKC+fPncvDgAdzcviAqKprBg79nzpx5vHz5klevXrF69Vr09PSYMGF8gX2ZN23KZ7t3UHvRD0ir5zocpmOMpaU2v/xijrPzp/8+Pyays7PJzs7mzZvip1f+1JDJZML7ySmJus/vkbxjzbN7+q9F/izZ7xTUUnVcpHh8tGW4jOvXw+Hgfv4ZMZq0v/8GlBePKVtWh7lzrWjc+K1maGhoyPTp05gwwZOFCxfx22++6Oq+DScLCQllyRIvnj59iqWlJRMnjsddjZjzT5FKlSri5bWEiIhLLF68lICAQE6dOk2tWjVJTExk4MABakcIWLu3xdq9LXE7dhJzIge/NZaYmn6U60cRkY8eCwsLOnbsCPBJW2GaNGmCgYEBdet+utbS0uCjFe6QW/vdbvtWHixbQbzfXqQ56cI5iUSLbt1MmDZNeRKZli1b0KlTR44c+YONGzcxZswonjx5ytKlXoSEhKKtrU3Pnh6MHDlCIRf8f5UGDeqzZ88u9u/3Z9OmTVy5chU9PT0cHR3Uuv7kyVN89pkLZmZmVPy2P999+54HLCLyiePg4MCRI0dKexjvnYULF5b2ED5J/hVqVeVJE6mx/CcMDHKHW6WKLn/+WUWlYJczfvw4LCws2LlzF+vXb8DDoxchIaFCkZcpUyaJgj0PEomEXr08OHBgH7179yI7O5spU6Yxdux47t69q/K6tLQ0Fi5cxJgx43j9uuQL/Ii8f9LT0wtvpCHZ2dlF7jc9PV1jU3RWVhYZGRlFup8yZDLZe3kvkPtusrKySrTPzMzMIpnvs7Oz38v/2/fRZ1HnOCcnp8jvW53rcnJySEtLK1L/QKHPlJGRofHc/iuEO4BpyxbU/cOfxfNNOHCgEoaGhQ/dzMyU3r17YW1txdatPujo6DB5csFFXj51ZDJZoR+JqakpkyZN5LffdtOgQX3OnDlLr159Wb58BUlJ+aMpvL1/JTExievXY5g7d/4nsT/4qeLq6oqrqysvX74kIiKCrl27YmxsjKGhISYmJnTv3p3Ll5X7qahDamoqCxcuxMnJCT09PQwNDTE0NKR169Zs3ry5wH3VI0eO0LFjRywsLDA0NERfX5+mTZuyc+dOpe2zs7PZtWsX7du3x9zcHD09PaRSKcbGxri5ubF7926Nx//mzRs2btxIkyZN0NfXx9DQEGNjYzp27Miff/6pcX/w9p0/efKEI0eO0LhxY/T19ZFKpdSsWZMFCxaQnJy/2sS1a9cU5kvOlStXcHV1pXfv3uTk5LB8+XJsbW0xMDDA0NCQhg0b4uPjU6BPQUJCAjNmzKB27dro6elhYGBAuXLlGDJkCP/880+RnhPg0qVLeHh4YGlpiYGBAZaWlowcObLAFNienp64urqyYsWKfOeKM8fp6emsXLkSR0dHpFIp+vr6ODo6sn79enJycujatSuurq78/b9tX4Dz58/j6urK999/T1paGh4euRFTZcqUYeDAgaSmpgptQ0ND6du3L5UqVUJXVxcjIyN0dXWpV68eixcvVirsx48fj6urK6dOneLhw4cMGTIEc3NzpFIppqamDBgwgMePHwO5zp+TJ0+mfPnySKVSpFIp7dq149q1a2rNxUcT517SJCYmsWbNWg4fPoJMJqNt26+YOHGCxrngPxWys7M5evQYW7b4sHTpYmrWtFX72pMnT7Fy5Wri4uIwNS3D8OHD+OabHmhra3Pv3n169eqj4Lw1ZMggRo4c8T4eQ2P+i3Hu06ZNY+nSpejo6ORzqpOHO27YsIGxY8eSlZWFlpYWWlpagjDQ19fn+PHjtGzZUqP7pqWl0bJlSy5dyk2WZGxsjJmZGU+fPhW0ny5dunDw4EGFsMusrCxGjBjB5s2bgVwLUrly5RSu+/bbb9m+fbvCvbp27cqJEycA0NHRwcrKisTERAWN0dPTk2XLlgl/p6amYmJiAkBgYCDt2rUTziUkJNClSxdCQ0MBkEqlWFlZ8eTJE2Ec06dP58cff9TovcifdcqUKXh5eaGtrY2TkxPp6encupVb3MnJyYmgoCDKly8vXBcaGirMwePHjylXLjdj5cmTJ/niiy+oUqUKzZs3x9fXF0NDQ+rUqUNcXBxP/pcrpHfv3mzfvl3B3wjg6tWrdOjQgUePHgFgZmaGoaEhjx8/RiaTIZVK2b17N926ddPoOXfv3s2gQYOEb6ps2bLCfNSoUQNjY2MiIyMZNWoU69a9jWRq06YNwcHBDB8+nI0bNwrHizrHAImJiXTq1ImwsNxcHPLFqzzqoGfPnhw/fpyEhATOnj1LkyZNADh69Cjt27fHxcUFBwcHfH19hT6rVKnC3bt30dLSYubMmQrfgaWlJVlZWQqLtCZNmhASEqIQaSQX7PPnz2fNmjW8ePECbW1tBaXL1taW06dP4+7uLkQw6ejoCAtjU1NTrly5QrVq1Qqcj3+N5q4uMpmMQ4cO06OHB4cOHaZixYps2LCeH39cqFSwf+wesyVBamoqv/22l61bt3HvnuaLN1fX1uzdu4exY8fw5k02Xl7L6N9/ABERl/Dy+imfANmyxYejR4+V1PBF3gNjxoyhVq1aBAYGkpKSQlpaGtu2bcPIyIjXr18zefJkjftcsWIFly5dwsbGhlOnTpGSksKDBw9ISkpi1qxZABw6dIj9+/crXLd06VJBsM+YMYMXL14I102ZMgWAHTt2sGXL2/THCxcu5MSJE0gkEjZt2kRaWhpPnjwhPT2d8+fP06BBA2FMDx8+LHTsMpmMPn36EBoairGxMT4+PiQlJXH//n1evHjBnDlz0NLSYvHixXh7e2v8bgC8vLxwdnbm77//5urVq9y8eZO//voLS0tLoqKiGDRokEb93b9/H19fXzw8PIiLi+PixYvExcWxdu1atLW12bNnTz6hFx8fT8eOHXn06BG1a9fm9OnTJCQkEBcXx927d+nWrRvp6en06dNHbQ0R4MaNG4Jgb9OmDbGxsTx58oTExESWL1/OvXv3iIyM1Oj5ijPHo0aNIiwsDKlUyubNm0lMTOTJkyfcvHmTL774Aj8/PxISEgp8Hl9fX9q2bYu3tzdz585l4sSJaGlpERQUJAj2UaNGER8fT3x8vPC99O3bF4Bz587h5+entP8FCxagpaWFn58faWlpJCcnC74Ht2/fxsXFhXv37vHLL7/w8uVLMjIy8PHxQSKRkJSUxKpVqwp9f5+UcI+NvcP33w9jwYKFpKenCzHrjRo1zNc2NTWVzZu34OHRqxRG+mExNjamb9/eeHj0KHIfenp6DBjQH3//fXTr1pWbN28xfPgIwsPP52urpaXFvHkLiIxU/8fhfaGjJF+CCFhZWREaGkq7du0wMjJCX1+fAQMGMG3aNADCw8NJfKeoU2EEBwcDMHToUFq1aiUcl0ql/PDDDzRv3hypVCpo9pCrLct/1KZMmcKiRYsoU6aMcN3SpUsFDXL16tVArhVKLmA9PT0ZOnSoEL6qpaVFo0aN2Lo1N/WxTCbj4sWLhY79jz/+4Nix3AXp5s2bGThwoKDxmpiYMH/+fCZNmgTk5hEoyr6vmZkZx44dw87OTjjm6urKnj17AAgKCuLkyZMa9dmsWTN8fX0xMzMDcktLjx49munTpwPw448/kpKSIrRfsmQJcXFxGBsbExgYqGCdqVKlCvv376dJkyZkZGQwc+ZMtccxZ84csrKysLe358iRI4JWaWBgwMSJE1m8eLFGz1WcOb5y5Ypgrt+6dStDhgwR5lK+oHV2di7w/hkZGbi5uREYGMj333/PvHnzhPj8DRs2ALma+bp167C0fKs0Vq5cGR8fH8HKcv58/t9H+fP5+/vj4eGBvr4+xsbGzJw5E0dHRyB3EbZ9+3aGDRuGubk5EomEgQMH8s033wBw5syZQt+hgnB/37nTNSU7O5upU6fz6pWy5DVv0TRm/e7de/z2mx/bt+8gMbF0MvKVBgYGxU8kY2FhwaxZM9i+3UdlPgCZTMabN28YN24C91VkG/xQiMJdOb1798b8nTwSkCts5Dz/X6VCdZGHawUGBirdYw0KCuLVq1cK5syAgABev36NRCIRtPR3mT59OlOnTmXChAnIZDJycnLYs2cPv/zyC6NHj1Z6jYODgzD3efdJVSE3+derV4+ePXsqbSO3Zjx//pzjx48X2ue7DB8+XMHsLqdNmzZ89tlnAPmsGoUxe/Zspd/4hAkTkEgkpKamKiTr2bFjB5C7AKtRo0a+67S1tfH09ARyFzzKfGzeJTMzk4CAAADGjRuHvn7+4lxjx44VFiDqUJw53rdvH5AryHv1yq+86evrq7VwGTZsmNIy2zNnzmT79u1KfQQAdHV1hQWcqm/PwcGBFi1a5Dsu/w6srKzo2rVrvvNOTk4AvHhRePnzjzoUbu3a9QQH/4mNTVkmTpygtM2FCxeZN2+BRjHr1apV5bvvhnDjxk2hmMp/AW3tklu8RUREkJmZWWCblJQURo0ay65d2wVtTOTjQJXmklfgy/eZZTJZgQtsY2NjIHcf8+jRo0RERFC1alXatWuHu7s77u7uVK5cGUPD/OmHw8PDgdwfu7waUF4+//xzPv/8c+FvXV1dvvzyS7788kuFdm/evCE2NparV68SFhYm7GGqkxzl3LlzAFSrVq1ATb9s2bI8e/aMCxcu0Llz50L7zUubNm1UnmvevDlXrlzh7Nmzaveno6ND69bK0nHn7gHb2dkRHR3N2bNn6dGjB7GxsTx79kw4r+o55XvEOTk5RERE4ObmVuA4oqKiBCHWvHlzpW3kzpGBgYFqPVtx5liu1RbkM1LYMwHUr19f6fGGDRvSsKGiNVgmkxEXF0dUVBTnzp0jJiYm37jyour/n3wBVLNmTaXKtjyVtjrfdJGE+6lTpzh6NIhnz54jkejw5ZdudOnSuUQTLZw4EczOnbsA8PX9jU6dOilUMctb5KWoMeufcmKI90lCQgLe3pvR0tIq1DP+8ePHjB8/kU2bNipNYStSOsidyt4lrxYo90e5ceMGderUUdmX/BsYPHgwkZGRrF69mtTUVPbt2ydoUc7Oznh4eDBs2DBsbGyEa+UOThUqVND4GVJSUtiyZQvHjh0jJiaG+/fvK/3RUyd6Q+6E5u/vj7+/f6Hti5IOtmrVqirPyc24mvRrY2ODVKraGleuXDmio6OFPuVe2ACzZs0S/CAKQp3xyN8dFDyPBT2/Kooyx/LnlL9TZVhbW6Orq1tgmJuVlZXKczk5ORw4cAA/Pz+io6OJjY1VulWj6tszNS24GJky64emFOnXtnXr1ty9e4/jx08webInPXt6FHsgebl9O5a5c+cLf8tkMhYtWsy2bVvIyclh3779/PzzRlJTU7G3t2fWrOlFCm1TZnIRKZx1637WKKYzMvIaCxf+yLx5czS6T3Z2Nnv2+BESEkJW1htMTU1p1aoF3brlN1eJaMb72oJbuXIlQ4YMYefOnRw+fJjr168DuWFd165d46effuLAgQOCFiuPI9d0++TYsWP07t1bwS/A1NQUJycnGjdujLu7O126dFEr1jpvzLmjoyOVKlUq9JqaNWtqNF4gn9d6XoryW1RQf8r6zPsuWrZsqdSS8i4WFhaFtskrIAuaR00FVlHnWD6ewrTbwhZ9qt7vnTt36Nixo/BtQ66i6OLiQsOGDXFzc2Pjxo2EhIRo3HdJUmRVKjb2Djo6OnTo0L4kx0NqaioTJ07KN2HR0dFs2LCRsLCzxMTEYGxszOTJk/Dw6CEK6Q/I9evX+f33Qxpfd+TIH1SpUoUhQwapfY2Ojg79+vUhKiqK48dPsHmz9ydd0OdjpXLlyhw+fFjt9s7OzixdupSlS5fy6NEjjh8/jr+/P4cPHyYlJYVBgwZx584ddHV1hW2AguKg3+Xp06f07NmT5ORkbG1tmTdvHq1bt6Zy5cpCm+zs7EK3jeTo6OhQpkwZkpOT6devn+CMVtK8fPlSZfiSXEMuSNtU1l9BvNtn3i2XpUuX0rRpU7XvVRB5LTHPnz9XubeuiYNmcea4XLly3L59Wwj1U8azZ8+KXHuhd+/eXL9+HWNjY2bPnk3nzp2pXbu2wsImb0hfaVEk4S6TyQgPP89nn7moNO8Vtd8pU6YTF5e/hCjA5s253pFt236Fp+cElXt0Iu8PPT19Ro0awT//3Ob27Vju3LmjdsGHn3/eQNWqVfjyy8L3u/Jy8+YtqlWrJgr2UsLIyIhOnToV2CYrK4tLly4RExND+/bthdwCFSpUYODAgQwcOJD169czevRo4uLiuHHjBk5OTsLeY1RUFFlZWUo1msjISJo2bUr16tU5dOgQAQEBQjxxQEAAtd+pSAi5YWJyzUwds3zdunUJDQ0lJCSkQOG+e/duypcvj5OTE9bW1oX2m5dLly6p3MeV+x68u5dbECkpKfzzzz9KrQjJycnCvq+8T3t7e/T09MjMzCQkJESlcH/+/DknTpz43/85l0I1/Dp16ggm7vDwcGrVqqW0nSbJkfbu3VvkOW7atClhYWGEhIQgk8mUWqlOnz6t9ljyEhUVJXjAr1ixgqFDhyptJ3ckLs2EXkVSeW/cuEF8fDzNmjUr0cF4e29WGTogp2nTpvz440JRsJcStrY1GDx4EIsW/cCePbsICzvN7t07WbToB4YMGUyrVi2VegTLmT17LtHRf6s8/y5xcY+4d+8erVrl9ywV+XjIyMigRYsWDBo0SGVsr4uLi/BveaRFhw4dgFxBpcpTfP/+/UKMc5UqVYQ9VV1dXWxtlSdjyhsTr0760C5dugC5pmBV8diHDx+mX79+uLm5ceHChUL7fJdff/1V6Y/9xYsXBeHevXt3jfrctGmTyuOZmZkYGBgI71gqlQrbIT///LNKJ8klS5bQt29f3Nzc1Eq/a2pqqtCvsmcMDw/XKM69OHM8YMAAAO7evStEB+QlKytL49C8d8cFqNwKDg4OFvKJlHSKYU0oknAPC8v1RmzevOSEe3j4eby9fy203dmzZ7l6VbNkCCLvD4lEQu3atXB3b8vIkf/HihXLOHz4IKGhp9i6dTOzZs2gb98+NGrUEDMzMzIzMxk/fqKCE05BhIbmZpgqyW9NpOQxMTERQndmz56dT/jJ09JCboiSXNt0cHAQ4tjHjBkjeK3LCQoKYsmSJcL53O8tV4vLyspS+uPt7e0tXCO/d2EMGzaM8uXLk5OTQ7du3fIJooiICIYMGQLkaqrt22u+HRkeHs748eMVzME3b94UQu9at27NV199pVGfK1euzJeC9dChQ8yePRuAqVOnKlhX5aFz9+7do3v37sTHxytc6+PjIyRIGThwoNpK1Pz589HW1ubs2bOMHj1awVx+69YtIbGLuhRnjp2dnQUBP2zYMNavXy/4CMXExNChQweFXAuakNcqsWXLlnwLmTNnztC/f3+l4/rQFMksf+bMWWxsbDRKYVoQDx8+ZMqUaWqbMObP/4G9e/eIMcwakpmZu4rMylJvL7I4GBgY4OzshLOzk8LxpKQkbt68RWzsHbX2F8PCwjAyMlLQ+kQ+Tn766SdOnTpFfHw8jRs3pkmTJtSoUYOkpCTOnDnDy5cv0dPTY+PGjQp+Mps2beLGjRtcv36d5s2b07x5c6pWrcqtW7cEjbZ169ZCgh0PDw8WLFhAbGwsgwcPxtfXFycnJ1JSUjh58iS3bt2ifv36vHnzhsjISGJjYwsdu6mpKfv27aNDhw7cuXOH+vXrC+O4e/cuoaGhyGQyypYty++//14kh8SyZcuyZs0afv/9d1q0aMHLly8JDg4mMzOTatWqKWii6mJhYUG/fv1YsWIFDg4O3Lp1S1ggffXVV/m2GJo0acKqVasYO3YsQUFBVK9eHVdXV0xMTIiMjCQ6OhrIDWlTFcetjEaNGuHl5cWkSZP4+eefOXz4MC1btiQxMZHg4GCys7Np0KABERERavVX3Dlev349t2/fJiwsjNGjRzNu3DikUqkgbLt3786BAwcANIriqVatGr1792bPnj34+Phw+fJlIeTu8uXLhIWFYW1tTYcOHQgICFDr23tfaKy5JyUlERUVTfPmJeOMkZGRgafn5EIT1eTl/v377NnzW4nc/7+APCWvv/9BALy9twjWlw+NqakpjRo1pFmzwr+fjIwMIiIu0bjx52IY3b+A6tWrExYWRvv27dHS0uLs2bPs2rWLI0eOkJCQQKtWrQgJCckXY2xtbU1YWBgjRoxAX1+fkJAQdu7cSXh4OIaGhkyePJmjR48K3taGhoYEBwcL/QQFBbFixQq8vb1JSUlhyZIlnDlzRjBxHzp0SC3nqWbNmnH+/Hm+/vprtLS0OH36NDt27CAkJAQtLS06depEaGioyj3lwli+fDnDhw8nLi6OXbt2ERgYiEwm49tvv+XcuXNKk8oURmBgIG5ubkRERLBjxw7OnTuHubk5c+bMISAgQKmH+ujRozl27BiNGjUiNTWVI0eO4OvrS3R0NEZGRowePZqAgAC1vOnz4unpyb59+7Czs+PBgwfs3r2bgIAArKysOHjwoJC/XR2KO8fGxsb89ddfrFq1igYNGiCVSpHJZDRv3px9+/bxww8/CG01DYnesmULw4YNQ1dXl6tXr7Ju3TrWrVvH5cuXGT58OJGRkUJCpujoaG7cuKFR/yWFQuGY58+fcf/+3QIvOHYsiJkzZ7N8uZfKBAqaMGPGLIKCCs/29G5MtYGBAf7++zR2ann33qGhYZw+/VeR+xB5f4SGhjF+/ETmzJlFly6aJQyRY2tbW6PMWCIlQ0JCAtHR0SQlJVGmTBns7OzUKuCTnp7O1atXefHiBebm5tSrV6/AWO4HDx4QExNDdnY2lSpVwtHRsUTC/JKTk7l27RqJiYmYmJjg7OysNKOfOsjHs3fvXr755hueP39OZGQk+vr6ODg4qBVulhd54RjIdX6zsrLi9u3b/PPPP1hbW+Pg4KC2wIqLi+PmzZukpaVhbW1N3bp1i53/Iycnhxs3bnD//n0sLCyoX79+says72OOz507JzgUPn36tEjFpRITE7l69SqpqalYW1vj4uJSIvHpJYXG6lBY2Bl0dXVp1KhRsW++a5evUsGuLDmKjo4Odna1cXR0xM6uNnXq1NH4P4WcFy9eEBz8J+Hh50lLS2PNmnW4u7fFzi6/R6ZI6XHmzFm0tbVL3HFT5P1jbm6uNL1mYUilUo00vMqVKyuER5UUZcqUUZltrbhYW1vny7xWXGxtbVU6nhVExYoVqVixYomORVtbmzp16hSY+EgTNJ3j/fv3s2nTJlxcXPDy8lLaRl75z8LCoshVI83MzEpEwX1faCTcs7OzOXv2HPXqfaaxyeZdIiIusWrVaqXntLW1sbWtgYODgyDQa9euVWKmWUtLS3r29Cjx5DsiJUtYWBguLnX/s2V6RURENMfc3JygoCCCgoLo2LFjPgF8584doVre119/XRpD/CBoJC3Dw8+TkJDAZ58Vz7np6dNnTJ06XYhBtLW1xd7eDnt7OxwdHbG3t/sgGXxEPh7WrFlHdnY2EybkVl46f/4CcXGPPpq68CIiIv8OWrduTd26dYmMjKRdu3Z8++23NGjQAC0tLaKjo9m2bRtJSUnY2NgoFDH61FBLuMfHxxMc/Cc+PrmVk06fDqVcuXJF3gcNCgpi8OCBODo6YG9vL+Z4/4/z7Nkztm/fQa1aueFRGRkZLFu2nFatWtK2rWahQSIiIv9tdHR0CAwMpF+/fpw8eRJvb2+hfKycFi1asGPHjiKb5P8NaOxQJyJS0uTk5DB8+AhMTExwc/uCvXv34eTkxPjxY4ttwREd6kRKmxMnTgC5WfBKQpgkJCQIIVv6LlsAAABzSURBVGWtW7cWrZwFcPnyZU6ePMnDhw/R09OjQoUKuLq6FlrP/VNAQbinpb3SKP+viEhJkZOTw5UrV8nMfI2dnV2RPZPfxcLCUrQMiYiI/OdQEO4iIiIiIiIi/37EcmoiIiIiIiKfGKJwFxERERER+cT4fxeKdIIBJ86YAAAAAElFTkSuQmCC" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![Screenshot from 2023-09-14 05-55-57.png](attachment:dac9ce3a-5960-445f-a5d9-f13e0ac44c80.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## LSS Specification" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "There are some constraints in the construction of these diagrams, e.g., matching colors at intersection of two pipes, but we are not going to introduce them here.\n", + "After all, the purpose of a compiler is to let a computer consider those constraints instead of humans.\n", + "The reader can refer to our paper, or even to the code in this repo for these constraints later on.\n", + "What we are going to detail now is how to specify a problem to the compiler, so that the reader can start using the compiler." + ] + }, + { + "attachments": { + "4fef384b-1f6b-4712-8dcf-8e3f7b973a2f.png": { + "image/png": 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mVq1aRUxMDCqVqsicmA0bNqCvr0+bNm04ceIE27Zt0xqmeBH984uHi4sLALGxsVV6XSMjI0aOHEloaCj37t2jefPmjBkzhsWLF2u1U6lUfPbZZ/Tt25fp06eze/fuCq+OEl5eNdXzovWunZaWxs2bN6lXrx7169evlgCEQu7u7pw4cYJbt27z6qtuNR1OneHm9phBg7KYNq3kb9ZeXqmicm4lCQ0N5Z133gGgZcuWWFhYcOPGjWLbWlhYMG/ePMaMGYOfn99L+WVIR0cHoFrqpSQlJbFlyxY2bNhAREQEgwcPZvDgwdL9crmco0ePcv36dcLCwujSpYsUm1zsOCqUkyZ56dSpU7X1vGj933r79m0A2rRpU6UXFYrSFPV78CCxhiOpPqVcDCHUEhkZGQwZMoRevXoRGxvLoUOHCA4OJiAgoNj2qampzJ8/n4YNGxIcHMzJkyerOeKXQ1hYGIMGDcLBwYGgoCD69OnD7du3CQkJ0SoWamVlhb29PZcvX5aSFoDExESxBYlQIZrkxcnJie+++44PPvigSq+nlbg8evQIgEaNGpV4QExMjDScVFskJiZy4MCBmg6jQjT7PWVmZtZwJFVv3z5rBgxwp2PH1/Hza8XFi6Y1HZJQCtHR0aSnp+Pj44NCoZBuT0hIKNJWrVYTEBBAdnY2Fy5coE+fPvj5+ZGUlFSdIRMbG0teXu3cDdzc3JzHjx9X+Dxz587l9u3brFy5kri4OBYvXkzjxo2LtOvYsSMpKSnSPCQo/He6fPkyHTt2rHAcwsutYcOGUvKybNmyKk1eik1cTE2LfpDcuXOHSZMm0a5dO3bu3FllAZXHwoULGTFiBH/99VdNh1JuJiYmQOG32hdZaGg9/vzTlBkz7jJ1aiwJCXpMnepKQoLe8w8WapSLiwuWlpYsWbKEI0eOcP78eT766COpBsjTdV2++OIL9u3bx8aNG7Gzs5NWzIwYMaJcwyZXrlxh9+7d7N69m5s3b6JSqaS/Dx4sfuuMHTt20KhRI/r27VuOR1vowYMH0nUiIyMB2L9/P7t37+bXX38t93mhsIp2SEgIBw8e5MaNGxw8eLBctXHWr1/PlStXePfddzE0NCyx3YQJE9DX18ff358rV65w8+ZNJk+ezM2bN6v8G7Lwcqiu5KXIHBcAMzOzIg2dnZ1ZsGBBjc8+VyqVREdH07x5c+m29957D1dXV6lAVF0kk8kwMzN74XtclEoZc+f+vezbyKiAoKAmXLpkir3985e4CjXH0NCQkJAQxowZI62E8fT0ZM6cOSxYsICrV69ib2/P6dOnmT17NtOmTaN3794AWFtbs2nTJnr16kVQUBBz584t07XXrFnDN998o3Wbpj5Lw4YNi538qkmQKlLS4dy5c0XqwIwYMQIonMPzdP2aslq6dCkDBw6UniNTU1POnTvHK6+8UqbzlLa9g4MDBw4cYOzYsbi7uwOFhTC3bdsmelyESqNJXrp06cKyZcsAKr3AoVbiolQWXUb6NBsbm0q9eHns3LkTmUymlbi4urri6upag1FVDl1d3Rd+VVG/ftrJiWbnZheXmqnCKmi/7idMmMCECROkv//Zi+nl5UVMTAxxcXEoFAppEv/8+fOlNp6ensW+l3h7e1NQUKB1m6GhYYl7Dk2ePJkVK1YAsGLFCun30ho2bBidO3fG1ta2TMc9bcCAAaWqTGtubl5su27dupV4fIsWLYiIiCA2NpaCggIaNWokTeatKh4eHkRGRhIbG4tSqcTJyUlMzBUqXVUnL2VaC1rTxehu377NrFmz+Pzzz2s0DqHyREQYM3z4A1xcnl1eXqhdGjZsWCnnCQ0NLXHoyMHBocLnr4xzVCWZTPbMOYVVRTOnThCqSlUmL5VWxGLz5s388ccfUgXGSZMmFVn+GBkZyapVq8jJySEhIQFfX19GjRol3R8TE8OyZcswNDQkKiqKZs2aMXv2bCwsLDh79izvvvsuaWlpbNy4kePHjzNq1CheffVVgoOD2bp1Kzt27MDC4u+S7tHR0axatYrs7Gzu3LmDh4cHgYGBGBsbA3D16lU2btyIubk57733HgsWLOD8+fN06tSJzz//XJrEplar8ff3x8zMrFzlyoXiXbpkyk8/2bFsWfHLaYUX39OrWwRBeLFUVfJSbOJS1q7D999/Hz09PSmw5cuXM2DAANauXSuND//+++8EBgaya9cuGjRowI8//siUKVNQKpWMHTuWJ0+e0K9fP/7zn//w3nvvkZSUROvWrcnLy2PZsmW8/vrrrF+/nt69ezN8+HB8fX1RKBSEhISwfv16rl27ptUNff36dfz8/Ni1axdNmjQhISGB/v37c+jQIX799VcSEhLYv38/69atw8fHhwULFtCtWzcsLCxYsWIFLi4uTJo0CSjsSj937pyU8NRmGRkZqNVgZlZ7V+rk58v48Uc7tm61IyVFwfDhLVm5MpKWLZ/UdGiCIAhCJaqK5EUrQynPUNCxY8fYtGkT06dPl26bMmUKzs7OzJw5k8zMTFQqFZMnT2bs2LE0aNAAKBzvrl+/vrQ8MjExkYSEBGmuio2NDS4uLtJMfl1dXWkJpkKhwMDAAB0dHYYOHSpNbnvatGnT6Nmzp1TJ0t7eno8//phLly6xevVqnJyc+Pjjj9HX10epVLJ06VIGDx7M/PnzsbKy4uzZs9K59PT0OH/+fLXUoSjvcFx2djZHjhxj9ep1bNiwkby8Z89Xqkm6umoCAhLYv/8SU6bE8uSJDl98UXT5pkZIiC39+rUu8jNhQlt27RJd3oIgCLVZZa820kpcSrs9+tO2bt2KmZmZVqVduVyOr68vDx8+5NSpU4SHh3Pnzh1pJjsUFqy5fv06H3/8MVC4aunatWv06NGD1NRUvv/+ex4+fPjcCcOAVl0CKJwLc+7cOZo1a6Z1++DBg9HV1dVazq2np0fDhg21Sp3Xr1+/yOoeGxubaimNXdZ/g/z8fH7//Rxr1qzj0qXLAOjr66Onp3jOkTVPVxcCAhLo2jWN69dN+L996IooKJCRmysv8pOXJy/xGEEQBKH2qMzkRWuoqDzf9m/evCntfPo0zYSzu3fvSsnH8wpBGRsbM2vWLJRKJe+++y67d+8u1Sqbf8Z98+ZNgCJx6erq0qBBA61N44p7zHK5vFxJXGUoy79BePgVzpz5Xar9oClo1ayZc1WFVyU8PdM4d86MkhZUDB2ayNChRSsKx8Tkk5urBmp/kiYIgvCy0yQvnTp1qtCwUbE9LmUpEGVpaUlWVlaRegb16tUDwNbWVtpl+sqVK0WOj4uLAwr32ejevTsuLi588cUXtGjRogwPo2hMULht+z/Vq1evQssjq1ppEqaoqBusW/cDhw4dISsrC1dXV2bNmoWTkxNAkZ6m2u7xY108PB5Tw4vWhDrk0aNHRTZ1FEovLi6O6OjoatlDSRCepkleGjZsWO6elwov4O/UqRNAkeqVSUlJ6Ovr4+XlxWuvvYaOjg7r1q3TerPJy8sjODgYgI0bNxITE8Pbb7+tdZ6nP8g1vRHP+3B/9dVXMTMzIzQ0tMh9SUlJxc6JqQtiY+PYsmUr+/b9SlpaGg4ODrz//vtMmTIFW1tbrl69ip6eHo0alX3eh1qtpqCggLy8PLKzs8nMzOTGjVvcunUbpVJZKT1QBQWwa5cNt2//Xd0zKUlBaKgVgYElb5IoCP/k6urKyJEjq/w6u3fvRiaTFftT0aHjlJSUclXKrYgzZ87g5uaGo6Mjzs7ONGrUiJCQkGqNQRCcnJwqlLyUaTm0Ztjm6SGfCRMmsG7dOr777jsGDx4szTfZv38/gYGB0vJkf39/tmzZwrBhw5g6dSr5+fmsWrWKTz75pDAQ3cJQ9uzZg7+/PyEhIURHR6Onp0dkZCR6enpSWfyoqChSUlK4dOkSPXv2lOLR/NfExIQPPviABQsWsGvXLmll06VLl8jKymLy5MlA4Yd1bm5ukSGl/Px8rSEqtVrN+PHjsbKyqpEaMsnJyRw7dlIa4rK2tmbAgAG0adNGSuYiIiIoKCjAxaVZqVaF5ebmkZGRTmbmE9LSUklOTiM5OYvY2HRiY9O4ezeD7GxdLA0j6NO3LYP8/DE3N6/Q40hNVbB8eSMyM3V4/fV0rK2VgJr//e8Gjo4vduE9oXLNmTMHFxeXKr/O66+/Ln252r59O9u3b2fjxo0YGxtr7ddUHnZ2drz//vssWbKkMkJ9rvv379OnTx+6dOnCTz/9hKGhIV999RVDhw7l7NmztG/fvlriEAT4O3nRrDYyMDBg0aJFpTq21InLw4cP+frrrwE4cOAA//rXvxg+fDhmZmbs2LGDcePG0b9/fwYOHMjFixdp0aKFNPEWYPHixWRkZLB7925OnTqFubk5X331FW3btgUKy2hv2bKFwMBAvvjiCxYtWkSvXr3YsmULGzduZNGiRajVary9vVm2bBkXLlzgxx9/5ODBg/zyyy8ALFq0iA8++IAmTZoQGBhISkoKU6dO5c8//8TExIRTp06xe/durK2tSUpK4rvvviM3N5dDhw6xefNm+vXrx08//cSNGzfQ09NjzZo1jB49GqVSya+//oq5uXm1Ji7p6emcOnWa69ejgMKS4H379sXT07NIhc3w8HAAXFyKDhPl5+eTkpJCfPx9kpKSuXfvLikpuaSnG5GVZURamjmZmZbIZA7o6TVAoahP/fqOyGU6GN3vT8Kv21iXmsa4994rdjuI0rK2VnLgwCXu3TNAJlNjb5+HiUnB8w8UqoWmx02z3012dvYz977JysqShoGr25QpU57bRqlUsmvXLtq2bYuzc/nmfTVo0ABfX1+gsO4TFFbTfV4Sr1arycvLQ19fv1zXLQu1Wl2quXGrV69GqVSyceNGrKysAFi5ciVhYWEsXbqUn376qapDFQQtTycvms/W0iQvMvVTYwDffPMNZ86c4b///S/29vZlCkCtVhMREUFWVhbNmzcv8YUdHR1NSkoKbm5uRd708vPzSUhIwMHBAblcTl5eHsnJydISao3k5ORSb8P+6NEjbt68iYWFRYXmzcTExKCnp1cklso0Z84csrKeMHbsaM6ePUd4+BVUKhX6+vr4+Pjg7e1dZAUVFM5JmjFjBnl5eUye/B4KRWE+mpyczJo167hzJ5aMDANksqbI5W7IZK+go9MIHR1TZDIDdHRMkcuNkMm0e2rUqixsE/vjo3eUYxk6PHL1YP78ORXueaksmsm5LVq8+JNzX3utNQpFxTai/OSTT/jss8/Yt28f/fr1k263s7Nj0KBBBAcHk5KSwuTJk4mIiODw4cO0aNGCw4cPSxVoMzMzmTt3Llu2bCEpKQkzMzOGDBnCkiVLpKGTiIgIfHx8GD58uFZvwp49e/j3v//NwoULGT9+fJnj7927N3/88Yf0d48ePZ65d9rKlSuZPHkyrVq1KnZ+XVktWLCA+fPnk5aWVuQ1kJ6eTtOmTaX3UM2weJs2bVi9ejX/+te/ANi7dy9jx44FCl+fhoaGUn0oMzMzbt++Xea4BgwYwGuvvcbEiROfWSn4jTfeIDExkcuXL0u35efn06NHD+7evau1aEEQqlNMTAxdunQhLi6OmTNnPjd5KbaOS3n2rpDJZLz66qu8/vrrz/xga9KkCe3atSv2m5quri6Ojo7S9UtKFEqbtEDhZNwOHTpUKGmBwsywKpMWjZycXNasWc+lS5dRqVR069aNTz/9lD59+hSbtADcunWLnJwcnJ2bSEkLwNq169i/5xQZGbOxsDiKhcUGzMxmYGraHyOj19DXb4Kenj06OiZFkpanGepAH4sCLCJOseTzxaSmptbYqiuh8qWkpHDt2jW2b99O7969WbFiBT169OCXX37h7t27rFu3Tmo7fvx4Nm3axPLly7ly5QpLly5l27ZtjBs3Tmrj5ubGRx99xJdffinNM7t//z5jx46lffv2vPvuu+WKc8KECQQFBREUFISBgQHp6enPbO/u7o6jo6O0IWRVUqvVJCcnM3nyZNRqNbt27WLz5s0kJibi5+cnDUd36NCBbdu2sW3bNuRyOf3795f+1uygXVatWrVi/O4ooAAAIABJREFU+fLlODk54efnx+nTp4tt988vfPHx8XTv3p2TJ09KFc8FoSY8Pefl888/Z9asWc9srzVUJD6MapYmYVMqlbRr14633npL6tJ9lkuXLgHQrFnTIvf1NH3IneT/ki7Twcy8LzJZ+Tdx622p5sTVE/zwrREjx0+oFZtuCpWjX79+eHl5ERkZyYEDBwgMDMTExARnZ2etb+KOjo6sWbOGQYMGAYUfmhERESxdupS8vDwpuZ46dSrHjh1j9OjRhIeHM2rUKAwNDdm0aVO5iyxqrgnw/fffP7d9586duXeveid9Dxs2TBpSh8JK1hMnTuTWrVu4urpia2srJVJyuZzGjRtXOLEKCgpi9uzZ7Ny5k02bNtG1a1dat27NlClT8PPzw8DAACjsmdU890eOHMHf358OHToQEBDwzJ4rQagOZRk2EtuC1iLdu3endevWfPLJJ4wZM6ZUSQsgdf02bVo0cWmoD/1MrqHz8EPS0vZWKD4dGXQyUqL3+37Wfr2MmJiYCp1PqH2eLsSo+fvpJbOLFy+mX79+HD9+nM2bN7Nq1SpiYmJQqVRFlidv2LABfX192rRpw4kTJ9i2bVup/5+uqzSVujU0E4hjY2Or9LpGRkaMHDmS0NBQ7t27R/PmzRkzZgyLFy/WaqdSqfjss8/o27cv06dPZ/fu3dVSWFMQSqO0PS/FTs4Va/trhpeXF15eXmU65s6dO6Snp+Po2BADg6ITAWVAEwMYJr/B6rgACgq+xdp6RLniU6shuwAUahXXTxxm1q27fP/9t5ibl3/CrlC3hIaG8s477wDQsmVLLCwsuHGj+E0yLSwsmDdvHmPGjMHPz6/IpqsvA80k+up4T01KSmLLli1s2LCBiIgIBg8ezODBg6X75XI5R48e5fr164SFhUkbXKpUqnJNDxCEquDk5MSxY8fo3r07n3/+ORYWFloLfUD0uNR5z1pNpCGXgZ0+zGiQjuLhf0hN/gGVqujyY7U6n4KCJ+Tnp5KXl0Bubgz3czL55ZE53yfaMDfekaAkD3apAnli/T1ZWfakpj6qsscm1C4ZGRkMGTKEXr16ERsby6FDhwgODiYgIKDY9qmpqcyfP5+GDRsSHBxcLXt9vYzCwsIYNGgQDg4OBAUF0adPH27fvk1ISAitWrWS2llZWWFvb8/ly5e1duVOTEws07xBQahqTZs25fDhw0BhLaV/KlMdF6H2+fPPPwFKVdPCUAfG2DzmQPpc4vJTMK03goKCVJTKh+TnJ5KX9wC1OoeCgkwKCtLIz3+EgUFfMgw/Qk+vEQ76TVEo/u7qT0ws+j+U8OKKjo4mPT0dHx8frRomCQkJRdqq1WoCAgLIzs4mPDyc8ePH4+fnx+XLl6t1blRsbCz169cvcWJ7TdJs0VFRc+fO5cmTJ6xcuZKRI0eWuIS9Y8eOnDhxQuu5UKvVXL58mY4dO1Y4DkGoTJptg4rrrRSJSx2WkJDAo0ePqF/fFhMT41IdY6mA3qax/PZ4ARHZUSgUNsjlRujoWKJQWKNQOKCrWw+Foj46OhbI5bXvDV+oGS4uLlhaWrJkyRIcHBwwMTEhODhY2mskKytLWlH4xRdfsG/fPn799Vfs7OxYv3497u7ujBgxgt9++61ahiZ27NjB0KFD8fb25tChQ+U6x4MHDzh37hyAtFP9/v37pQJ0ffv2LXd87du3JyQkBF9fX5o0aUJ0dDRdunQpc22c9evX88orrzy33YQJE1i+fDn+/v4sXrwYQ0NDli1bxs2bN/nhhx/K+SgEofqJxKUO00zKfdYwUXHqKaCTcQbx+r0xM+uGTKaPXG6ATCb+dxBKZmhoSEhICGPGjJFWwnh6ejJnzhwWLFjA1atXsbe35/Tp08yePZtp06ZJ22tYW1uzadMmevXqRVBQEHPnzq3yeDXf1Mq7igng3LlzUuVtjREjCueIWVhYFNmjrSyWLl3KwIEDpefI1NSUc+fOlSoJeVpp2zs4OHDgwAHGjh2Lu7s7APXr12fbtm2ix0WoU2rsk0qlUpGRkSH9LZPJSqzKWt7JY6WtKFna4/7ZrWtmZlahN8WKKs38lpLoykBXtx66ui/2Kg/h+TS7t0Pht/IJEyZIf//1119abb28vIiJiSEuLg6FQkH9+vUBmD9/vtTG09NT65wa3t7eFBRoV0o2NDQkJyen2LgmT57MihUrir0vJSXluR/Yw4YNo3PnzhXaVHXAgAGlKhNhbm5ebLtu3bqVeHyLFi2IiIggNjaWgoICGjVqVKQidmXz8PAgMjKS2NhYlEolTk5OYmKuUOfUWOISFRWFp6cnHTp0wMrKCoVCwYYNG7TanD17liVLltC3b1+tAlfPs3z5cs6cOYOJiQnGxsYsXLgQU1PTZx6Tn5/Pp59+ytatW8nOzqZTp04sXboUR8fCDQtzcnL4z3/+AxROZvvjjz+4fv269MZd3R4/fkxsbCyWlpbSTtyCUF0aNmxYKecJDQ0tccVNSVVgT58+TWxsrFSN9lmeVUm2NpDJZNJYfnXSvK8JQl1U42MDn3zyCZ07dy5y+08//cTOnTs5duwYffr0KfX5goKCOH36NPv370culzNv3jwCAgIICQl5Zu/IvHnzsLS05LvvvuPYsWN8//33DBs2jNOnTyOTyTAwMGDLli1A4Rj3qFGjyv5gK5Gm9LmLS9HaLYJQVzy9uuVZNJsb5uTkcPLkSdzd3aUvEoIgvFxqPHEpib+/P+7u7tKSqNKIiopi+fLlbNy4Uer+nDhxIq+++qo0Ua84ycnJ9OjRQxq39/HxITk5mR07dnD//v1a+a1NM0zUrFnZh4kEoa6xtbXF2dkZfX19AgIC8Pf3r/DuzIIg1E21NnEByjy7fvPmzRQUFNCpUyfpNnt7exwdHdmwYUOJiYu1tXWRstvu7u4cP368QuPjVSUzM5Nbt25hbGyEvb1dTYfzQlCpVOTm5pKbm0tOTg7p6RkkJaVy924i9+/H06ljK9q93q5advsViurevTvdu3ev6TAEQagFanXiUtZJY0ePHsXAwKBICeumTZty+vRpcnNzS/3BEx4ezpIlS2rlt7q/J+U+v3aLULycnBxSUlJISkomISGBtLQMkpLySU2F5GQ19+9DXp4Z+vrO5GY94v7ZRSQNH8MbffuWWCdDEARBqHq1OnEpK81k1X8yNTVFqVQSHx+Ps7PzM8+hVqtZv349Dx8+LHP5/epSkdVEL6uEhAdERkYSH3+fe/fukZSUTW6uFXl5DcnKqo9a/SpyuTW6uubo6NTD2toWubxwc7rHSdl0yP+Ws1vWkJuXxzB//xp+NIIgCC+vFyZxycvLIzMzs9jZ8ppKkVlZWc88R0JCAsuWLePHH38kKysLHx8f9u/fX6tW7eTl5REZGYmenh4NG9a+uTe1TWpqKtOmfUhcnC6Ghu0wNGyPoeFoFIomyGQ66OjoYmamC+iUOHlbBtgowIdUNq9eSYEahg8XyYsgCEJNeGEW8Ovq6iKTyYpdWpmXlwdQYp0YDXt7exYvXsxff/3FwIEDiYqKKrGORE25evUqBQUFNGvWVNRfKIVbt26RdOcmBup61Ks3DUvLf2No2Pr/elZMpMJ7panHY6ELo62VHF+/km1bt/LkyZNqeAQCFK4+XLhwYU2H8cKIi4sjOjpabKgr1EkvzCefXC7H3t6+2L0/Hj9+jI6OTqk3EtMsi7axseHixYuVHWqFlLda7svMxQh66R/nyf0PyM6+WqqCYiUx1YUR9ZREbV9P8JbNFaqcKpReaGgox44dq/br7t69G5lMVuxPccPSZZGSkvLcXuDKdubMGdzc3HB0dMTZ2ZlGjRoREhJSrTEIQkW9MIkLFO79kZKSUqQSZ1xcHG3atCnTKiV9fX06d+5cq1aR5Ofnc+XKFXR1dWnSxKmGo6lb2pkU4KV3mMz7H5CXd69C5zLSAS+9DFIO/sy3y5aVWPlVqPtef/11goODCQ4OllYlbty4keDgYDZu3Fihc9vZ2TFv3rzKCLNU7t+/T58+fXB2duby5ctERUXRv39/hg4dyvnz56stDkGoqBcqcfHz80OpVGr1kqSlpRETE4Ovr2+Zz5eWloaPj09lhlghUVFRKJVKmjRxqvLS4C8ahRzameTT3/AotyI9ycm5Wa7zPM6H39Nhbwqce5jF/gMH+f333ys52ppRUFBAdna29PfTvxenunsLykqpVLJjxw7u3LlT7nM0aNAAX19ffH19cXNzAwq3AfD19eWtt94q8Ti1Wk1ubm65r1sWpe1BXL16NUqlko0bN+Lu7k7z5s1ZuXIlTk5O0kaZglAX1OrERfPC18xReVpkZCRdu3ZlxowZ0m29evXCy8uLPXv2SLf99NNPuLi4MGbMGKDwzVbzRvTo0SMAHj58yA8//EBycrJ03PHjx8nMzGT06NFV8dDKRTNM1KyZqJZbHnIZtDJWM6tBPLl3e/M49RdUqsL/t9RqNSpVDkplEjk5t3jy5A/S04+QlLSORxnnWZf6KvMTO/J52mAOKRYTa7MHw2bXsWu4nPv3E2r4kVWMnZ0dkyZNws7ODmNjYwIDA+nZsydGRka4uroSHx8vtc3MzGTatGnY2tpibGyMubk548aN0xoyi4iIwMHBQeu1CbBnzx5sbGxYvXp1hWPOycmhf//+tGjRgtu3bxfbZvXq1QwdOrTIJolVIT09HRsbG37++WemTp2KqakpRkZGtGvXjj///FNqt3fvXmxsbLCxsSE/P5+VK1dKfzdtWr7X9cCBA5kzZ47Wv1Nxzp49S/PmzbGy+nt/MrVajYODA2fOnCnXtQWhJtTaVUWHDx9m69atAPz444+YmZkxYsQIaULqhQsXuHr1KlevXsXX11fa3XTt2rWMGzeOoKAgFAoFFy5cYOfOndLKooSEBI4ePQoUbgf/4YcfcvnyZWbMmMGcOXPw9vZGoVBgY2NDcHBwrRkqUqvVhIeHI5PJaNr02Uu6Xx4qcnKyUalMyzRR2UYBwyzucPDRhyQpE9FR2JGTc4OCgnRph2yVKge53ACFogGWVv4o9D7GXtEAHR1TZLK/r5WRcayyH1S1S0lJ4dq1a2zfvp0lS5awYsUKFi5cyOTJk/H392fdunXSbs7jx48nNDSUFStW0LJlSy5cuEBgYCCpqanSXAk3Nzc++ugjPvjgA3x8fOjVqxf3799n7NixdOjQgXfffbdC8ebk5DBgwADOnz/P4cOHS/zAd3d3x9HRsUhxyaqgVqtJTk6WnrNdu3bx8OFDPv74Y/z8/IiIiEBXV5cOHTqwbds2oPCLVv/+/aVNLXV1y/d23KpVK5YvX87nn3+Or68vU6ZMwdPTs0i75ORkrXl+8fHx0rYmZS32KQg1qdYmLt7e3nh7e7Nu3bpi7x8+fDhubm789ttvWnMMLC0tCQkJITo6Grlczscff6x1XNOmTTl58iR3797l0qVLQOEbSGRkJHFxcRgaGuLk5CQlOrXF7du3efLkCY0bN6o1yVR1y8rK5tatW9y+fZv4+PtERcWQnp7JK684MXXqlDIVhmugB31N7/Bj+npyTIZjYOD2f7tlm6OjY45cbvx/SUqtfYlUqn79+uHl5UVkZCQHDhwgMDAQExMTnJ2duXv3rtTO0dGRNWvWMGjQIKDwQzMiIoKlS5eSl5cnvW6mTp3KsWPHGD16NOHh4YwaNQpDQ0M2bdpUoR3Vc3JyGDhwIGfPniUsLOyZGy127tyZe/cqNp+prIYNG8bXX38t/Z2RkcHEiRO5desWrq6u2NraSomUXC6ncePGFU6sgoKCmD17Njt37mTTpk107dqV1q1bM2XKFPz8/DAwKKxHpFKppOf+yJEj+Pv706FDBwICAvj5558rFIMgVKc6+66so6ODu7s733zzDdOnTy9yf5MmTUo89tVXX2X79u34P1VIzMrKSqsLtbZ5GVcT3bhxk+vXrxMRcZ1Tp07z6NEjnJyccHFxwd7eDi8vL5KTH/HXX+f58MOPCAr6tNQrPWQysNMDa2M38u3er+JHUndoeq40H3ByuVxryezixYvJy8vj+PHj3Lt3j6ysLGJiYlCpVGRnZ2sl/Bs2bKBNmza0adOGxMREjh07VqHXmFKpZOjQoYSFhXHs2DE6dOhQ7nNVlX++72iqW8fGxuLq6lpl1zUyMmLkyJGMHDmS+Ph4PvzwQ8aMGcPdu3e1JgCrVCo+++wzPv30Uz799FNmzJjBtGnTqiwuQagKdTZxuX37NsHBwcybN0/6RlEa6enpbN68mW7dulXpG0ll01TLbd78xSjzn5ubR2ZmBpmZT8jMzCQtLY2kpGTi4+OJj48nLi4eAwN9GjRwwNbWhnHj/o25ubnWFgzZ2WqSkx/h4eFJeHg4X321jPHj36VhQ4cKfasXShYaGso777wDQMuWLbGwsODGjRvFtrWwsGDevHmMGTMGPz+/YocvyuLEiRPo6uqiUqk4c+ZMqXeWrkmaSfTVUS8lKSmJLVu2sGHDBiIiIhg8eDCDBw+W7pfL5Rw9epTr168TFhYmPX8qlUrUhBLqlBpLXPT19XF1dWXRokXo6emhUCjYvn17qY+3s7MrMgxUGnp6ekycOLHMq3JycnKkHprc3FxcXV2rbR+juLg4Hj16RIMG9nVynxylUklycjIPHiTy4MEDUlJSSE/PIDs7m6ysLPLz85HJZBgbm2BpaUnbtm3p2bNnmZ5fd/fXuHr1Gj/8sJFx4/4tNp+sAhkZGQwZMoQBAwawbt066d/nyy+/5MMPPyzSPjU1lfnz59OwYUOCg4N57733KpRsmJiYcODAAdasWcPs2bNp06YNvXr1Kvf5XhRhYWF8++237N+/H1NTU8aNG8fevXtp3LixVjsrKyvs7e25dOmS1uaxiYmJpa5xJQi1QY0lLs7OzhWayW5sbFyu48rSO/PP43755ZdyHVtRmt6WurKaKCMjk2vXrnHnzh1iY+O4f/8+KpWKevWsMDY2wtzcHFNTU2xsbNDX18fIyKjC83Z0dXVxc3uFW7du8cUXXzJ9+jQaNLCvpEckAERHR5Oeno6Pj49WUpmQUHRVlVqtJiAggOzsbMLDwxk/fjx+fn5cvnwZGxubcl2/Q4cOeHp60rZtW65cuYK/vz8XLlx45v5jsbGx1K9fv9bNWQMwNzcvtmBmWc2dO5cnT56wcuVKRo4cWeKXm44dO3LixAmt50KtVnP58mVpcYMg1AV1dqjoZaKZ39KiRfMajqSorKws/vzzEjdv3uLKlStcu3aNjIxMmjZtSpMmTjRo0IB27dpVyweHnp4ebm5u3LkTzYcfzuDLL7+o8mu+TFxcXLC0tGTJkiU4ODhgYmJCcHCwVAMkKysLc3NzAL744gv27dvHr7/+ip2dHevXr8fd3Z0RI0bw22+/VWhowsDAgJ07d9K2bVsGDRrE2bNni10Vs2PHDoYOHYq3tzeHDh0q17UePHjAuXPngMISDAD79+/H2NgYhUJB3759y/042rdvT0hICL6+vjRp0oTo6Gi6dOlS5hU+69ev55VXXnluuwkTJrB8+XL8/f1ZvHgxhoaGLFu2jJs3b/LDDz+U81EIQvUTiUstl5KSwv3797G2tn7uXkvVLS3tMXPmzKN+fTvs7e1xdnamY8eOmJqa1miBPGfnJujr67Nw4We0adMatar8Jf6FvxkaGhISEsKYMWOklTCenp7MmTOHBQsWcPXqVezt7Tl9+jSzZ89m2rRp9O7dGwBra2s2bdpEr169CAoKkpZXl5eTkxNbt26lb9++jB07Vlpi/DTNvJKKzHc6d+5ckTowI0aMAArn8FRky4elS5cycOBA6TkyNTXl3LlzpUpCnlba9g4ODhw4cICxY8fi7u4OQP369dm2bZvocRHqFJG41HKaJdsuLrVvmMjIyJBhw4Zhb1/7hmQaNLBHLpdx9OhxzPOVNR1OraZU/v38TJgwQaorAvDXX39ptfXy8iImJoa4uDgUCgX169cHYP78+VIbT09PrXNqeHt7U1BQoHWboaFhiVsmTJ48Wdrk9MKFC0Xuf+ONN4qc72nDhg2jc+fOWvM5ymrAgAGlqkxrbm5ebLtu3bqVeHyLFi2IiIggNjaWgoICGjVqVOUJv4eHB5GRkcTGxqJUKnFychITc4U6RyQutdzf1XJr4zJoWa1905PJZNSvX58WLZrzMPEmUPIHnFB2DRs2rJTzhIaGlrjixsHBocLnr4xzVCWZTEajRo2q/bqOjo7Vfk1BqCwicanFMjMziY6OxtTUFFvb8k1ofJnJ5XIMDQ2RIZZG11Z1YUmzIAi1S+38uiwATw8Tlb+3JUkJeVVfQkIQBEEQqoVIXGoxzTLoiiQuvyuNOJ9RO5OXUm5qKwiCIAgSMVRUS2VnZxMZGYmBgQEODg3KfZ4W7Tpy8fZNMtJi6WUJOjU8aqJWw+nT7hw92pa0NFNsbNLo2fMc7dpF1mxggiAIQp0gEpda6q+//kKtVuPi0qxCyzkLJ6i2YPfuPeSnxNPHCnQrmLwUrpJQAWXvMjl5sjW//96KTp3+IidHn7NnW/Hjj3148sSQbt0uVSwwQXiJzZo1S5rM7+/vL23NUNfExcVp7SC+efNmUdlX0CKGimqpK1euAJVTLdfOzo4BA94iyqoZu1LkZJZxgY1KlYdSmUhOzi0yM38nM3MvT578gIWFskwVb9VquHvXnunTf6Rnzwv073+KqVN/QqHIJyysoxg6El4YqampZGVlVes1L168yI0bN2jZsmWFloDXNH19fVq2bIlCoeC3334jNze3pkMSahmRuNRC+fn5XL16FV1dXRo3rpylknZ2dgwZ8jZ5r3QgLF1RYvKiVhegVCaTmXmO5OQtJCQsICXlA1Sq/2JltRQXl/W0a7eTLl3OM3BgRywsLEodw5MnBrzxxu/o6Pw94cbWNo1XX73DkycG5OfXXNE6oWalp6dXSvn7ynb37l1kMhmrVq0q03Fubm68+eablRJDWZ4bNzc3lixZIhW1e9rKlSuRyWTSj76+Pu7u7nz55ZfVkhzk5+eTkpJSbI2fp9nY2LBkyRICAgKqPCahbhJDRbXQtWvXUCqVtGjRvFILUhkaGtK5e3dOAaFXzoMpqFS5ZGVd4smTS2RlXUKtvk69emoaNrTBwcEWGxsLTEys0NNToKurQFdXBx0dnXINX5mY5GBiUrTYmLFxNlZWj1EoRK2Vl5Wvry9paWnFFpqri+bOnUuDBuWfm/a0yn5udu7cSb169cjJyeHUqVPMnTuXc+fOlWmT2/I4d+4cnTt3Zt++ffTr169KryW82ETiUgtVxmqikhgYGNC5e3d+y8klKurfGBsX4OLSkLZtnbCxscXWtm+5N6Isr7g4Wzw8rlTrNYWSPXnyBENDw+cWF8zIyMDExKTUSWxWVha6uroV3rcqLy8PuVyOru6z376USiW7du2ibdu2z9yIsSpMmjSpVO2ys7MxMDCo0Dy2svLw8JAqHr/xxhs4ODgwadIkjh8/Trdu3bTa5uXloVKpyvSekJGRgZGRUY1u+yG82MRQUS2jUqkIDw9HLpdX2ZutgYEB/fr1w9u7JY0b29KhQwfatGlDo0aONZC02JCVZUjXrn9W63WFv+3duxcbGxvWrl2Li4sLJiYmWFhY8N///rdIufqCggIWLFiAjY0NZmZmWFpa8v7775OdnV3kvD179iQgIIDQ0FBeffVVjI2NMTQ05OjRowA8evQIGxsbbGxsOH78uLRztObn6tWrWuc7ePAg//rXvzAyMsLQ0JDXX3+dsLCwEh/X6tWrGTp0aJG9hqpKly5dtOL39fUtse2yZcto1KgRRkZGmJiYMGDAAG7duiXdX9bnpiI0+05dv35dui08PBwvLy8MDAyk5/r48eNFjn3y5Ak2NjasWrWKr776Cjs7O8zMzDAxMZG2cpg5cyY2NjZSL8vw4cOlx1FXJxALNatSelxOnz5N06ZNsbOzAwqz9F9//RUfHx+MjY0r4xLldvjwYZo3b15nSlzfvHmTnJwcmjRxQqGoug4xhUKXdu3aEhUVxcmTJ+nc2bPaS4+rVDL27u1KQMBedHVLLjRz9WpT/vjDtcjtBQVqrK0v8K9/Xa7KMF94eXl5JCcn8//+3//js88+w97enu+//56FCxdiZ2fH5MmTpbYzZ87kq6++IigoiF69enH+/HmmTZtGQkICP//8s9Z5Hz9+zLVr19i9ezdDhgwhICCAtLQ0XFxcgMJNBTWbI86YMYMnT57w7bffSsc7OTlJv4eHh/Pmm2/y9ttvs2LFCrKzs1m0aBH9+/fnwoULvPbaa0Uel7u7O46OjtIHc1WbMmWKtOniZ599Rnp6erHtvv32W6ZNm0ZQUBA9e/YkJiaGmTNn0qtXLyIiIjAwMCjTc1NRmoRFM7SVkJBAt27daNasGWFhYejp6fHpp5/i4+PDhQsXpA0aNZKTk1m4cCEqlYp33nkHGxsbHj9+LH0JGjNmDD4+Pvz111988MEHfPTRR9KmjjY2oiK4UHYV+mQMDQ1l0aJFhIeHs2fPHilx2bVrFxMnTmThwoWl7jKtCvHx8QwZMoS+ffuyZcuWGoujLKpymKg4zZo1Q61Ws2/ffoYP9y/TZNuKOnDAAw+PcBwckp/Z7uFDSy5fbl7sfa+9Fg+IxKUyrF27Fh8fH6BwM8V79+6xZMkSKXGJiYlh+fLlzJw5k1mzZgHQtm1b5HI5EydOZNq0aXTo0EHrnElJSZw5c4b27dsXuZ5CoZCSCisrK3R0dEpMMo4ePYpSqeSbb76hXr16ALRr145Ro0Zx8+bNYhOXzp07c+/evXI+G2U3dOhQ6fe1a9eW2C40NJSWLVsye/ZsANq3b4+9vT3/+9//uHfvHs2bNy/Tc1NWmqQiNzeXM2fOMGXKFNq2bStN6J03bx4FBQWEhoZKz/X+/ftxcXFh5syZHDhwoMg55XI5ly5dwsrKqsh9LVq0oEWLFlIi07p162pLJoXt8GrbAAAgAElEQVQXU4USl169enHv3j3pw1bjjTfeYM6cOc/sKq0KERERuLm5SX87ODjwv//9j7Zt21ZrHBWhKfNfGcugS0NHRwdXV1fkcjmrV69m5MiR2NnZVfnmiWfPtsTCIgN391vPbdup01+89lrRdjk5apKSnn+8UDqaDyko3Pxv2LBhTJs2jZSUFKysrDh48CBKpZJRo0ZpHTdixAgmTpzIvn37iiQuHTt2LDZpKasuXbqgp6fHqFGjCAwMxNPTEwsLC/bu3Vvhc1e3nj17EhgYyLRp0xg6dCjt2rWjS5cu1bZvU4sWLaTf5XI5vr6+LFu2TJp7tHfvXvr166f1/4Oenh5Dhgxh+fLl5ObmFimDMHLkyGKTFkGoChX+dNJM8nqaubk5H3zwQbXWEsjPz2fBggVFbh83bhxt2rSptjgqIiYmhvT0dBo2dMDQ0LBar928eXP69u3LkSNHiIqKIj8/v8qu9ccfrmRnG+DpqT0h9+5du2LbGxrmYm2dVuTHyioNA4MnVRbny06zA/T9+/cBePjwIVB0x2UTExMsLS1JSkoqcg6FQlEpsbRt25ajR4+Sl5fHm2++Sb169fDx8SE0NLRSzl+dJk+ezA8//MChQ4fo1KkT1tbWjBo1iqioqGq5/qFDh7h8+TLXrl0jMzOT7du3a62AevjwYbG7ajdq1Ij8/HxpOOxplfXvLAilUeHEpaq/mZfW7NmztSa31UWanqvq6m35p8aNG+Ph4cG1a9ekAniV7cKFVzh8+HUUinxOnmzNyZOtOXbsX/z4Y2+iohpXyTWF8klMTAT+/nKi+QauSWA08vLyePz4MZaWllUaj4eHB2FhYTx69IidO3eiUCjo3bs3Bw8erNLrVoV33nmHK1eucP/+fZYvX84ff/yBp6cnDx48qPJrt2zZEnd3d9zc3Ir9glSvXr0i/8ZQOOwnl8sxNzev8hgF4VmKzTqelYzExsYSGBjIlClTGDNmDCdOnNC6v6CggAMHDjBs2DAOHToEFC6D3Lp1K3369CEuLo7//ve/dOnShXPnzgGQm5vLV199xfjx4+nVqxfTp08vktVHRkbywQcfMGnSJAYOHMjmzZuBwp6WwMBA1q5dS3JyMv/5z3+YM2cOUDjsMnXqVBYvXqx1rszMTD7//HOmT5/OwIEDCQwM1BoLz8rKYsuWLfTu3ZvExET27t3LG2+8gY+PDydPntQ6l+Zbk+axVERERARQffNbimNtbY2Hhwdnz/7OsWNFVxFUxB9/uPLTT71JSLBm504v6Wf37m5cvPgKbduK/Ypq0j+LkO3duxd7e3up57RHjx7I5XJCQkK02u3ZsweVSkXPnj3LfW1zc/NnFlkLDAxk9OjRQGEPT//+/dm3bx8mJibs27evxONiY2PJy8srd1yVLT8/nx49erBs2TIA7O3tCQgIYOPGjaSkpHD69OkixzzvualsPXv25LfffitS+XfXrl14eHiUuzdYk/DUxkKDQt1Spjkud+/epXfv3nz//fd069aNzMxM+vTpo9Xm9OnTbN++nbCwMIYPHw78f/bOOyyqa+vD7zTKUEURqQYBBbsCYiMWUBM7FmxEo/EmMSqxRMWo8SbXaOzdGE2uRk2isUSj2HuMDY0lFqJGRRQVkI6UGWa+P7icz5Ghd3Le55lH5px99llnOzNnnb3X+q3sYLQNGzZw+fJlvv76a5RKJY8fP+b+/ft4e3szfPhwxowZw6RJk3j8+DFdu3blwoULnDhxAoVCwfnz5wkODmb37t3Y2dnxww8/MH78eFQqFaNGjWLBggU8e/aMe/fusXjxYiQSCXfv3iU0NJTNmzczevRowb6XL1/SvXt3Jk2aREhICJmZmYwcOZLOnTtz8OBBXF1dOXToEP/973+5evUq69atw8jIiDFjxvDll1/y3nvvcePGDWE9+NatW/z111/cuXMn1/p+UXn58iWGhoaYm5uXqJ+SIJFIMDMzo1+/AHbu3IVMJsXHx6fE2hsAnp7hFeKcVMLC2JWS4OBgVq1ahZ2dHWvWrOHw4cMsXLhQ2O/h4cF7773Hv//9b2rWrEmnTp34448/+PDDD+natWuJAi5btWrFzp07Wb16NV27duXZs2c4OjoK2TONGjXiww8/xMHBgZEjR6LVatm+fTvJycl5fu+2b99OYGAgfn5+wkNUcbl+/TqhoaG5tvv4+Ah1dI4fP05ycjKQLfmfmZnJnj17gOxlN09PT+RyOTY2Nnz22WfCGMbFxbFo0SKMjIxyZewUZmxKmzlz5rB7924CAgKYO3cuBgYGLFiwgFu3buV6UC0Kbm5uWFpasmzZMiFY99mzZ2KgrkiR0eu4aDT6f+qnTJlCq1atBJEiU1NTgoKChAwDgDfffBONRiN8YQH69u1LVFQUly9fxtvbm759+/Lpp58ikUjYuXMnCoWCjh07Atlf8CFDhrB06VIOHjxIjx49GDduHKNHjxbWYf38/LCxsRHW1I2MjJBKpUgkEiFyPScCfsmSJTrXsHTpUjIzMwVtBwMDA+bNm4eXlxczZsxg27ZtBAQEEBERwdWrV/H396dNmzZA9lTptGnTuHv3Lo0aNQKyUyC7d++Oq2vFzZKUBaampgQE9OW3384QFnYJb2+vUnFeyhszMzNiMeRxhhqHwpdV+kfi5eVF9+7diY+PRyaTMXHiRCZNmqTTZs2aNZibm/PRRx+RmZmJTCYjKCiI1atXl+jcwcHBnDp1SshgksvlrF+/Xphl+eCDD8jMzOTLL7/kyy+/BLKzbRYtWkRQUJDePnN+x0pD3G3NmjU66cg5HD16VLjxfvzxx7n0VXJ+Z4KCgoRZ4m+//ZaQkBA++OADQf/G3d2dX375Re/vSEFjU9q4uLhw5swZgoKC8PLyArJ/lw8ePEi7du2K3a+hoSEbN25k5MiRQr+urq7cvXu3VOwW+edQ6BmXyMhIjh49yr///W+d7TkBfK+ir/BeTvBWy5Ytgf//MTl06BCPHz8WlncA0tPTGTJkCEZGRly7do379+/rPInUqVNHRywpL+Ryea5lrx9//DFXsK6TkxOtW7fmyJEjJCUlYW5uLtykX9U2yUn3TklJEbZJJJJq57TkYGZmRrt2bQkLu8TJkyfp2rVrRZtUZKysrGjo25k9pw/TyywDp/LV16tS/Otf/2LFihVERkZiZWWlN2ZFLpezaNEiPv/8c548eYKNjU2eMQ9Fkag3MjIiNDSUmJgY4uPjcXJyyiWGOH78eMaPH8+zZ89Qq9XY2dnlu6w9aNAg2rdvX6Ikgbp16+YS4cuLP//8s1DtTExMWLlyJcuXLycyMhITE5N8qx8XZmwKw9ixYxk7dmyh2np6enL79m0iIyNRq9XUrVtX71ibmJgUenwA+vTpw/Pnz4mIiECpVJZaWQSRfxaFdlxyAkcLo/NRlCecJ0+e4OzszH/+8x+9+3PSHYu7Tv2qLcnJyTx9+pTGjRvnapfjoERGRtKoUSO915DzxS3KF7UqI5FIsLCwoFOnjpw8eYqtW7fRr19AlZt5cXd3x8DAgAMnD9JXmopN1TK/XDEwMMDFpeDgcBMTE+rX16+tUxJyFFXzI+cBojDoy46pLEilUurWLXxAemHGJiwsjICAAAYOHCgs1ZeEshDuVCgU+T7sPXnyhHHjxvHkyZNSP7dI9aDQKUE50645qZGlhZGREVeuXNGbfhsdHY1SqQTQm+Xy+PHjIp3LxMQEQ0NDvV+InKdLUclRF4lEglwux9/fD1NTU3bv3kNCQkKVct4kEgnOzs7Ubd+FPZlWPM0ETQnM12q1aDRpqNUvUKtzp4aKiFQEffr0YeDAgTg4OFRonFxJkcvlODg44OPjw7hx4ypcfV2k8lHoGZccYbfQ0FCmTZuWa0Yir7iYgmjevDknTpxg/fr1Oiq7YWFhxMbG4uXlhUwm47vvvmP06NFCRHtmZiY7duxgwoQJQPbNqaCbqVSaHWj622+/ERkZqfM0ERsbi6enZ7lqz1Q12rdvx+XLlzl27Bh+fv5YWladtEipVEqDBvUxNjZm79mTeKU8pZlp4Y7VaNJRq2PJzIxCpXqCSvUUuTwGI6NEpNLzQMmCsiua5s2bs2rVqnIv+SBSurxamqEqY2Njw8qVKyvaDJFKTKFnXFxdXfHz8+PmzZssWrQIyH7yPHfuHJCdcZQTaJaTVqlSqYTjs7KyAN34EIB3330XU1NTZs2axbRp0zh06BDffPMN8+bNw9/fH2tra4YMGcKjR48YNGgQx44d49ChQwwePFhHadLU1JTo6Gji4+PZtWsXKpUKtVpNVlaWzjJTTlDwihUrhG0pKSmcOnWKmTNnCttyCoS9OhOU8/eraaOnTp3irbfeKjPdk8qETCajWbNmgmJpamrVE39zcnKkhf/bXDJ7g/NJkKXH11WpoklKOkl09NdERATz6NEQVKqp1Kq1isaN9/Lmm2F07fqMt9+W0rhx1XHe8sLFxYWxY8eKs40iIiJVgiKlQ69du5YRI0Ywb948fvzxR6ytrfHx8UEqlXLw4EEaNGiAoaEhX3/9NQDfffcdDg4OJCQksGnTJgBmzpzJtGnThBRGR0dHfvjhBz788EPWr1/P+vXrcXNz48cffxQCeufPn09ycjJ79uzhzJkzWFhYsGTJEh0p/+HDhxMaGkqzZs1YvHgxsbGxQhbAoUOH2LVrF/369aNVq1Z88803fPLJJyQkJNC0aVNOnjzJf/7zHyFb6tixY/z888/CuT/66CMSEhJYt24dAKtXr8bCwoLmzZtz/vx5Ll68yJUrV/TWS6luGBoa0qpVK/744w+++WYdI0e+W+bCY6VNrVq1aNO1O8cPHOBFQgo1kk6SnHyGlJQzvHx5DTOzDBo2bIijowOOjo7Y2uYtxf7w4cPyM1xEREREBIn2lfWVVatWcfbsWWbOnImtrW2eB4WHh5OcnEzTpk1JTk4mPT1db3ZRUVCpVFy/fh2pVErTpk2RyWS52jx48IAXL17QsGFDIfblVV6+fIlWqy3Ummh6ejo3btxAoVDg7u6uNxOqKHa3bNmyxGmXs2bNIjU1lXHjSqcw5VdfzcfAwBB399yVlUuDGzdu8PjxY9q0aVNghkdZkJam5eHDCMzMFMjluT8vGo2GzMxMMjIyyMjIID09nbS0NFJTU0lOTiExMRGNRoOjoyNWVlbY2tpSq1bNIq2pnz17FicnR4YOHVKal5aLpk2bo1CULKp4xowZzJ07l3379tGjR49SskxERESk9ElPT8fY2BgfHx/Onz+vs69YRRZfvREW94b/OgqFosBiiM7Ozjg7O+e5X58zkxdGRkaClkBJKIzd1ZUcB/LMmd9p0aK5TvG28kar1ZKenk5ycjKJiUkkJyeTkZGOVpu9TyaTYWRkhFJpjL29AzVqWGJpaYmJiUmlKVshIiIiIlIwJaoOLfLPJiedU6Ew4MSJE6SlpdO8eW7lz7JAq9Xy4kU09+7dIS0tgfj4eNTqLGrWtMLc3AIrqxrUqGGFiYkSAwMDjI2NMTY21juTJ1L6WFtbExsbK7yvU6cObdq04bPPPqN58+Zlfv60tDRevnwpViwWEamGiI6LSImQyWQ4OjrQs2dPNm/egkwmpUmTJqV+ntjYWCIiInj8+AkPHjwgOvo5Vla1sbe3p359F+rVq1cojSGR8qN3795MmjQJrVZLVFQUa9asoXXr1pw9e1YQoiwrlixZwsyZM0lJSRHTaUVEqhmi4yJSKlhYWDBw4MD/FYmT0KhRw0IvwajVatLT08nMzCQtLY3k5GTS0tKIi4snPj6e+Pg45HIF9vb2uLq60rFjB6ysrNBqDXn8+AnW1qbI5eJHubJhZ2cnBLwD9OvXDw8PDyZPnsyJEydytU9NTcXQ0LDQ/5cajYbU1FTMzMxKbOuxY8dQKpVCeQ8REZHKi/hrL1Jq1K5tTZs2bbh+/TpZWWq9SwIajYa0tDRiY2NJSkoiLi7ulfRyCVKpBIlEioWFOfXqOWNh0RxLS0u9N6e0tKojgieSHVfWtm1bjh07prN9x44dzJgxgzt37iCXy+nZsyfLli3LpSp7+PBhhg0bxr59+9iwYQObNm0iLS2Njh07Co6Qr68v4eHhQmXjunXrCkHzc+bM4YMPPshl182bN/H390cmkxEVFSVqOYmIVHJEx0Wk1JBIJNSpY4NS6cOpU6d5+vQZHTq8yfPnz3nyJIq4uBfExsb+zzGxoHbt2lhbW2NpaYlSqcTQ0BClUikUzRSpfoSHh+vUp9m3bx+BgYEMHTqUTZs2ER0dTXBwMB06dOD27duC4CRkZ/DFxsYycOBAbGxsmDp1KkZGRjp1fhYuXEhqaipbtmxh48aNbNy4UegjrxIFtra2NGnSBEtLy1x1l06fPs3s2bPzvJ7Dhw8Lsg0iIiLlg+i4iJQqOfWNevfuxYEDB5g/fwFvvFGXevXq0bx5C5ycHMWYg38IGRkZJCYmotVqefbsGUuXLuWPP/5g+/btQHaA9eTJk2nbti1btmwRjnN1daVRo0asWLGCadOm5eq3RYsW/PLLL3qd29atWwMI6ZOdOnUq8PNmZWWVp4Ckubm53tpmOZRG5WkREZGiITouImVGhw4d8Pb2zveHX6T6smHDBjZs2CC8t7Oz4/vvv2fAgAEA3Llzhzt37jBx4kSd4zw8PGjZsiX79u3T67iMHz++3GbkmjdvLsrPi4hUMkTHRUREpEwYMGCAUEajVq1auSo1R0dHA/orODs5OXHr1i29/Zbn0syTJ09yiV+9SkBAgLisKSJSzlRbxyUqKooffviB48ePA9lPTu+88w4NGzbk3r17hISEkJqaio2NDf369aN3794VbLGISPWiVq1aNGuWt66PlZUV8P8OzKvExMRUilIS58+fF2aI9JGenl5qIpwiIiKFo9o+KtjZ2TFmzBguXLjAixcv+OKLL4QK1w4ODjx58oQOHTqwdu1a0WkREakA3N3dcXBwYOfOnTrbo6KiuHjxIv7+/sXuOyfINjExsVDtY2Nj9bbt378/Wq02z5fotIiIlD/V1nGB/y+AFxAQIEwvP3v2jPfff5+vvvqKkJAQjIyMKtBCEZF/LjKZjPnz53PgwAGmTJnCX3/9xZkzZ+jVqxeWlpZ88sknxe67VatWQHZR1/DwcC5fvszly5f1tn306BGOjo44OzuTlJRU7HOKiIiUD9XacclZJnr77bcBOHnyJNOnT2f+/Pk6wlgiIiIVw9ChQ9m8eTPfffcd7u7u+Pr6YmhoyLlz53KlJheFVq1aMWvWLDZt2oSHhwdeXl5C1frXyakzK2YIiYhUDaptjAtkayzY2dnRuHFj5s+fj0ql4ttvvxXr1YiIlDExMTGFbhsUFMTgwYOJiIjAxMSEOnXq6G3Xo0cPXilmXyBffPEFU6dO5cmTJ9SuXTvPmJm6devy5MkTFApFqajwioiIlC3V1nFJSkri4sWLdOvWjYEDBzJmzBi6du1a0WaJiIjoQS6X4+LiUur9mpqaFqpqeU6gsIiISOWn2i4VHT9+HLVaTWJiIqdOnSIqKqqiTRIREREREREpIVXWcVGpVKSnp+u8Xp1GPnz4MDKZjA0bNuDl5cXs2bNF50VERERERKSKU2UdlyFDhmBnZ6fzunv3LpBdyO/YsWO0atWKmjVrsmLFCtLT00uUpSAiIiIiIiJS8VTZGJcxY8bQp08fnW05QX1//PEHMTExjB07FsjWi5gwYQILFy5k586d9O/fv9ztFRERERERESk5VdZx8fPzy3PfkSNHAHSCcSdPnsyePXuYPn06HTp00KkoKyIiIiJSPG7evKkzmx0aGiqWQaiGDB06lPj4eACmTJlC586dK8yWavnp2rNnDzVr1sTd3V3YZmBgwPvvv09sbCxjx44lKyurAi0UEREpChcuXGDIkCE6r7/++quizSox8fHxvHz5sqLNKBEJCQkcPHiQWrVqiQVVqzHu7u7Uq1ePgwcP8vTp0wq1pVo5Lr/99htjxozhzp07JCYmMn/+fCIiIgAICwtj69atQPaMzIABA9ixY0dFmisiIlJItFotarUatVpNZGQkW7duJTY2tqLN0suLFy8K7Yw0bNiQXr16lbFF5UPOcvzrsy2JiYlIJJI8X9euXSv2OZOSkgpd1iE/Jk6cmKd9AQEBxe5XrVbz4sULVCpVieyrDGP42Wef8cUXXxT7PKVJlV0q0oevry++vr56FTK9vb05fPhwBVglIiJSUlq3bs327duB7KWInj17VrBFeVOnTh3hJl4Qn332GXZ2duVgVcWhVCqFh8SbN28ye/Zspk6dKpRleOONN4rdd//+/UlISCAsLKxENr777ru0b98egNmzZ5OamsqiRYsASvT/c+HCBdq3b8++ffvo0aNHsfupCmNYnlQrx0VEREQkh8zMTDQaTYH1yLRaLS9fvsTExKTAdunp6RgbG5eajWPGjClUu9TUVAwNDZHLC/7JTktLK9BGlUrF7t278fT0pF69eoWyobgoFAohISIntrBt27a5kiteR6vVkpmZWS6FLJs1ayZUMl+1apWOzflRmLEuDarCGJYn1WqpSEREROTatWt06tQJIyMjjI2N8fb25tSpU7naqdVqpk6dioWFBaamptjZ2fHFF1+QmZmp0+7+/fv069cPc3NzlEolDg4OzJ07V6fN3r17sba2xtraGrVazerVq4X3rysC+/r6Cvusra3zvUHu2LGDBg0aYGpqirGxMQEBAcLydw6dOnVi2rRprF27Fnt7e5RKJU5OTvz000959rtu3ToCAwPp27dvnm3Km6SkJKytrdm2bRsff/wxZmZmKJVKvLy8+OOPP4R2cXFxwtidOnWKq1ev6oznjRs3yszGmTNn0r59e06dOkWLFi1QKpVYWFgQEhKioyMWEhKCtbW1MMsydOhQwb7hw4eXmX1VYQxLA3HGpZKhQVPRJoiIVFmePn1Khw4dcHV15ciRIxgYGPDFF1/QpUsXwsLChKdqgGHDhrF3716WLVtGixYtOH36NDNmzCAhIYElS5YAkJ6eTpcuXbC0tGTXrl3CTWHGjBmYmZkxfvx4AHx8fIQYuq5du9KzZ08++OADgFyzJOPHjxeyM+bOnZtnRep9+/YRGBjI0KFD2bRpE9HR0QQHB9OhQwdu374tPOknJCTw3Xff4enpydq1a5HJZMybN48RI0bg7e2Nq6trrr6bNWuGo6NjvtmZ5Y1WqyU2NpZx48YxZMgQdu/eTXR0NNOmTWPw4MHcunULuVyOmZmZMNZTpkwhNTWVNWvWCP2UZNmkIFJTU7ly5QoTJkxg4sSJODg4sHXrVubPn4+HhwcjRowAYOTIkXTp0oU///yTiRMnMnXqVFq3bg2AtbV1mdlXFcawNBAdl0qGFCnJmmTStenUktYSK9aKiBSB2bNnk5WVxeHDh4X6Q6Ghobi5uRESEsKBAweA7GD9n3/+mXXr1vGvf/0LyI6De/HiBYsXL2bu3LkYGRkRHR1N7969GTVqFE2aNAGgefPmHDlyhG3btgmOS+3atQUnQCqVUrdu3TydgsDAQOHvb7/9Vm8brVbL5MmTadu2LVu2bBG2u7q60qhRI1asWMG0adOE7fb29hw4cEAIjHVxccHd3Z2jR4/qdVzat2/Po0ePCjGi5c+gQYNYsWKF8D45OZkPP/yQe/fu4e7ujkKhEMa2Zs2ayGSycnXAVCoV+/fvx9bWFoCOHTuyf/9+Dhw4IDguDRo0oEGDBsIyZfPmzcvVxso+hiVFXCqqhJhJzTDAADXqijZFRKRKsXfvXnr06KFTNNHAwICBAwdy9OhRMjIygOwMRMj+gX+V6dOnc/36dRQKBQBOTk4sXboUe3t7Dh06xH//+1+++eYbMjMzSU1NLbPruHPnDnfu3CEoKEhnu4eHBy1btmTfvn06252cnHSyedzc3ACIjIwsMxvLCmdnZ533le1aDA0NBacFsh3VevXqVRr7oPKPYUkRZ1wqKUqpEhky4rPiqSGrUdHmiIhUCaKjo7G3t8+13cnJCbVaTXx8PHXq1CEyMhJjY2PMzc112pmZmeWqJv3VV1/x+eef4+joiKurKyYmJsTExAhK3WV1HUCe13Lr1q18j89xYjSaqr/0LJPJgMp9LTKZrMQpz2VJVRjDoiA6LpUUhST7ic9UasoD1QOcFc4FHCEiImJlZSXc9F8lJiYGqVSKhYUFALa2tqSlpfHy5UuUSmWe/Z06dYrp06ezdu1aIWYFoFevXjx+/Lj0L+B/5MwY5XUtNWqIDzMi/1zEpaJKjkKi4A35G2RqM9Foq4e3LCJSVvj7+3Pw4MFcAnC7d++mbdu2QkCrj48PAL/++qtOu82bN9OyZUvh+Bxhr+7duwtttFotz549y9MGCwuLEouiubu74+DgwM6dO3W2R0VFcfHiRfz9/UvUP2QvG7yeQVXVKI2xLktyHOXKbmNltk8f4oxLFUCDhpealxhKDDGWlL1mgIhIZSMqKkoQyMr59/Tp04J6rr+/PyYmJsyZM4fdu3cTEBDA3LlzMTAwYMGCBdy6dYvTp08L/XXo0IFu3boxduxYTExMaNGiBefOnWPixIn07NlTmIXJEfiaPHkyU6ZMITk5mRUrVnDp0iXq16+v19ZWrVoJxVydnZ158OABvr6+Qp/Hjx8nOTkZyJb8z8zMZM+ePQA4ODjg6emJTCZj/vz5DBs2jClTpjB69GhiYmL4+OOPsbS0LHGl++3btxMYGIifnx9Hjx4tUV8FoVarCQ0NBRDSbC9cuCDs79SpU64lu8KSM9arV6+ma9euPHv2DEdHx1xZMXPmzGHPnj2cPn1ar+7KjRs3+PvvvwGIjY0lNTVV+D+xtbUVPgdFxc3NDUtLS5YtWyYE6z579ixXIGx0dDQ9evQgKCiIjz/+OFc/lWEMKxOi41IFkElkWMosydJmEZsVi6HEEDOpWUWbVSpoNCDWYxMpiHPnzjFgwACdbeq59oAAACAASURBVJ9++qnw971793BxccHFxYUzZ84QFBSEl5cXkO0MHDx4kHbt2ukcv3PnTsaMGUNAQABZWVkYGxszZswYHY2W1q1bs3z5cmbMmMH27duRy+VCraQdO3aQmpqaS7hu6dKl9O3bl7feegvIjpu5cOECHh4eAHz88ce5dDJy9FSCgoLYvHkzkK39odFoCA4OFlRc27Rpw7lz54Qn+eKSE+tQHlmLqampufRi5s2bJ/x99epVnTT1ohAcHMypU6cYN24ckJ16vn79et59912ddg8ePODSpUs6Wiuv8t1337Fs2TKdbTk29+3bl19++aVY9hkaGrJx40ZGjhwpfB5dXV25e/euTruMjAwuXbpEp06d9PZTGcawMiE6LlUImURGLVn1qGodE2PGgQMtyMyUM3r08Yo2R6SS079//zxvOq/j6enJ7du3iYyMRK1WU7duXb3Vik1MTNi0aRMrV64kNjaWunXr6lWmDQ4O5qOPPuLRo0fUqlVLeLL98ccf9Z6/QYMG3Lp1i8jISLKysnBychKCIwH+/PPPQl0HZDsygwcPJiIiAhMTE70BwVeuXNF7bH7jNWjQINq3b0/t2rULbUtxsbCwKNT/XV7tOnTokOfxRkZGhIaGEhMTQ3x8PE5OTnqVkp8+fYq1tXWe8UxLly5l6dKlBdqYV7sTJ07keUyfPn14/vw5ERERKJVKvSUEcooW5jXLURnGsDIhOi5VkHRNOmrUmEhMqqTOS3i4HX/84cyZM+60bPmgos0RqaY4OjoWqp2FhUWBMxhyubxI0vgSiQQnJ6dCty/o3K+r75YG+jKWSsLkyZOpUaMGO3fu1OsoliU5iq/6SE5O5uzZs4JeT0WgUCj06unkcPDgQUxMTApVZqCsyG8MIVtU7/nz5+VoUd6IjksVxEhqRJomDS1a4rMSsKpi6dLu7lG4u0cRFpb3F1lERKRqYGtrKywzVEZSUlIYNmwYn332WUWbkieOjo6sX78eGxubijYlT2xtbTE1NWXcuHF5xneVF6LjUkUxllb9IF1Dw8qreyAiIlI46tWrx8qVKyvajDyxtbVl9erVFW1GvowcObKiTSiQ1+tzVSRiWGQVx0xqylN13qmZlZkquMolIiIiIlLBiI5LFUchUWArr0OyJpk0TVpFmyMiIiIiIlKmiI5LNcFMakaSRn+VWRERERERkeqCGONSjbCSWZGlzSJNm4ap1LSizSk1njyxIiIid7R7ZqYWmQysrauW6qOIyD+dzMxMrl69Wmxht7IgLi6OqKgoGjduXKTjwsLCaNq0KYaGhmVkWcVz48YN7OzsdIqXViTlNuOSnp6eq6JpWZCZmcnu3bvLtHLr77//riP5XR7nLAwKiQKZRIZaqyZFk0IhZS8qPTduOLJxY4dcrx9/7Eh4eNF+ZESqFxMmTMglHJaDVqslKiqqnC0qGzIyMgSV4KpORkYG3bt3Z/369RVtig6PHz/mzTff1FFYLoj9+/fTpUuXalN1OS/Onj2Lj49PvqUuypNycVxWrlxJ48aNyyWPfvfu3YwaNYpNmzaVet+HDx+mU6dO9OrVi3v37pXLOYuDpcwSU6kpiZrqMRPh4fGEIUN+z/UaMOB33NxuV7R5IhVIaGgov//+u95969atw97evkg3ovLkxYsXuWoq5cW7775L3bp1SU9PL2Oryp5JkyaRmJjIqlWrSqU/b2/vUskaatq0KQsWLCAgIKBQeiUPHjwgMDCQ7777LpdGy549e5BIJHpfeRXIDA0NzVdHRR/Lly9HIpEQERGRa19qaioSiYSbN2/qPbZJkya8/fbbOtuePXuGvb09TZs21XkQf//99/Hx8WHgwIGFFoIsS8plqWj8+PGcPXuWkydPlvm5unXrxqxZs8pEyKdr1648evRIKLxWHucsCQqJArU2q6LNKDFOTrE4OeV+2kxL0/L48ROg+iyLiZQe/v7+zJgxg6ZNm1a0KXqpU6cOEyZMYOHChQW2HT16NC1btqz0iqYFcenSJdauXcv58+cr5dLKe++9x7p165gyZUqBD6Iff/wxHTt21Pu77+3tzY4dOwD4+eef+fnnn/n+++8xMTFBoVCUie0lRaVSMWDAANLS0ti9e3euUhaLFy/G1dWVDRs2MGrUqAqyMptyWyoqL2EdCwsLJk6cWGZS1vquo6zPWVxMpEpkEilZ2qxKWVlarZaiVssKbigi8gqpqalkZRXskLu4uDBnzhwsLS0L3XdycnKefWu1WqE4YmFsLE38/PyYMmVKoc6rVqsL1WdaWsFZiCqViu3bt3P//v1C9VkQixYtok2bNnh7e+fb7vbt29SoUYNdu3aVynkLi0QiYcKECfz000/5Lv/cvn2bffv2MWHCBL377ezs6N+/P/3796dhw4ZAtvR///796d27d5nYXlI+/vhjzp07x9atW/WqRNvY2DBkyBAWLVpU4bMu5ea4lLcEdFlR1a5DggSZRIYESYV/2HKIjLRizx4vkpKU3Lljy7FjjUlI0F9DREQkh3PnztG0aVNMTU0xNzdn1qxZuW7Se/fuFaTLc16vVtF9ldTUVKytrfnmm29YsmQJderUwdzcHFNTU50lGZVKxYwZM6hZsybm5uZYW1uzfPlyvX1u2rQJR0dHTE1NsbS0ZPjw4TpxAa/ap1arWb16tfD+dVn/kJAQnevQV6cohx07dtCgQQNMTU0xNjYmICAg1/LBzJkzad++PadOnaJFixYolUosLCwICQnJ87dh3bp1BAYG5irwVxxynuQDAwMLbKvRaEhISEClKn+Ryr59+6JQKIQZE3389NNP1KxZk86dO5ejZWXHd999x9dff828efPo2rVrnu2GDh3K7du3uXr1ajlal5siLRWNHz9eqCr6OtOmTStUbY6MjAzmzZvHoUOHsLe3Z8aMGbRo0ULY//DhQ5YtW4axsTF//fUXrq6ufPrpp8JTk0qlYunSpaSmpgpPDF5eXgQGBpKVlcXhw4fZuHEj//rXv/D39y/wmIKIjIxk4cKFaLVaUlJScs2q6Dvny5cv2b17N5s3b2b9+vWsXbuWU6dOsWjRInx8fFi4cCGHDh3i559/Lrco7UwyUaBAQsWrvjk6xuHoGEefPpcq2hSRKkJsbCxvv/02tWvXZteuXSiVShYuXMjDhw+FqrsAjRo1Ys6cOQBcv36dNWvW5DsDERsby5dffolGo2H48OFYW1uTmJiosyQTFBTEgQMHmDt3Lp6enhw+fJjJkyeTnp7OtGnThHZr165lzJgxTJo0icGDB/P3338zdepUevfuzdmzZ5HL5fj4+LB161Yge+m5Z8+efPDBBwC5Cjz27NkTZ2dnINsxyWupfd++fQQGBjJ06FA2bdpEdHQ0wcHBdOjQgdu3b2NsnK2ynZqaypUrV5gwYQITJ07EwcGBrVu3Mn/+fDw8PBgxYkSuvps1a4ajoyN+fn55jmFh+f3338nIyMDHx6fEfZUlSqWS5s2bc/z4cSZOnKi3zfHjx/Hy8qpyD7L6uHDhAmPHjiUwMJCpU6fm29bHxwepVMrx48d17tvlTaEdF7Vazd9//83GjRuF6qhnzpxh8ODB9OnTp1BOi1arZeLEidjY2ODt7c1PP/3E+fPnOXPmDG+88Qapqan06NGDsWPH8tFHHxETE0Pz5s3JzMwUMgeWLFlCjRo1hAHOCfSC7C/Gzz//zJEjRxg6dKhw3vyOyY+IiAjeeust1q5dS4cOHUhJSckVzKTvnIcPH2bDhg1cvnyZr7/+GqVSyePHj7l//z4+Pj6EhYVx7do1YmNjy81xMZQYotFq0Gq1aNEilVT9L5zIP4fly5eTnJzM5cuXhZkJX19f4caeQ7169QRHIDQ0lDVr1hTYt1Qq5cqVK9SsWTPXvjNnzvDzzz+zceNG4cbepk0bYmNjWbBgAZMmTUKhUJCWlsasWbMYOnQoixcvBrLjHKysrOjWrRunT5+mc+fO1K5dW3ACpFIpdevWzdMpaN++Pe3btwfg3r17eh0XrVbL5MmTadu2LVu2bBG2u7q60qhRI1asWKHjXKlUKvbv34+trS0AHTt2ZP/+/Rw4cECv49K+fXsePXpU4BgWhvDwcIA869ycO3eOixcvAv9fLXn//v3CjJWzs3O5LbPUq1dPsEUf4eHhDBs2rFxsKUueP39Ov379yMjIYPTo0QW2NzY2xtbWlr/++qscrMubQjsuWVlZvP/++8KMQ3R0NOPHj8fZ2TnPdMTX0Wg0zJw5Uyjr3a5dO8aMGcOCBQtYs2YNz58/5+nTp7i7uwPZ1Srd3NyEDzzAyZMnad26tfB+6tSp7N+/H4A333wTjUbDnj17dM6b3zH5MWXKFFq1akWHDh0AMDU1JSgoiOnTpwtt9J2zb9++REVFcfnyZby9venbty+ffvqpUMl548aNxMXF4eDgUKhxKy2kEilarbZSzLqIiBSFCxcu4OnpqbOcolQqhYeokhAUFKTXaYHs2QyJRIK5uTmHDh0StteoUYO4uDgePXqEi4sLt2/fJjY2lkGDBukc7+fnR3h4uPCbV9rcuXOHO3fu5JoZ8PDwoGXLluzbt0/HcTE0NBScFsh2nurVq1cu6bzR0dFIJJI8K3Hv379fmC3LYdOmTUKQbM+ePYvsuKxfv15vjR0XFxeOHj2a53FWVlZ5Zhap1Wri4uLyzA6qSly5cgV7e3vq1avH2LFjuXbtmjBDlxf5jU15UWjHxdDQUFjn1Gg0fPjhhyQmJrJ9+3bMzMyAbOfm9TVJhUKBTJYdgCmTyXS+wIGBgcyfP59Ll7KXDOrVq8fNmzextbUlPj6ebdu2ER0drfNFc3NzY/ny5Tx+/Jhp06bh6urKO++8o2Pn6+R3TF42R0VFcfToUf7973/r7NPnbOg7Z07keMuWLQEEpwWyf3CVyoqJ6ZBIJKi1arK0WRhgoGOXiEhl5fHjx2VWkTa/LI9nz56h1Wr1LivL5XKioqJwcXERbvyvx6HIZDIaNGhQuga/QnR0NAD29va59jk5OXHr1q0C+5DJZOUSS5KRkYFMJstzeWX69OlCsOvt27fx9fVl3bp19OvXD8j//ykv2rZtm+s3HMjTecrBwMAgz9RzlUqFVqvNtbRXFTE3N+fAgQO8ePGCzp07M2vWLBYtWpTvMfmNTXlRrJFfuHAhJ0+eZPny5ToqgytXruSLL77Qabt48eI8K19KJBLc3Nx0gudMTEyYPn06KpWKf/3rX+zZs4eMjAxh/5w5c0hMTGTnzp388ssvDBs2jC+//FL4UOu7Eed3TF425+TTFyYjoard/OUSOXLkqLQqFFTO1DwRkVextbUlJiam3M9ramqKoaEhycnJ+d44cx6uXrx4UV6mAQhLzTkOzKvExMRUqlmBnIDktLQ0vU/1rz7Q5dhtbm6e52xYYWjUqBGNGjUq8nGJiYl5ZokaGxtjYmJS6Ayz0iA0NJQHDx4wbtw4ne052WsGBgbF6rdt27Y0adIEyNZqWbp0Kf3796dNmzZ5HpOYmIiHh0exzldaFDnQ4bfffmPhwoUEBgbqzHQAdOnSheXLl+u82rVrl29/KpVK+NLHxMTQsWNH3NzcWLRokd4nFXNzc77//nt2795N48aN2bx5M++9916+58jvmLxszglCri7Km/rI1nkpXOpkZUOlUpGUFE9CQlyFe/8iZY+XlxdhYWFC7ANkK1anpKSU6Xn9/PzIyMhg586dOtu1Wq3OdLmHhwdmZma5lqlv375NixYtOHPmTK6+LSwsChVrlx/u7u44ODjksi8qKoqLFy8KCQolITIykszMzBL34+joCMCTJ09K3FdZExkZme9SvqOjY7lex+3btwkODubhw4c6248ePYqNjU2pyI0sWLAAOzs7Ro0aledvqkajISoqqtzDHF6nSDMu0dHRvP/++7i5uQkBaJAdqGRvb19k71aj0XDnzh1hGvb777/n4cOHDBgwQKfdq6l6a9as4aOPPuLNN9/k6NGjjBo1in379pGenp6nOFN+x+Rlc850ZmhoKNOmTcs1q5JXdlVVQ4aMTG0mMmTIJJVTUyUrK4uUlFRevHhBYmIicXFxqFQqjIxMyczMJDr6MV5enrkEk0SqDxMnTmT16tX06dOH+fPnY2VlxZw5c3JJkEdFRREWFgYg/Hv69GlBLt/f379In5OAgAD8/f15//33iY+Pp1u3biQkJPD5559z8+ZNwsPDkcvlmJmZ8emnnzJjxgzc3NwYNGgQDx8+JDg4mIyMDDw9PXP13apVK3bu3En//v1xdnbmwYMH+Pr6CrMO169f58GDBwDcvXtXJ5bOyMiIbt26IZPJmD9/PsOGDWPKlCmMHj2amJgYPv74YywtLfnkk0+KONK6bN++ncDAQPz8/PKNCSkMb775JpAdV/G60uzrGBkZ4eXlVWEzRlevXuXdd9/Nc/+bb76p1xnN4dmzZ8JKQk6MZmhoqCBA17179yLZM2LECBYvXkzv3r1ZvHgxtWrVYsOGDZw4cYINGzaUSnaTubk533zzDT169GD27NnMnz8/V5u//vqLly9fCnGfFUWhHZecuJbk5GR++eUXnS//r7/+ypgxYwrVR2xsLLVq1QJg69atGBoaEhwcnG3M/9YMf/31V4YMGcLOnTt58OABBgYGhIeHY2BgwJEjR+jUqRMeHh7I5XK6d+/O9evXBaclZ1np1TXbgo7Rh6urK35+fhw7doxFixYxZcoUtFot586dA7IzjnKmPPWdM0fESt8T4apVqzh58iT//e9/SyW4sCRIJBIMMCBDk4FMIssO3i3HpS+tVotWqyUrKwuNRoNGoyEjI4OkpCSSkpKIi4snJSUFpdIYCwsLzMzMsLOzxdTUlLQ0LWp1Fn//fYNLly7TsGFData0qhYpiiK61KlThyNHjjBgwAA6d+6MRCJh8ODBuRyCc+fO5Xrw+fTTT4W/7927l0svpSB2797NtGnTmDBhgjDz0KZNG3bt2qUT5xASEoJcLmf27Nl88sknSKVSevXqxcqVK/UujSxdupS+ffvy1ltvAWBmZsaFCxeEafj169fnksXPiTN0cHAQ4mqGDh2KRqMhODhYiE9o06YN586dKzCWoyByHtBK4zfB1tYWLy8vQkNDGThwYL5tXVxcBMezvLl8+TLPnz+nV69eebbp3bs369at4/79+3rF2i5cuJBL+yYnC8nS0pL4+Pgi2WRtbc2RI0cYPXq0oLNSo0YN1q1bl6+DVVS6d+9OUFAQixcvpn///rmKYO7fvx8LCwvBCa0oCu24rF27lpMnT+Li4sLKlSuF7fHx8Rw5coRJkyble3xQUBA3b97E19eXwYMHk56ezv379/n111+FOJJhw4axZcsW4QuYI4azZcsWvv/+e+bNm4dGo2HgwIF8+OGH2NjY8NNPP/HNN98AcO3aNb7++msgW1DHwcGB1q1b53tMQdc8YsQI5s2bx48//oi1tbWQx37w4EEaNGiAoaFhrnMmJCQIkfAzZ85k2rRpOtoFhw4d4uzZszx79qzCHZccDKXZAcYqVBhQvPXSwqDRaEhPTycjI4OMjAzS09NRqVSkp6cLgdJabfZ6t7GxMfXr18LExCRPZ0Qmk9K8eXPu37/P33//jUqVSZ06dUTnpRrSpk0bIiIiePjwIVZWVnqlBPr3719ooUUTE5NCtTUxMWHVqlUsWLCAJ0+eYGVllWfcxSeffML48eOJjIzEzs4u3yD8Bg0acOvWLSIjI8nKysLJyUlIZIDsmMFXf2vzIygoiMGDBxMREYGJiYlesbqlS5eydOnSXNtPnDiRZ7+DBg2iffv2paYKHhwczEcffcSSJUsqTaXh19mwYQOenp75hjm8/fbbuLq68u233+rNWurTp0+pC342btyY8+fPk5SURHR0NG+88UaJAoT//PNPvds3b97M5s2bc23XarVs3LiR0aNHV1hySQ6FvuqPPvqIjz76qNgnatmyJYcOHSIyMlJYP3xd+8Xa2prz58/z9OlT7O3tkUql+Pn5ERISImQj/fDDD8jlcsLDw9FoNGzbtk2YOWnWrJkg7vQq+R2THzVr1mTfvn2Eh4eTnJxM06ZNSU5O5oMPPtBZ49N3zpynKH1s2rSJ58+fl1mWREmQIs0O2pWUPGhXq9UKVW1TUlJITk4RZqfkcjkymRSFQoFCocDS0hIDAwMMDQ2Ry+VFfsKrW/cN5HIFERGP0Gg0Fb4GK1I2yOXyApcZygqlUombm1uB7QwNDQtto0QiKZQGVmGQy+VFnk0qDPoylorL0KFDWblyJV9++aVOuEFl4e7du2zYsKFAuQypVMrixYt55513GDt2bKmOUUGYm5tXyAPvli1biI6OJiQkpNzP/Trlns/l6OgoBGnpQy6X6+w3MDDQSaE2Nc0uqNe8efNCn7M4x7xKjq4M6E99Lio1atSoVNH+ryIj+4mvOM6LRqMhPj6B+Ph4EhISePHiBXK5HLVajZmZGRYW5hgZGSGTZTstUmn2qzSmoWUyKQ4O9kgkEu7c+QutVpvv50xERKT8kclkbNmyhXbt2uHt7c3gwYMr2iSBmJgY+vXrx+TJkwsVw9G7d2+GDx/OgAEDOHToUKWZPS8LLl68yIQJE/jxxx+FUI+KpOonoouUKjlOhAIFWdosIWA3Ow5Fg1qtJitLLaQ1pqSkkJKSSkJCAhkZGZiammBpaYm1dS1sbeug1YKHh3t+pyw1pFIpjo4OSCQS7t27J8y8vDr9LiIiUrHUr1+fI0eO6Aj6lYQVK1aUyoxHdHQ0Q4YM0YmJKojly5czffp0kpOTS+y4tGrVim3btpWoj1cxMjLi4MGD1K1bt8R93b17l82bN9OtW7dSsKzkiI6LiF7UajUJLxPQZmhJS0sjPT2DrKws1GrV//7NQiqVYGJiipVVDezt7TE0NNBxEnKOK28cHLJtuX//AVlZGpycHKuFWJSISHWhefPmxZ4Bf538NEeKQnE0X6RSqd7sm+JgbW1dqkUbZTJZqTkala28gfhrLkJWVhZpaekkJyeRlJRMcnIy6elqtFoFL9PiMTYxwNbGFhMjJQqFAgMDAx1F5MpIrVq1kMvl3Llzh9TUFBo2bFip7RURERERKRyi4/IPJDMzkxcv4oiLiyMhIYH4+ES0WjnGxrWRy80wNHTFyMgUCVoUmmukJj3DwMGpRAqW5Y1EIsHS0pImTZoQFnaJK1eu0rRpk2IrTIqIiIiIVA5Ex6Wak5SUTGTkE5KTU0lJSSMxMYmMDA0GBpYYGlqhUNhSp44FMlnuQFytNgtTQwU1ZYbcvnkV5wYNsK1th0xaNWYuJBIJSqUSH59W/PHHFcLD/6J+fTcMDQ2rXJkGkdLl0qVLLF68mP/85z8VlqUE2XIShoaGFZpeOmHCBN544w2hTtCraLVanj59WmZFIsuTjIwMkpOTK0VwqUjJEMUuqjm//36eK1ciiYlRolY7YWnpg51dR6ytW2Ju/gbGxrX0Oi2vYmZogJuFKTF/PyAy8nGpyH+XJ0ZGRjRp0pjMzEzu3bunU/tK5J/JkydP2Lp1a7nXFnqdhg0b5it0Vh6Ehoby+++/6923bt067O3tOX36dDlbVThevHjBy5cvC9X23XffpW7dulWyREhiYiISiSTP17Vr13Idk5qaikQi4ebNm4U+z7Vr15BIJHz//fd693t7e7N69Wq9+8aPH59LaDErK4suXbpgZmZWqIKfhUWccanm1FXHkxL7jFq1GmNsXHwVTRMDBU4yKU+jInmYno6Lq2uVihkxNTXF3b0Bd+7c4fr1P2natEmhtHxERMqSzz77rFLPZvj7+zNjxgyaNm1a0abopU6dOkyYMIGFCxcW2Hb06NG0bNmySn7vlUolO3bsAODmzZvMnj2bqVOnCsq2b7zxRgValzfTp0/n2LFj7Ny5k4YNG5Zav6LjUs3xNski+eVVzl1LpZn3kAJnV/JDIZVib2pIRMxT/tSk0dyjdLICygOJRIKpqSlNmjThzz9vcPHiRZo1a1ZiSXSR6kFqaipKpTLfJUStVkt6erpe+f7XSUtLw8jIqMAlycKUSoHsuDSpVFpq2XGpqan/01TK/+HDxcWFOXPmFKnv5ORklEql3r61Wi0pKSmYmZkVysbSrD/m5+eHn59fge0yMzPRaDSFcnDyqnT9OseOHUOpVBY7A0qhUNC/f38AYamrbdu29OnTp1j9lQfbtm1j4cKFzJw5k4CAgFLtu9ovFe3du5d33nmHt99+m969e7N69Wqh4No/AbkEOlpoeUt7h/Dz3xEf/xittngFIjVa0Gi12JgYkfD4Oddv/Vmlik1KJBIMDAzw9GxJ7dq1uX07nLi4uIo2S6QQTJw4EWtra72vwt789XHs2DHq16+Pqakp5ubmTJ8+Pddn+v79+/Tr1w9zc3OUSiUODg56Zd4Bli1bhpOTE0qlElNTU/r06cO9e/d02vj6+urYn3ND0sehQ4do2bKlUALD29ubI0eOFPt6z507R9OmTYXrnTVrFmq1boX4vXv35hrjnIKBr5Oamoq1tTXffPMNS5YsoU6dOpibm2NqaqqzJKNSqZgxYwY1a9bE3Nwca2trli9frrfPTZs24ejoiKmpKZaWlgwfPlynmOar9qnValavXi28f105OCQkROc69JVCyOHatWt06tQJIyMjYaxPnTql02bmzJm0b9+eU6dO0aJFC5RKJRYWFoSEhOQp8X/z5k38/f3x9fUlOjo6z/NXJ65fv857771Hjx49+Pzzz0u9/2o/49KrVy9iYmL45JNPmDlzJmPHjq1okyqEFmZg9PIxx2/uQlW/O7VqOSPNJ8hWo8lCk5XGy4x0YjTppGdlkZklQSsxJktihIGyBmnJqWRkZmBoaIhUUrV8YDc3Nx4+jODOnbu4ublWqYypfyJDhw6ldevWOtvWrFnD6dOn8fX1LXa/S5YsYe7cubi5ubFr1y6++uorjI2N+eyzzwBIT0+nS5cuJKodOwAAIABJREFUWFpasmvXLqytrdm2bRszZszAzMyM8ePH69gzadIk5syZg7+/Pw8fPiQkJISuXbty69Yt4Ql+/PjxQpG9uXPnkpSUpNe2a9eu0atXLwYMGMDKlStJS0tj3rx59OzZk7CwsCIv38TGxvL2229Tu3Ztdu3ahVKpZOHChTx8+BAvLy+hXaNGjYRZluvXr7NmzZpczs3r/X755ZdoNBqGDx+OtbU1iYmJOjMWQUFBHDhwgLlz5+Lp6cnhw4eZPHky6enpTJs2TWi3du1axowZw6RJkxg8eDB///03U6dOpXfv3pw9exa5XI6Pj49QZqVr16707NmTDz74ACDXjFTPnj1xdnYGYMeOHZw8eVLvNTx9+pQOHTrg6urKkSNHMDAw4IsvvqBLly6EhYXRrFkzINtRu3LlChMmTGDixIk4ODiwdetW5s+fj4eHByNGjMjVt62tLU2aNMHS0vIfMcMbFxdHQEAAdnZ2/PDDD2VSN67aOy4AN27cQCKRVDoRnfLGQwlG0mj2/rUfiaQX1tbOwr6srAwyM5PIyEggIyMRtToVqVSOQq4gTe6E1NAcmcwImdQAA6kcU5kBKtVN0P6vPACKKuW8yOVy6tZ1QqPRcP36nzRu3Ahra+uKNkskD7y9vfH29hbe//rrr/z2229MmTKFoUOHFrvftWvXCtWkO3XqREREBCtWrGDmzJlIpVKio6Pp3bs3o0aNokmTJkC2eNqRI0fYtm2bjuNy+PBhGjduLCivtmrVCltbWxYsWMCjR4+E2mSBgYHCMd9++22etp04cQKVSsWqVauEgoReXl6888473L17t8iOy/Lly0lOTuby5cvCzISvr69wY8+hXr16giMQGhrKmjVrCuxbKpVy5coVvQ8AZ86c4eeff2bjxo3Cjb1NmzbExsayYMECJk2ahEKhIC0tjVmzZjF06FChjpG3tzdWVlZ069aN06dP07lzZ2rXri0s+UilUurWrZvnElD79u1p3749kF0ZPC/HZfbs2WRlZXH48GFhrENDQ3FzcyMkJIQDBw4IbVUqFfv378fW1haAjh07sn//fg4cOKDXcbGysuL69esFjmF1QKPRMHjwYO7fv8+nn35aZo7aP8JxOXr0KC1atMDGxqaiTalwnI3gLU00W69uQ9usJ1lZCaSnx6HVajEyssLAwAIzMyeMjWsikRQUfJu9fp9TWTpNk4axtOD13sqCQqGgfn03FAo5f/75J02aNBGdlyrAzZs3CQoKolu3bsybN69Efb1ez6pv377s3buXe/fuUb9+fZycnFi6dClxcXEcOnSIJ0+eoFKpyMzMJCsrS+dYf39/goODmTRpEoGBgXh5eeHr61vsGSFfX18MDAx45513CA4Opl27dlhaWrJ3795i9XfhwgU8PT11llOUSmWp1NgJCgrKc9Zy3759SCQSzM3NdWT+a9SoQVxcHI8ePcLFxYXbt28TGxvLoEGDdI738/MjPDy8TIOY9+7dS48ePXQqVhsYGDBw4ECWL19ORkaGUKfO0NBQcFog23mqV68ekZGRZWZfVSEzM5MTJ07QunVrFi9ezLBhw0o1KDeHau+43L59m8ePH//jZ1tepb4SemalsOnyb3h4NMXevjMKhRJJCWdMjCRGaLSaKjXzAuDs7IxEIuXvv++jVquxsbEpk+lNkZITFxdHnz59sLW15aeffir1zLach5tXY5+++uorPv/8cxwdHXF1dcXExISYmJhc8RLjxo3D3NycRYsWsXTpUiwsLOjVqxczZ86kQYMGRbbF09OTEydOMHv2bCFlukOHDkyZMoWuXbsWub/Hjx+XWUV6hSLvoP9nz56h1Wp1ZppykMvlREVF4eLiItz4Xx9XmUxWrPErCtHR0XrrHTk5OaFWq4mPj883PkYmk6FSqcrSxCrDt99+S48ePWjYsCEjR47k7Nmzpf49rfa/zocPHwayn4ZE/h9rBVhbf0J0dB2eP39IVlbea9hFQYMGlVaVZ6BaZcXJyZE33qjLgwcPiYiIyHdNX6RiyMrKIjAwkJiYGPbs2YOlpWWpnyNH1yWn71OnTjF9+nSWLVvGnTt32L9/P9u3b9eJCXmV4cOHc/36daKioli+fDmXL1+mXbt2OsGlRaFt27YcOXKEuLg4du3ahUKh4K233ipWgUJbW1tiYmKKZUdJMDU1xdDQkJcvX6JSqXK9cmakcmYxKkJbx8rKSm/gbExMDFKptNrFpvz555/Mnz8/V3JCamoqQLEVxo2MjBgxYgS1atVixYoVXLx4UVj2K03+EY5LrVq1aNmyZUWbUulQKptTs+YsoqIsePToRon7k0gkyCVypEhRUbWePqRSKTY2Nri7NyAi4hF3794TnZdKxqRJkzhx4gQ//vgj7u6lU3H89ZvV/v37MTMzE9R0c4S9unfvLrTRarW5HBG1Wk3nzp1ZtmwZkH0THjFiBN9//z0vXrzIU+AtP4KDg3n33XeB7Jt/z5492bdvH6ampuzbt6/I/Xl5eREWFsbTp0+FbZmZmaSkpBS5r6Lg5+dHRkYGO3fu1Nmu1Wp5/vy58N7DwwMzMzP27Nmj0+727du0aNGCM2fO5OrbwsKCxMTEEtvo7+/PwYMHc4nZ7d69m7Zt2xYq5Tk/YmNjS8XO0iIjI4OQkJBcn6OjR48ClIpuz+DBg+nduzezZ88mPDy8xP29SrVeKkpKSiIsLIwBAwaIEu95YGjojI3NVzx48C4ZGcfx8Ch5dVKZRIYMGWmklYKF5YdUKqVmzZr4+LTi/PkLyGQyXFzqVSmhverK999/z4oVK+jXrx+mpqY6aapyuZx27doVq98PP/wQjUZD/fr12blzp5AxlJOdkiPwNXnyZKZMmUJycjIrVqzg0qVLOssucrkcGxsbPvvsM2rWrEmnTp2Ii4tj0aJFGBkZCVkpAMePHyc5ORnIlvzPzMwUbtYODg54enoC2dk9H374IQ4ODowcORKtVsv27dtJTk7Gx8enyNc6ceJEVq9eTZ8+fZg/fz5WVlbMmTMnlxMWFRVFWFgYgPDv6dOnBRkJf3//IumrBAQE4O/vz/vvv098fDzdunUjISGBzz//nJs3bxIeHo5cLsfMzIxPP/2UGTNm4ObmxqBBg3j48CHBwcFkZGQI4/IqrVq1YufOnfTv3x9nZ2cePHiAr6+vUELh+vXrPHjwAIC7d++i0WiEsTYyMhKqJ8+ZM4fdu3cTEBDA3LlzMTAwYMGCBdy6davEqsGPHj2iQYMGGBsb8/Dhw2LFFKnVakJDQ4HsZBNAJ0W9U6dORerX09MTf39/JkyYgEQioUWLFpw8eZKvvvqKESNGFLlKdl58/fXXNGzYkFGjRnHmzJlSW4Kv1o7LyZMnUavVxVoP/ichl1vi7PxfHjwYhURyhnr1PDEwKJ0gWy2aKhf3olQqadasKeHhfyGTZWctlJbwl0jx2L17NwC7du1i165dOvssLS2F9OKi8vH/tXfm4TGd7R//zJ6Z7IkREhJJRATVELGrnSKKV2lVG9X2pUVJUUtVVX9VxNKWarXaUrpoLdWithZvG1uVotaKKkmIbLIvs53fH+lMjUz2ycb5XNdczJnnPOc+J2e5z/Pc9/eeMoVx48aRlJSETCZj/PjxvP7665bfO3bsyLvvvsucOXPYtGkTcrmcUaNGMWrUKDZv3mwlkvbxxx8za9Ysxo8fT15eodPevHlzvv32W6t6SFOmTLE8fMwMHToUKAxy3bBhAwDjx49Hp9OxYMECFixYAICnpydLly7lySefLPe+NmjQgH379vHoo4/Sq1cvJBIJjz/+eBGH4MiRI5ZMKzPmTCkozM65Wy+lNLZt28bMmTOJioqylAzp1KkTW7dutbq2Zs2ahVwuZ968eUyfPh2pVMrgwYNZuXKlzVGPt99+m6FDh/Lwww8D4OzszLFjxwgJCQFgzZo1vPfee1brmI91o0aNLHE1gYGBxMTE8OSTT1qmARs1asTu3bsr7BSbMU+bV+blOScnx2K3mTsD00+dOmXlHJeGRCKxZMWNHTsWo9GIQqFg4sSJxWoUVQRvb2+WLVvGc889xzvvvMPUqVPt0q9EuCMY4b333uPw4cO8+uqrVlHTdZVJkybx7bffcunSJZycnGranFKZO3cuOTk5TJpUcUGtO1m0aDHaQ1t50Maux+XDZs0BXFx6WJYZDJkkJy/F0fE4QUHtUChKVo4sKDhN06YNih1GzcvLIzc/l5DmIQgIyErNUiofeXkCgiCg0djfKTKZTCQnJ3Px4iU8PDwICAhAoym6n4cPH8bXtzFPPDHK7jbcSevWoSgUlatsPWfOHN566y127NjBoEGD7GRZ7WLAgAHs3r3b5m+tWrXijz/+KLLcYDAQFxeHu7t7sXEzBoOB69evU69evVLfbE0mE3FxcTg6OtqtoF9iYiIGgwFvb+8ib61qtbrY+juTJk1i5cqVVssMBgN///03Hh4eVlk01UFubi4JCQl4eHiUqJ1UUFBAXFwc3t7epRagFASBuLg4jEYjvr6+lR4hjYuLw2Aw4OfnZ7cRgrS0NBQKRZkUg+1FTk4OTk5OnD17tsQRFPOxbtCgQanPyfDwcJ5++ulq0UMzq1R36NCBo0ePWv12z7xGfvPNN+zatYt33nnHMu/5/fff89hjj9UJp6U2IJe7oNVOJTV1DRcu7KZ168pPG0mRIZVIa32wrtFoJCcnh5ycHDIzM7l9Ox29XgCcSU7OIz//PC1ahNRoFV+R0omOjmbWrFk2fytuekMulxfRMrHVJiAgoEw2mLVF7ElJGS179+4tVsHaVqaMXC6vsYrYGo2GoKCgUtupVKoy2yiRSPD19a2saRbuTpG3B9XtIJaH8hzr2sI947hER0dz48YNcnNzcXV15dVXX8Xd3Z25c+fWtGl1CrncDS+vl7lxQ8/PP39Khw4jUSpLruFSFiQSCTpBhwKF5Xt1IggCJpMJQSgcpdHpdGRlZXP7dgbp6elkZeUilzujUrmiUmlxdm6OQlHo8Bbkx5OV+htn/zhLqwdaic5LLcYsEnc/URnlYBGRusg947gMGzaMb7/9liNHjrBt2zby8vLYvXs37u7uNW1ancTb+xVSUnw4c2YdzZq1wsXFq9LOhgIFBgzIkCGhehwXo9HI7du3ycnJJysrj4ICA/n5RoxGKQqFI0qlFienQNzdnZBKbV8OUqmEAHdn4jOyOX/uHCEtWti1+JuIiIiIvXFwcGD37t12Hf1bsWKFzVG86uaecVzmzJnDiBEjSExMZMGCBVUy3He/4ek5mrQ0CX/+uZ7gYCkuLvUr1Z9EIkGBAqNgRBCEahl1yc/P58L5C+j0Dri7N0OhcESjcUQmK1+8iEouw8/NiWvp2fzxx1lCQprfc9oOIiIi9w4ymcySNWUvKlrd2t7UnVSPMtCsWTMeeugh0WmxExKJHHf3kSgUT3HmzP/Iy8uyS79SpBgxlt7QDhiNRjyd1Lgq8tHpslAqXcrttJhxUMgI8HDG0VjA2bPnKpzJIiIiIiJScawcF3MtBnO6mkj1UlBQgFJZvHR2TSCVOlCv3hjc3N7i8OGvyMxMqnSgrVmoziAYKBAK7GRp8SikMvzdVUjzr5CV9TeCYDuQsUx9yaT4uTviJjFw7uxZ0tNrj6iUiMi9wqBBgxgwYAADBgzg1KlTNW2OSBWwaNEiy9/YLNxYVqwcF/PQd1UrKYoUxZzVUlsDP93cBtKw4XouXrxOSsrfxWYxlAe5RI4CRbVkHCllMvzcHCD3IpkZf2EyVUzZV28wkJWbh9KkJyclye6KkPcbs2bNYtGiReVap6CgwCKGdjfHjh2z6KyYP5cuXSq1z8TERLuc0/ca2dnZ/P3330UKSlY1e/fuJS8vj1atWtWqeLJ79fwq6ZqqKho3bkyrVq04fvw4586dK9e6Nh2XzMxM+1knUibMx7w2XaR34+zcDTe317lypYCbN+37wM4zVb3KrkYpx9/dAQf9JdJSz2Iw2Na+MGM0GsjKSiY+/gq/XbzMnmMn+T7mInuOSzlw2pfY+EHk5XWvcrtrI6mpqUXk0SvCnj17rFRwy8LTTz+Nn5+fTe0SQRAwGAwWbZaNGzeWekM2Vx42i7yJFIrQdenSBWdnZ/z9/fHy8mLp0qWVcmAMBgOpqallLkY4ePBglixZYjN9esSIEUgkEsvH1dWVhx56yCJUWFXUhvPLXtfenZR0TVUVo0ePZsmSJRXSjLMKzjXnwsfFxdWaIJz7BbOCo1arrWFLikcikaJWP0C9evO5ePFJmjQpoGnT4vUlyoJZUVeFigJTASqpyh6mFotKLsPXVcOt7FvcSsnHs14b5HIHBMFEfn42ycnXSUq6yu3bN0lLS0IiaYyDQyga9TgUyhbI1Q2RS51QShVIJA7ojZ8Cf1apzbWRBg0aEBUVxZIlS6p928899xxt27bFwaGoQGLHjh3ZtGkTADt37iQiIqLU/vz8/Hj11VeLKJPer5w7d45+/frRqlUr9u7di6enJ9u2bWPGjBkkJSURHR1doX6PHTtG165d7SaA6Ovry/r16wFIT0/n22+/ZdiwYaxatYoJEyZUun9b1IbzqyquvZKuqdqIlePSrFkzVCoVp06dslmCXKTqMCt6+vvbV7jK3kgkUhwcAvD338Lly2H4+FymZcuWlVarlEqkyJHbRR7bFoIgYDAaMRhNGE0mVOjRp13k1ytXyMtXkZycgF7viFrdFkfHITg4NMPPrzVyeckqqVWdGSWYh5erUb8vNzfXrlOWZe3PaDSi1+tLvXn27t2b3r1728s81Go1b7zxht36g8IpFo1GU2bl1dzcXORyebFVeXU6HVKptNTSE0lJSezfv5+BAwdWqCYOwPvvv09ubi7bt2+3KP+2bduWmzdvsmzZMl566aUib8mCIJCdnV2tyrAajYbu3f8d8RwyZAj5+fm8/PLLPP3000XOufz8fFQqVbVrSJXn/LL3tXdnvyWdX+W5pvLy8kotOmkOe6iqY211VclkMh544AEyMjKsKoiKVD2nTp1CLpfXmVILSmVDHByacft2OhcuXLRLJWWZRIYRo10qS+fl5ZGUlMT163FcuX6NUxcvc+LUGY4fPczxg/s5uW8Xwh+HyY6XIpXOxc/vJ0JCjtGkyQdotc/g7Ny1VKfF3gj/HENTRgam3FwEvR5jcjKCTodgqtoYg6ysLCZOnIi7u7tFqn7KlClW8W7bt29Hq9Wi1WoxGAysWrXK8v3u2jXZ2dlMnTqV+vXr4+joiKurK88995zNTKz8/Hz++9//4ujoiEajITw8nJMnT1q1mTVrlmVbWq22RCXZspCWlmbVn1arZfny5UXabd68uUg788dWBd3PP/+cwMBAnJ2dcXR0ZPz48TaH9fv06cOYMWPYu3cvLVu2xNHREbVazYEDB6za7dmzh7Zt26LRaFCr1YSHh7Nv375i92vixImMGjWKV199tQJHpZC8vDykUmmRh9zUqVOJjo62itXQ6/XMmTMHT09PXFxc0Gq1vPvuu1brmf925lGWJ554wnIMIyMjK2ynLXr37k1ubi7Xr1+3LHv//fdp2rSp5Rj269evSK2ohQsX2hzt7tSpU4VsLOv5Bfa/9qBs51dZr6mePXsyc+ZMVq9ejY+PDxqNBl9fX7766qsibWNiYmjVqhVOTk44Ozszbdo0hgwZwjPPPFPeQ1giRdz3nj178ttvv3HgwAGeeOIJu25MxDYnT54kNzeXtm1D7VYbozpwdHRk1Kih/Pbbb5YiXwpF5bKizNlGAAbBgFxSutSQXq8nLS2N5OQUUlKSSU1NRSaT4+LiTH5+PldPHKO7pgBHKTjLwEUBjh4gl0Bqni8G566VsrkyGG/dQuLqipCdDSYTsvr1EXQ6JP8cR6mDA1IHByRVXKH62WefZf/+/axcuZLg4GCOHDnCzJkzSUpKstygOnTowMaNGwHo168fERERjB8/HqDISMC4cePYu3cvK1eutATgTZ48mdu3b7NlyxartgcPHsTT05Pvv/+e9PR0Zs6cSf/+/bl06ZJFKj0iIsIiy79582YOHjxYqf3VaDS8+eabQKHjFBUVZSmMeCfh4eFFivQdPHiQ1atX85///Mdq+QcffMCECROYOnUqw4cP59KlS8yYMYPr16+za9cuq7YZGRmcO3eO7777jhEjRjBmzBjS09Ot4jlOnz7N4MGDefTRR1m5ciV5eXksXLiQiIgIjh8/btNx6ty5M4cPH6Zz584VPjZPPvkkn332GSNHjuTDDz+0CJiFhIRYihfe2XbXrl289dZbhIWFsXfvXqZNm0Z+fj4zZ84EYOzYsfTt25c//viDl156iRkzZtCxY0fA/lPjFy5cQCaT4eXlBcBHH33EpEmTWLBgAQMHDiQ+Pp5p06YxaNAgzp8/b4kpzM3NtRmrUqiqXX4ZiLKeX2D/aw/Kdn6V9ZpKT0/nk08+ISwsjNWrVyOTyVi4cCFjxowhPDzcUi4gKSmJAQMG0LBhQ7Zu3YparWbFihXs2rWrSNHOylJkj9u0aYOfnx+HDh2iZ8+edWYEoK5iNBrZunUrMpmM9u3Da9qcciGRgI+PN23aPMcnn3zK7t17ePjh/nZxXgCEYuZHbt++TVxcHNeuJRAfH09ubiYBAQEEBQXRuXMnGjVqhLu7GwqFgj/+OMuW338hvPpGsIvFkHgLmbYexps3kTo7g1yO1MMDZDIkdxT3k3p6IvnHgZVUk8jd3r17iYyMtFQdDg8PRy6Xs3//fotYYP369S3DyeZ6PMUNLzdu3Jg1a9YwbNgwoFCK//z587z99tvodDqrt/kHHniATZs2WYaVmzZtSlhYGJ9//jmTJ08GoGvXrnTtWuhgxsbGVtpxcXBwsNz4c3JyiIqKstnOz8/PSnn06tWrTJw4kc6dO1sVL8zOzmb27Nk8/fTTLFu2DCh0IlxcXHj00Uc5efIkbdu2teo7OTmZw4cP0759e5vbPnDgAHq9nvfee8/iwLVr146nnnqKy5cv23RcXnrpJV566aVyHImi9OrVi/Xr1/Piiy8SGBhI9+7diYyM5IknnrC6tmNiYvjmm29Yt24dY8aMAQpHKFJSUoiOjmbq1KkoFAqCg4MJDg62TAGGhobaZarPaDSSkVEoR5CRkcG2bdt47733eOGFF6wU0xcvXszLL78MwIMPPoggCAwePJgjR47Qp0+fStthi7KeX2D/a89MaedXea4pHx8fdu3aZXmxDgwMpHnz5vz4448Wx2XFihXk5uaya9cuyyhQr169aNKkSYl2VgSbr7OPPfYY0dHRfPrpp8yaNavS8QsixbNt2zZu375NWFibWp1RVBIajYYXX5zEmjUfc/DgQTp16oyjY/nnac11hAwGA3q9Ab1BR25eLimpKaQlp3HrVhJJSUmo1WrCwtoQEtKZhx9uSvfugcWeo2q1A9JqmNIWjEYQBJDJQK9H+Cc633DjBoqAAIwpKYVOilSKvFGjoh3cMdImqYFRtz59+rB+/Xr8/f0ZOHAgwcHBTJgwocJBjosXL0an0/G///2P69evk5uby99/F6bR5+XlWTkuPj4+VnPhbdu2pXHjxhw9etTiuNQGcnJyGDJkCGq1mq1bt1rtQ0xMDBkZGQQEBLBnzx7LcnPM1u+//17EcenYsWOxDxUorEGkVCp56qmnmDx5Ml26dMHNzY3t27fbec+KMnr0aAYMGMC6dev47LPPePrpp1m6dClbt261vLXv2LEDiUSCi4uL1T67u7uTlpbG9evXbU5j2IvLly9bVfNWq9VMmzaN+fPnW5aNGzcOKDz+sbGxpKWlce3aNaDw71kbsPe1Z6a086s8+Pr6Ws0GmM8Bc1IJwG+//UZYWJjV31ypVFaJwrhNxyU0NJT27dvz66+/8s033zBq1Ci7b1gEzp49y/79+3F2dqZz57qfxfXUU08ilUo5c+Y0bdq0KbW9yWQiNzeX7OxscnNzycrKQqfTodfrMRiMGI165HIFrt4utG8fjq9vYxo29MbFxRmpVMrffxsoKBBq3rE2GjFlZoLRiNTNDWNSErJ/5ouVzZsDIPf2rkkLS2XDhg0sWrSIZcuWMXXqVBo3bszo0aOZMWNGhep9md8iAVq1aoWbmxt//ln27CsvLy/S0tLKvd2qQhAEIiMjiY2N5ZdffrFMRZhJTEwEYP78+UUCEuVyuc2YwdJGJsPCwjhw4ADz5s1j8ODBAHTv3p2XX36Zfv36VWZ3yoSHhwdTp05l6tSpHDx4kJEjRzJo0CDOnj2LUqkkMTERQRBsJnLI5XJu3LhRpY5LkyZNLOnPjo6O+Pv7F7kXxMXFERERQWxsLGFhYWi1WtLT06vMpopg72vPTGVHvkvC7MTcGe9048aNMldQryzFBhC88MILJCQkEBMTQ0BAAB06dKgWg+4Xbt26xaeffopMJmP48KHFRnvXJRwcHHj00eHI5Qp++SWG8PB2cEcxxby8PFJTUy2xKJmZmajVapycnPHwcMfHxxsXFxdcXV3x8PDA1dUVNzdXZDIZ+aZ8HKS1NFVPKkWq0SD5R3na5ohKLUetVjN//nzmz5/PhQsX2L59O4sWLeLnn3/m0KFD5eorKyuLESNGMGTIED755BPLDXTZsmVMnz69TH2kpqZW6UOvvMyfP5+tW7fy5ZdfEhYWVuR3J6fCSuIHDhywa7Xmzp07s2/fPrKzszl48CDvv/8+Dz/8MLt27bJ7HRozy5Yto3Xr1vTt29eyrEePHixevJhnnnmGY8eO0a1bN5ycnFCpVGRlZVXpQ7I4HBwcePDBB0tsExkZadFcMU+3nThxgnbt2lm1Mz+IjUZjtb8I2fPaq0m8vLxITk6ulm0V67ioVCqmTZvG7Nmz2bBhA9nZ2XZNQbyfuXr1KqtWraKgoICBAx/G09Ozpk2yG66urowePQpXVxc++OBDgoODOX/+PFev/oXBYCQ4uBkhISH07dub4ODmODlSdwuNAAAgAElEQVQ5IpVKkclkyGSyYoOTVRIVBsGACRNKSS1z8iQSi9NSFzl58iTTpk1j3rx59OjRwxKEKZFImDFjBqmpqUXOUVdXV0t8wd1cvXqVzMxM+vbta/VAKy5T8e6b3YULF7h69SrPP/98JffMPmzdupU33niDmTNnFjv63LVrV1QqFV988UURx+XmzZsVihWcPHkymZmZrFu3DicnJyIiIhg4cCBubm7s2LHDpuNiNBqJi4urVFzBxx9/jCAInDlzxuqFypzlYv6b9u7dm1WrVrFlyxYef/xxSztBEEhKSioyKmWeMijuvKkKTp8+zbBhwyxOC9g+D80ZNXceO4PBUOWjM/a+9mqSNm3a8M4771id70ajsULBzaVRYspGgwYNmDt3rmVuMzk5mUcffbRULQGR4jl69CgbNmwAoG/f3oSENK9hi+yPXC5n6NAhNG3alAsXLuLt3ZDAwEAaNPAqfeVikEgkyJGTaEjETepWe0df6iDNmzcnLi6OF154gVWrVhEcHMyVK1f44osvCAoKsjlc3b59e7Zs2cLw4cPx9/fn6tWrdOvWDY1GY1lnyZIl+Pj44OTkxObNm3n77beBwgyOO+e9T5w4wbhx43jxxRdJS0vjxRdfxNXV1SqF8syZM1y9ehUojG0wmUx89913QOGbt/khfuPGDY4fPw5g+ffnn3+2ZIz06dMHR0dHdDqdJdPHnO1x/vx5S5+hoaH4+flx7tw5IiMjCQwMpF+/fkVUftu1a4ejo6PlXjl37lwcHR155plnUCqVrFu3jiVLlnDu3DmbCrAl0bJlS55//nkaNWrE2LFjEQSBTZs2kZWVVewI+OTJk3n//ff5v//7vwqnRK9YsYKHH36YiIgIZs2aRcOGDTl06BBz586lc+fOlriJYcOG0adPH8aNG8ft27fp378/6enpzJ8/n3PnznHx4kWrZ0VQUBBubm688847lmDdxMTEKn0h7tChA5s3b6Zv376WjB3zcbkzTb1///7IZDKmT5/O66+/TlZWFtHR0UWmK+19ftn72isPZb2mykpUVBTvvfceQ4YMYfHixZZ7QEJCQrn6KQuleiABAQEsWLCA6OhofvnlF06dOkWfPn3o3r17jQwP1kUEQeD06dP88MMPJCQkoFKpGDJkMI0b170phfLQqlVLWrVqadc+G8gbkGsqm9y1oNcjGKq3xkpdRKPRsGfPHiZPnkzfvn0t89a9e/dm9erVNkfB3n77bYYOHcrDDz8MgLOzM8eOHSMkJAS1Ws2WLVsYO3as5aHUpUsX5s6dy/z58zl79qzVCMSQIUNISkqyZMn4+fmxa9cui/gZwJo1a4qkJZuVSBs1amQJEjxy5EiR1MtXXnnF8v/Y2FgCAwPJysoqomT65Zdf8uWXXwKFow7PPvssP/74Izk5OcTGxtp8wJplAMzb8fDwYM6cORbNDn9/f8tDqLyMHz8enU7HggULLHLxnp6eLF261JKBcjfmv11lhL/69u3LwYMHiYqKsuyzSqUiMjKS6Ohoq/Nh27ZtzJw5k6ioKEtx3k6dOrF169YiL7gqlYp169YxduxYy1RN06ZNuXz5coVtLY0PP/yQ0aNHW0bKmjRpwuLFixk3bpyVlktAQABr165l4sSJbNmyBZVKxezZs4sE8Nr7/LL3tVceynpNlRVvb2/27dvHiBEj6NWrF1KplMcee8wqK89eSIQyVrgzGo3s2rWLrVu3kp+fj4ODA6GhoXTo0IGgoKBqVyOsCyQlJXH06FGOHz9u8dxbtmxBt25dK5R1U14WLVqM9tBWHnQq+ltcPmzWHMDFpUeF+791axDLl4+pknS3kigwFaCUKPnz7zzQKQgOVhQqzBoMGNPTkbm7Y7hxA5lWy/HfTrBx4RxGu9muQv1Z3hgMDddV2JakpNUMH36JJ56o2gD21q1DUSgqN0U2Z84c3nrrrRIl1wsKCoiPj8fLy8sSt1EcgiAQFxeH0WjE19fXZmxAfHw8CoWiyLSBLdLS0sjIyMDPz69O6RndjcFg4Nq1a6jVaho2bGiXe2NiYiIGgwFvb+8Sj43JZCIhIYHGjRtXeptQGIuXk5ODr69viSPtubm5JCQk4OHhUerUt16v59q1a2g0GryLCVpXKBQsWrSIadOmVcp+M2lpaWRmZuLn51fi38NgMHD9+nXq169f6vlvb+x97dUU5vPf09PznzhFNx5//HE+/PBDm+0feOABOnbsyJo1a6yW5+fno1ar6dChA0ePHrX6rcxzPjKZjIiICLp168bGjRs5fPgwR48eLdKhiG0aN25E9+4P4eVVv9q22bt3L1bu3IqfA7jdQ7N7KqkKfcINJL9doMCvMfnndKiaBWNMu42svhYkksIAWakUSR2pvVFbUKlUZQ6KlUgklvpmxdGoHIHKHh4eVrEIdRW5XG73wOKyKgVLpVK7OS1AmRxOwDJFWBYUCoVF+6Mk1q5dS0xMDPPnz7epWVMeynpuyeXyasuMuRt7X3vVTUJCAlFRUaxYscKyH0uXLiUzM9Oi53Qny5YtIyYmhmvXrlkECctKuR9nrq6ujB8/nmeeeYbTp09z9OhRmzLe9xqFtTjKF2SkUCgICmpKQEBAtYyw3E14eDhDo2aw74uPeUhIo768UDSutiMYDAg5OQj6QgVdQVeAISEB481EBH3hcLS8vheNurTgrOtNbijdaSwHxZ0xNP+8gdSF/RUREbFmwoQJlmkTVR0OfL+fUKvV3Lx5k4CAANq2bUtSUhJXrlxh+vTplmmtO/Hw8KBRo0aMGTOm3EWdK/werlAoaNeuXZG0snsVg8HA6dMnS29Yyxj8yCO4u7mzb91qwnOu0biW3QMEnQ5jWhqm9IxCp8RoAkFA0OnAWBifIlEqkTdsiOrBB5HckeWQl2eipcmLv4TzXNJdoqmiqRi0KyJyD3B3vSOR2o+HhwcxMTEcPHiQI0eO4OLiQpcuXQgNDbXZfuzYsYwdO7ZC27qHJhBEbKFQKOjSrSsaJyfWLl5Ap5xEWlZCoFcQDOj1KeTmnkIuzy59hTvXNZkwZWRgjI/HcDMRBAGJQoHU1RWJs3OhDL7JhESpQurpiVRdshNiMhX6Ng84tiLOEMdl/WWaKZqhktYy70xERETkPqFHjx706NGjSrchOi73AUqlkg4d2uO7ajVTnnsORW4K6jLGPhqNuWRnHyYz8yfy8s6Sn38Cb28HwsLa0qPH8BIDcwW9Ht2fl9FfuoQpJQWkUmRaLYqQENR9elda2t7R8d/1G8sL5/Uv6f+khTKkTMUZRURERETqHuLd/T6iYcOGvL5kCeui30KbdAU0YDBkYDRmYDJlYzRmIpUmI5H8hVR6GYUiDkfHHB54wIemTQPx9h6Cv38ULi6FFQtNefkYk5IQDP/EouTlYbhxs1D+3mRCIpch92mEulfPwlEVOwecZGebMBrB1bXQgWksb0y+UMA53Xn8FU1wkbrYdXsiIiIiIjWP6LjcZzRv3pwnoqaz7YvPKbi6BYViD+7uOjw9BTw8jGi1KrRaLVptO3x9/4Ozc2FanqDTYUxOxnj1Lwr+cVQsxZv/8UckKgcUzYKQ1auHpBrS8+RyCVKpYKmgChCkaEq8IZ5Y/RV85fbLrhCpGxw7dox33nnHatnrr79OcHBwieslJiZSv379WpuGXVBQQFZWlpW2jYjI/YrouNxnSKVSWrduTcOGM0hKSkKhUODk5ISTkyNOTk7I5XIEvR5jcgqGM6fJSSvMGJMoFMjqa5F61kOiKDxtJA4OSJ1dLN+rG50ul2XLlqHX68jLyyM0NJQxY56ikbwRzlIXruhjSTPWnkJ99xNardaiJgqF6bydOnXitddeKzZYzx6Yq4tDobT7oUOHmDRpUomOy8WLF2nRogXz589n7ty5lbYhNTUVtVpdbiXTknj66af5/vvvSU1NxUFM8Re5zxEdl/sQqVSKl1d9i6aMKSsL3fkL5F/5C1lKMgYXF2Q+PihbtcKhS9n0I6obo9HIlClTadGiNS+/PBGj0chzz43DYNDz7LPP4Cp1obmiOUcNv2IQDDVt7n3JI488wtSpUxEEgRs3bvD+++/TsWNHDh8+TNu2batkmx07dmTTpk0A7Ny5k4iIiFLX8fPz49VXXy2idFpRGjRoQFRUFEuWLLFLfwDPPfccbdu2FZ0WERFEx+WeRzCZEHJyMeVkF6bhCAKm7BxMyckY/9HfkarVyP38CIw5hNemzZzdsgmdj21Fy9rC999v59y5MyxduhgoFEh87LGRvP76G/Tv359GjXzQSDWEq8K4LPkSEKX/qxtvb2+6d+9u+f6f//yHkJAQpk2bxoEDB4q0z8/PR6VSVbsKt1qt5o033ihT29zcXLuOpNzZr1wuL7ZKfO/evctc0ycvLw+1Wl1im5ycHDQaTanHWq/Xs23bNsLCwmpMmE1E5G5q54SuSIUx5eWhv/IXBSd/p+DECXQnf0d/6RLG+ASMN29ivHULAEWLEBwHR+A4OAJ1n94ogpoiODshMRiot3NnDe9F6WzZ8i3+/v6o1f8G4LZu/QAGg4Hvv99eg5aJFIeDgwOdO3fmwoULVsvff/99mjZtikajQa1W069fP6s6MgALFy5Eq9UW6bNTp05ERkaW25a0tLR/Yrn+/ZjrC91NVlYWEydOxN3dHUdHR+rVq8eUKVMs1ZIBtm/fbunHYDCwatUqy3dbaqh9+vRhzJgx7N27l5YtW+Lo6IharbZy6GbNmmVlX3HquT179mTmzJmsXr0aHx8fNBoNvr6+fPXVV0XaxsTE0KpVK5ycnHB2dmbatGkMGTLEqqDlnXz00UeMHDnSbqNRIiL2QBxxqePor17F8PffmLILi4FJHNTIvRsUSt9LpSCRIHV0ROLohERWsp+aMnAgDdd8gsfOXdz473O1VnY2PT2dS5cuER7eAb3+3+Xe3t7I5XJ+//33mjNOpEQuXrxoVZ/mo48+YtKkSSxYsICBAwcSHx/PtGnTGDRoEOfPn8fRsVB0KDc31ypmxkx6ejpZWeVTtIZCifo333wTKBzpiYqKslTxvZtnn32W/fv3s3LlSkuF4ZkzZ5KUlGRxDjp06MDGjRsB6NevHxEREYwfPx7AZo2fjIwMzp07x3fffceIESMYM2YM6enpVrL5ERER+Pv7A7B582YOHjxo07709HQ++eQTwsLCWL16NTKZjIULFzJmzBjCw8Mt8vpJSUkMGDCAhg0bsnXrVtRqNStWrGDXrl1FCgeaefDBB2ncuLHN0Z6ff/6ZefPm2VwPYO/evWIhXpEqQXRc6hCGpGR0Z85gTLiBUJAPgKJFC5ShbZC5u1W6f10jH7LbtsHpxEkcz54j54FWle6zKrh58yaCIODh4WpJhTbj6KipkjLqIuWnoKCAjIwMBEEgMTGRt99+m5MnT1piUMwsXryYl19+GSh8UAqCwODBgzly5Ah9+vSpEtscHBwsjkVOTg5RUVHFtt27dy+RkZGWiszh4eHI5XL2799vyWirX7++5eEulUrx8/MrdWonOTmZw4cP0759e5u/d+3ala5duwKFVYeLc1wAfHx82LVrlyUrKjAwkObNm/Pjjz9aHJcVK1aQm5vLrl27LKNAvXr1KlGLqWvXrly/ft3mby4uLrRqVfw9Qiy8K1JViI5LLUHQGzBlZRXW6DEawGjElJuL6XY6wj9vglIXF5QtWyJ7qJuV9L09SYkYhNOJk3js3VtrHZeMjEwANBpnMjNNuLj867woFEry8vJryjSRO1i7di1r1661fPf29uazzz6zersfN24cAL///juxsbGkpaVx7do1oNChqA306dOH9evX4+/vz8CBAwkODmbChAlMmDChUv127NixWKelvPj6+lqlcptHbuLi4izLfvvtN8LCwqymrpRKJa6urhXaZmhoKCtXrqygxSIiFUd0XGoAwWTClJ6OIT4BwTxPLpEgUShAoQCpBIlMjtTFFUVAAFLHSmj0l5PbvXvhu2QZHnv2ET9lMkIJpexrCrm8UCNGEATulovR63XVXo5exDaPPvoor776KgD16tXDx8enSJu4uDgiIiKIjY0lLCwMrVZLenp6dZtaIhs2bGDRokUsW7aMqVOn0rhxY0aPHs2MGTNwd3evcL9VOY1idmLMhQoBbty4YdcA24SEBI4ePVrs78OGDau1ujgidZva91S6BxEMBvSxV9BfvoygKwCJFJmHB3LfxkjN8/0yKRKVAxKVslrE24rDpNGQ0bEDmj8vo7iVVCuzi8xBijk5WahU/w5HF1bwzsHPz8+qfb6YUFQj1KtXjwcffLDENpGRkRgMBuLi4vDw8ADgxIkTRYq3mh+ARqMRWTVfH2q1mvnz5zN//nwuXLjA9u3bWbRoET///DOHDh2qVlsqg5eXF8nJyXbr7+jRo8XGxsC/WWIiIvZGdFwqiSAI/1b7EwqlZI0pqYWxKCkpCEYjErkcZfPmqPv2QVoHdBiuz56Jwc2t1gbn+vj44Onpyc2bSWRmmvDwKHyQJScnYzQarTRCwsPDed8niP2J5+juKiCrnbt033L69GmGDRtmcVqgMIbpbszOalxcnCUmw2AwVPnozMmTJ5k2bRrz5s2jR48ehISEEBISgkQiYcaMGaSmpuLp6Wm1jqurKxkZGVVqV0Vo06YN77zzDjdv3qRhw4ZAoSNYWnBzXFwcXl5eRVK1hw8fXnj/ExGpZkTHpZyY8gsQMjMR8vMKNVL0BoTsbEzp6Qg6HQBSV1dU7cORurnV6OhJRTFUYvi7OpBIJAwc+DBff70JhUIPFB7jCxcuIJFI6NvXOqBz+fKlLH3zTY7E/ko7Bx0O4uh1raFDhw5s3ryZvn37WjJ2zNNLubm5lnb9+/dHJpMxffp0Xn/9dbKysoiOjiYtzVoZ+caNGxw/fhzA8u/PP/9syUjq06cPjo6O6HQ6du3aBWDJJjp//jzfffcdUBi/4efnR/PmzYmLi+OFF15g1apVBAcHc+XKFb744guCgoJsThW1b9+eLVu2MHz4cPz9/bl69SrdunUrt/7LmTNnuHr1KgCXL1/GZDJZ7HNwcKB///7l6i8qKor33nuPIUOGsHjxYtzd3VmyZEmJweybNm1i5MiR9O7dmx9//LFc2xMRqSpEx6WMCAYD+YePgFRaGBgrlxXGpcgVyLzqowgJQeogDotWF2PGjGHnzl3ExBxiwIDC7I3vv9/BI48MJji4mVVbd3d3Jk2fzjdrPyHmyB56OOqQiyMvtYIPP/yQ0aNHM2rUKACaNGnC4sWLGTdunJWWS0BAAGvXrmXixIls2bIFlUrF7NmziwTwHjlypMj0xSuvvGL5f2xsLIGBgWRlZRXRJvnyyy/58ssvAfj444959tln0Wg07Nmzh8mTJ9O3b19LzEjv3r1ZvXq1zRiOt99+m6FDh/Lwww8D4OzszLFjxwgJCSnXsVmzZg3vvfee1TKzzY0aNbIKvC0L3t7e7Nu3jxEjRtCrVy+kUimPPfZYkanVOzHvr5ghJFKbkAjiWF+ZMOh1nNz/ExK5HInaARQKJPd64JnJVKgFU0s5efICy5dHM2hQf2JjryCTSZkx42WbuhmCIJCZmck3X3xB7LbPecTdiEoKn+WNwdBwXbm2Kwgm8vMvk5d3gdTU9Uyf3oaHHy7f2295ad06FIWicplkc+bM4a233mLHjh0MGjTITpbZh7S0NDIzM/Hz8yvxIWkwGLh+/Tr169ev9iDsgoIC4uPj8fLyKnXbgiAQFxeH0WjE19e32uNySsJgMHDt2jU8PT1xdXXFzc2Nxx9/nA8//NBm+4SEBOrXry9qsohUK/n5+ajVajp06FAkCFwccSkrEimyep6lt7sHUMYn0HDdZ0jz8ri64P9q2pxiadOmOZ9++hFxcXEMGPAwbm7Fa9lIJBJcXV3574QJfCRXsP6bz3jCQ2+zrSCYEAQDYEQQDBgMqej1F8nLO05e3nEKCk7i5+dJ27bNaN68RZU7LfcDHh4eVnEuxSGXy2tMel6lUtlUwbWFRCLB19e3ii0qHwkJCURFRbFixQrLfixdupTMzEyGDRtW7Hq2ssFERGoS0XERscL5t99w/+kA9bZ9x+1ePWvanBLJyxMwmWQEBpbvQTZu3H/51tOTH776lHSDHqUuEYPhFnp9EgZDGnJ5ChqX20jVSbir0vBwL8DX15eGDRvi7x+Jl9d0sdidSJ1DrVZz8+ZNAgICaNu2LUlJSVy5coXp06dbprVEROoCouNSBdTb9h3uP/6E88lC6XmTgwPJ/xlGyiMRFNSyt7C7yWrXjqx27fDYu7emTalSBgwaiATYsfN3TMI8GjVS0bChCq1WiaenM271PUlyNBHs0ZlAd7G4nEjdx8PDg5iYGA4ePMiRI0dwcXGhS5cuhIaG1rRpIiLlQnRcqoCUoUPIbB/OA48UDr/+tXwpmR071LBV5cPoUHJ12dqAg4OEikZoOTg4MHBwBA/17IHJJKBUKlEqFSgUCmQyGYIgoEPHkfxjOBucqC+vb1/jRURqiB49etCjR4+aNkNEpMKIjksVofpHi6LAt3Gdc1qAWh2UayY7W8BoBHf3imU8KJXKYuMqJBIJKlT0UD/E/rwDtMBEfVl9pJLaf1xERERE7mXEu3AV4XysUEMi/aGHatiSexcHBwlqddWmaRowkN4og8ktXiLOFIdJMJW+koiIiIhIlSE6LlWE66HDAGR06VzDlohUlH3uPzKy1eO81WQhcU5x/Or4G3HG8mlniFQdx48fp6CgoKbNqFOkpaVZ6eOUh9TUVKvaR7UJnU7Hr7/+WtNmVDmHDh3CaCy9hklKSkqt/VvZA9FxqQLkKalo/vwTk0ZDdmjJtVpEKk5+vkBenv1liNJlGSz0XczsgDlcV8XRK70nm85+zZC8wSQbUjie/5vdtylSPn744Qf69u1bbhG2+534+Hgeeughfv755zKvo9PpeOqpp2jcuDF///23ZXlWVhajRo2y+nz77bdVYHXJFBQUMHDgQNasWVPt265uVq1axfDhwzEYDCW2Gzt2LIGBgZw+fbqaLKteRMelCnA9dBgEgcz24QiiaFOV4eQkwcXF/lNFr/vPZ4t2K03ym/DhpQ+IvrKIRjoflBIl7RzCcJe580fBH+gF2zowIlXL1atXGTlyJJ988glNmzatdH87d+5Eq9Xa/G306NEolUquXLlitfyHH35AIpHw5ptvFlknJycHiUTCuXPnivzWo0cPtFqtpcyAmdu3b+Pk5FSsnkp4eDirVq0qsvzEiRNIJJJiP6tXr7Zq37p1a6Kjoxk2bBi3bt2yua27efPNNzlw4ADXrl0roqFjMBgwGAzk5+ezceNGzp8/X6Y+7cnUqVPJyMgoojJcGzAYDKSmpqLX2+desWbNGi5cuMC8efNKbLd9+3YGDx7MsGHDyjRCU9cQHZcqwPXwP9NEnTvVsCX3NuUZcTFR9mHTCQkvEBU/mY3nviAsu22R3wPk/mikGi7rL6MTdGXuV8Q+TJkyhR49ejB8+PAq31Z0dDRKpZI5c+ZYlplMJmbOnIm/vz/Tp08vV3+vvfYaKSkprFu3zmr5Bx98QE5ODnPnzi1Xf4GBgWzbtq3IZ/DgwUilUquCo2aeffZZAgMDefnll8u0jXXr1jF06NAizp2zszObNm1i06ZNfP755+Wy21789ttvrF69mvfff79WVqI+duwY9erVY6+d5CUcHR1Zvnw50dHR/PnnnyW2feaZZ7h69SoHDx60y7ZrE6LjYm8MBlyOFc61ZnQW41uqEnNh7pL43ekUE4JeZLN2S5n7bZYXxJO3RiMvJulOKpHSRN4EF6krf+j+KI/JIpXkwoUL7Nixg6ioqGrZno+PD3PmzOGbb76xFG1ct24dZ8+eZfny5eUWIuzVqxddu3Zl+fLllhiEgoICVq5cyeDBg206GiXh5ubGkCFDrD6tW7fmp59+4vnnn6d9+/ZF1pFIJERFRfHVV1+VOtWm0+mIj4+nfn37yAEIglBqNeo725YWw7R06VI6depEeHh4qf0ZjUarwp3FodPpyM/PL5ONUOjIlnWfSqMs9g0aNIiAgACWL19eYjtzBfDY2Fi72FabEB0XO+N0+gyy7GzyAgPRN/CqaXMqjESnQ2qn4c2qQqOR4ORU/FTRDs+drG24jl9dfsXekTAyiQwfmTfeMh8O5v3Pzr2LFMdXX32Fp6cnvXr1qrZtTp06lYCAAGbMmEFubi6vvfYaffr0KVKksazMmzeP2NhYS6XnL774gsTERF577TW72DthwgTc3NxYuHBhsW2GDh2KQqFg8+bNJfal1+sRBKHStZb0ej1z5szB09MTFxcXtFot7777rlWbzMxMtFotX3/9NVOmTMHZ2RmNRkO7du04efJkkT7z8vLYtm0bI0eOLHa73bp1Y/z48URGRqLRaHB0dKRDhw6cOXOmSNvTp0/Ts2dPHBwcUKvVhIeH87//Fb229+7di1ar5dixYzz//PM4OTnh4uJCz57/Ko3PmjULrVZrqQn2xBNPoNVq0Wq1REZGWvWXlZXFxIkTcXd3x9HRkXr16jFlyhSys7OL3a9Ro0bx9ddflxiAa67ZVh4nrK4gOi52xpxNlNmlbk4Tqf+8jPfqD1GkpeF88iT1N36NIiWlps2ySXa2QGZm8S5JROogJsdPqrLtSyQSGsob0FQeyLH8X8kz5SHWLK1a9u/fT7t27WxWZa4qVCoVb7/9NgcPHmTo0KHcunWryEO3PPTp04fOnTuzdOlSBEFg2bJlDBo0iHbt2lXa1q+++ordu3ezYsUKXFxcim2n0WgIDQ1l//79JfaXnp4OFE4LVYYnn3ySlStX8sYbb3D48GEmTZrEtGnTWLx4saWNIAikpKQwadIkBEFg27ZtbNiwgVu3bvH4448XCUg9dOgQBQUFdOhQvE5Weno6H330EQ4ODuzevZu1a9dy+fJlBgwYYDWac/PmTbp3705WVhb79qTjUJUAAA43SURBVO3j559/xs3Njb59+xYJcNXr9aSkpDBixAhOnDjBjBkzWLhwIaNHj7a0GTt2LBs3buT1118HYMaMGWzcuJGNGzcWmV589tln+frrr1m5ciW//vorr732Gh999BH//e9/i92vzp07k56ezu+//15sG2dnZ2QyWYkOUF1FFKCzM3U9DTqvWRB5zYK48fz4mjalVJRKSalTRQ7GqlcA9pH7IJFIOa+/QHNFMI4Sxyrf5v3KxYsXrR4Q1cXgwYPp378/e/bsISoqihYtWlSqv3nz5tG/f3/mzp3L+fPnWbt2baVtTE9P56WXXmLw4MFliv8JCAgoNYX4q6++QiaT0a9fvwrbFRMTwzfffMO6desYM2YMAJ06dSIlJYXo6GimTp1qVXn6scceY8WKFZbvWVlZPP/888TGxtK8eXPL8osXLwLQrFmzErffuXNnPvroI8v3+vXrM2jQIL788kvGjh0LFP49jEYje/futYhS7ty5k6CgIGbNmsWuXbuK9NumTRu+/fZbm050cHAwwcHBlqnE0NBQevfubdO+vXv3EhkZyZNPPgkUBmLL5XL279+PIAg2q6Wbg6QvXbpEWFiYzX6VSiU9e/bk22+/ZcqUKdVeTb0qEUdc7IjiVhLqK1cwOWrIflBMg65qpFIobQRbStUK1EHhyIuP3Bt/eRNOFJwk3Zhe5du8HzEYDKSlpeHu7l7t274zNiMzM7PS/fXr14+OHTuyYMECBgwYYDMWpbzMmDGDnJwcm9lHtvDw8Cg2s+iXX34hLCyMBQsWsH79eiuHobzs2LEDiUSCi4sLe/bssXzc3d1JS0vj+vXrVu39/f2tvgcFBQEUicdJSkqyVH0vibvVsQcMGICrq6vV9NP27dsZNGiQVVulUsmIESP48ccfbcbavPjii3YZ+evTpw/r16/n7bff5tKlS0DhdN/mzZttOi137lNpmWHmFHGzA3avIDoudsT9wAEAssLCEOTiYFZVk5srkJ1de0SWPGQedHLoyG+6E2VyXj5rsJ4nWjxJ57bd6Ny2GwNaR/BOoxVccfirGqyte5jjLeQ1cG1t2LCBw4cPM2rUKNauXWsXsbOXXnrJ6t/KEBMTw8cff8ybb75J48aNy7SOUqksNv7B2dmZgIAAdDpdpbVyEhMTEQSBkSNHEhERYfksXLgQuVzOjRs3SlzfHF9zdzxHQUEBMpms3M6DRCLBx8fHartJSUn4+PgUaevr64vBYOD27dtFflPYSepiw4YNTJkyhWXLltG8eXN8fX2ZPXu2zW2aUSqVQOnxK5mZmSQnJ+Pj42Nz/+oqouNiL4xGtN9uAyDvrjcGkaqhUMeldp3CComCrqouXDbEkmZMKzHmZUxiJPOvzkMn0aGT6FhyZRFR8ZMJzBerUdtCrVbj6OhotwyOspKZmcnMmTMZMGAAGzZsICQkhBdffLHS8Uz16tWz+rei6HQ6xo8fT1hYGJMmlT2mKyMjo9hsodDQUDZt2sQHH3zArFmzbAbHlhUnJydUKhW5ubno9foin27dulWoX61Wi8FgKKKJUxZu3bqFl9e/yRMeHh4kJSUVaZecnIxUKi11VKcyqNVq5s+fT3x8POfPn2fSpEl8+OGHREREFLtORkYGQKnZXubU9+PHj/Piiy/a1e6apHbd9esgsvQMGqxdR/D4F3C4UvimrN22jUYrVlq+i1QNOp1AQUHtC4Z1kDrQVB7IdUMcyaaSA5vjVPEAtMgNoVVOq+owr07TuHFjEhISytS2oKDALsq68+fPJzk5mSVLliCTyViyZAm//vprpeNSzCMFlZ1uWLx4MZcuXeKjjz4qV/ZPXFwcjRo1KrFN//79AcqltHs3vXv3pqCggC1brCUJBEEoswieLcwjS6WdD3dP8xw5coTU1FRCQ0Mty/r06cPu3buLpCNv27aNzp07o1ZXLFbO7PCYHY27OXnyJD179rRorYSEhDBjxgxmz57N4cOHSU1Ntbme+bwu6e+Xl5fHiRMn6Nu3b7FTTnUVcT6jkhjdXEkc+zSJY5+uaVPuO4zGwk9txF3mjkqi4pzuPCnGZFoobQdzHnU9CkD3292r07w6y0MPPURMTEyZ2g4cOJD9+/fzzTffMGLEiApt78KFC6xYsYJnn32Wli1bWvrt3bs3s2fPZvjw4RV+G7eH4/LXX3+xYMECunXrxo0bN4pMu/j4+Fg9oO/k1KlTPP300yX2bw7ozMnJKfKbTqezBK2aRz3Onz9vSfMODQ3Fz8+PYcOG0adPH8aNG8ft27fp378/6enpzJ8/n3PnznHx4sUKTf899E8B299//71EBeWffvqJpUuXMnLkSK5fv05kZCRardYSDAuF6sDbtm1j2LBhvPXWWyiVSqKjozl//nylnLagoCDc3Nx45513LMG6iYmJlkDd5s2bExcXxwsvvMCqVasIDg7mypUrfPHFFwQFBRUbz/X7778jl8vpXIJWWG5uLoIgoNFoKmx/bUUccRGpszg5SXF1rb2nsEaqIdyhHSYEzuqKyr8DHHItzELrklE3s9Cqm0ceeYTz58/z11+lj2aaYyIq87b54osv4uDgwBtvvGG1fMmSJaSkpJQqvV4SZoelMvadO3eOgoICDh48aBU/Yv4sW7bM5nonTpzg1q1bDB48uMT+VSoVcrncZnBqVlYWQ4cOZejQoYwaNQqAL7/80rLsxx9/tLTdtm0bkZGRREVFERgYSFhYGMnJyWzdurXCMUsNGzakXbt27Ny5s8R2YWFh7Nq1Cz8/P8u01I8//mj1QA8MDCQmJobr16/Trl07WrduzcGDB9m9ezddunSpkH1QePzWrVtHbGws7dq1o1WrVjz//POW3zUaDXv27CEgIIC+ffvSqFEjunfvTr169fjhhx+KdWp/+OEHevToUWKautmZvJeyicyIIy4idZbsbBNGI7XaeQEIUTTnsj6Wv/RXaSL3QyoptPdP9WVuKZKop69HcF7JKZ0ihQwYMICmTZvy8ccf89Zbb5XYds+ePaSmploURCvCnQ/fO2nTpk2la8B07dq10nEygwcPrlAfa9euJSwsrNSHslwup3nz5pZslzvx9PQs87YdHR157733iI6OJiEhAQ8PDzw9Pa3auLq62uyve/fuxW5n8uTJTJgwgeXLlxfJHjLj5eXF9u3bSU5OJjMzE39/f5sOQVhYGBcuXCAuLg6DwYCfn5/NdoMGDSrXMR8yZAi3bt3i2rVraDQavL29rX4PDAxk586dFBQUEB8fj5eXV4nORkJCAnv37i0y9XY3Fy5cAKBVq3tvCrp23/FFREpALpdQWmC/TlKo/quX1lxNIZlERoDCH51QwJ/6y5blh1wPAdA5oxOSakjbvheQSqUsW7aMVatWlRrboFQqK+W03KtcvnyZtWvXFjsaczcvvfQS3333XZmn6EpCo9EQFBRUxGmpKE888QQhISEsWLCg1LZarZbAwMBSp+YaN25crHNTURQKBU2bNi3itNyJSqUiMDCw1BGS1157ja5du1pUeW2Rnp7OggULaN++fYkCfXUV0XERqbPI5aBQFP/AP+xyhI98CnUMttfbwXf1vi9XsUV7opQoCVQEIkPKsfxjAMSI00QV4pFHHiEyMpJHH33ULpoq9xPJycn85z//Ydq0aXTvXra4qmeeeYYFCxYwbNgwLl++XPoK1YhMJuPzzz9n/fr1bNy4sabNqXI++OAD9uzZw7p160qcYhw+fDgqlYodO3ZUo3XVhzhVJFJnyc4WMBgE6tWznUnRObMTnTM78RZvVrNltlFIFAQpg4g3xPOz8RfOOp1FLsjpkHnvvRFVNe+++y6zZ88mKyurRGn7stC+fXu+/vprO1mGRV7ez8/Pbn2uWLHCLjocSUlJjBo1ildeeaVc602bNo1p06ZVevtVQbNmzdi3bx979uwp8tsrr7xS6fOjNnHr1i32799fqlbPTz/9VE0W1Qyi4yJSZ3FykiAIdW+KxVvmzT7XHzFipE12KE4msURAeZFKpVZ1biqDVqu1a9FGmUxmSSO2F5062af2WcuWLS3ZUfcSoaGhNrOnzEHD9wrm2kf3O+JUkUidxWAAvb726biUhlQi5arH3wAEpgaSYyqaaioiIiIiYhvRcRGps+j1Arqai7mtMEaMHPlHv2V4xn84pTslOi8iIiIiZUR0XETqLIWS/7V7quiA20FOOFnLpR9z+ZXb8tt0zOxAkKEpDygf4KL+Irmm3GJ6ERERERExIzouInWWwiKLtXeq6Lt63/Ny4EwmBE8iS1ZYX8eEiU8arkUmyBh/YxwALlIXGsgacEn/JynGkksEiIiIiNzviMG5InUWO8osVAmJykQAwjPb4WwsVLj82PsTzjidYVrcSzxwR20iH7kPSomS64Y4CoQCfOT3TiVXEREREXsiOi4idRalUkIlhUerlCHJQ9jh+QN50nw21v+aIy5HiXeIZ+mVxXRPL6qhoZVpcZY6c0F3Eb1goInCfum0IiIiIvcKouMiUmfJzhYwGgU8PMpeEbc6aaD3YsvZbzjldJocWQ4TEl6gWV5QiSq5DhIHWihDOKc7j9qoxktWctl6ERERkfsN0XERqbNoNLVfx0UpKGmfFV6udVQSFSGK5pzXX8AkmGgob1BF1omIiIjUPUTHRaTOYjIVfu5F1FI1LRQhXNRfIsuUSWuKimtVlIiICLv1JSIiIlLdiI6LSJ1FpxMwGkGtrt2jLhVFLVXTStmSy/pY8oUCFCgr1V/Hjh3LXJ9GREREpDbQs2fPIsskQmXrqouIiIiIiIiIVBO1PKFURERERERERORfRMdFREREREREpM4gOi4iIiIiIiIidQbRcRERERERERGpM4iOi4iIiIiIiEid4f8ByoWM4yWEBMwAAAAASUVORK5CYII=" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![Screenshot from 2023-09-14 06-26-00.png](attachment:4fef384b-1f6b-4712-8dcf-8e3f7b973a2f.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The LSS specification is shown in part b) of the figure above.\n", + "`max_i`, `max_j` and `max_k` are the bounds of spacetime.\n", + "In our example, they are 2, 2, and 3, which means all the cubes and pipes are within 2x2x3 volume." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "input_dict = {\n", + " \"max_i\": 2, \"max_j\": 2, \"max_k\": 3\n", + "}" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are certain *ports* that connects the LSS to the outside (which makes sense since a subroutine in classical computing always has some arguements and some returns).\n", + "In this example, there are two ports on the bottom floor corresponding to the two qubits before the CNOT; then, there is some manipulationi of these two qubits implmented with the pipes in the gray box; on the top floor, the two ports are the qubits after going through the CNOT.\n", + "\n", + "We need to provide three things to specify each port.\n", + "Let us look at the port for the output of control qubit in the CNOT indicated in the callout in part a) of the figure above.\n", + "In the code block below, it is the third port in `input_dict[\"ports\"]`.\n", + "- Its `location` is `[1,0,3]` because that is where the information is going out of the LSS.\n", + "- In general, the pipe connecting a port can also be in I, J or K direction.\n", + "Additionally, we need another character (`-` or `+`) to indicate the direction from the port to the other parts of the LSS.\n", + "In this example, the pipe is in the K direction, and we need to go downward from `[1, 0, 3]` to everything else, so the `direction` of the port is `-K`.\n", + "- Finally, surface code patches have a space orientation of the X and Z boundaries indicated by red and blue above.\n", + "We provide which one of I, J, and K is orthogonal to the face of Z boundary (blue).\n", + "In this example, it is J that is orthogonal to the blue faces, so the `z_basis_direction` of this port is `J`." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "input_dict[\"ports\"] = [\n", + " {\"location\": [1, 0, 0], \"direction\": \"+K\", \"z_basis_direction\": \"J\"},\n", + " {\"location\": [0, 1, 0], \"direction\": \"+K\", \"z_basis_direction\": \"J\"},\n", + " {\"location\": [1, 0, 3], \"direction\": \"-K\", \"z_basis_direction\": \"J\"},\n", + " {\"location\": [0, 1, 3], \"direction\": \"-K\", \"z_basis_direction\": \"J\"},\n", + "]" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, we need to provide the stabilizer constraints on the ports to ensure that the LSS indeed realizes the logical operations we want to perform.\n", + "Although intuitively there are input and output ports for the CNOT, in LSS, there is no inherent distinction between inputs and outputs.\n", + "What matters is that the given stabilizers have to match the ordering of the ports.\n", + "Our ordering is (control qubit input, target qubit input, control qubit output, target qubit output), so the correct stabilizers are ZIZI, IZZZ, XIXX, and IXIX.\n", + "If we change the ordering of the `\"ports\"` list above, we also need to change the stabilizers." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "input_dict[\"stabilizers\"] = [\"Z.Z.\", \".ZZZ\", \"X.XX\", \".X.X\"]\n", + "# Note that we use a . for an identity in a stabilizer" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Solving LSS" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By now we have finished preparing the specification of the LSS.\n", + "We can use our software package `olssco`, specifically the class `LatticeSurgeryCompiler` to solve the problem.\n", + "It can be intialized with the specification dictionary.\n", + "When we invoke `solve` method, the compiler gives us a solution." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "from olssco import LatticeSurgeryCompiler\n", + "\n", + "lss = LatticeSurgeryCompiler(specification=input_dict)\n", + "result = lss.solve()" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "result" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## To-do" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We're ready to really solve the problem.\n", + "Isn't that existing!\n", + "There are a few optional arguments to get more information about the solving process.\n", + "When solving using Kissat, we will generate a `.dimacs` file for the SAT problem, and call Kissat on that file.\n", + "Then, we will analyze the output of Kissat to derive the solution.\n", + "The optional arguments are:\n", + "- `print_detail`: if set to `True`, you will see the Kissat log on screen during the solving process.\n", + "- `dimacs_file_name`: a file to store the `.dimacs` we generated for the problem.\n", + "- `sat_log_file_name`: a file to store the Kissat log.\n", + "- `result_file_name`: a file to store the solution in terms of value assignments to our defined LSS variables." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "c ---- [ banner ] ------------------------------------------------------------\n", + "c\n", + "c Kissat SAT Solver\n", + "c \n", + "c Copyright (c) 2021-2023 Armin Biere University of Freiburg\n", + "c Copyright (c) 2019-2021 Armin Biere Johannes Kepler University Linz\n", + "c \n", + "c Version 3.1.0 630d64d4d63c2816fc79a1a0340286b39677e97d\n", + "c gcc (Debian 12.2.0-14) 12.2.0 -W -Wall -O3 -DNDEBUG\n", + "c Mon Jun 26 11:52:55 PM UTC 2023 Linux qutanum.c.googlers.com 6.1.25-1rodete1-amd64 x86_64\n", + "c\n", + "c ---- [ parsing ] -----------------------------------------------------------\n", + "c\n", + "c opened and reading DIMACS file:\n", + "c\n", + "c ./cnot.dimacs\n", + "c\n", + "c parsed 'p cnf 462 2164' header\n", + "c closing input after reading 39292 bytes (38 KB)\n", + "c finished parsing after 0.00 seconds\n", + "c\n", + "c ---- [ solving ] -----------------------------------------------------------\n", + "c\n", + "c seconds switched conflicts irredundant variables\n", + "c MB reductions redundant trail remaining\n", + "c level restarts binary glue\n", + "c\n", + "c * 0.00 2 0 0 0 0 0 0 634 1470 0% 0 402 87%\n", + "c { 0.00 2 0 0 0 0 0 0 634 1470 0% 0 402 87%\n", + "c } 0.00 2 31 0 0 0 31 22 639 1469 45% 3 402 87%\n", + "c 1 0.00 2 31 0 0 0 31 22 639 1469 45% 3 402 87%\n", + "c\n", + "c ---- [ result ] ------------------------------------------------------------\n", + "c\n", + "s SATISFIABLE\n", + "v 1 -2 -3 -4 5 -6 -7 -8 9 10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22\n", + "v -23 -24 25 26 -27 -28 -29 30 -31 -32 33 -34 -35 -36 37 38 39 40 41 42 43 44\n", + "v 45 46 47 48 -49 50 -51 -52 -53 54 -55 -56 -57 -58 -59 60 -61 62 -63 64 65\n", + "v -66 -67 -68 69 -70 71 -72 -73 -74 75 -76 -77 -78 79 -80 81 -82 -83 -84 85 86\n", + "v -87 -88 -89 90 91 -92 -93 94 95 96 -97 98 -99 100 101 -102 -103 -104 105 106\n", + "v -107 -108 109 110 111 112 -113 114 115 116 117 118 119 120 121 122 -123 -124\n", + "v -125 -126 127 128 -129 -130 131 132 133 134 -135 -136 137 138 139 140 141\n", + "v 142 143 -144 145 -146 -147 148 149 150 -151 152 -153 154 -155 156 -157 -158\n", + "v 159 160 161 -162 163 164 -165 -166 -167 168 169 -170 171 172 -173 174 -175\n", + "v 176 177 178 179 180 -181 182 183 184 -185 186 -187 188 189 190 -191 192 193\n", + "v 194 -195 -196 197 198 199 -200 -201 202 -203 204 205 206 207 208 -209 -210\n", + "v -211 212 213 214 215 -216 -217 218 219 220 221 222 223 224 -225 226 -227 228\n", + "v -229 230 231 232 233 -234 235 236 237 238 -239 -240 241 242 -243 244 245\n", + "v -246 247 -248 -249 250 251 -252 -253 254 -255 -256 257 -258 259 260 261 262\n", + "v 263 -264 265 266 267 -268 -269 270 271 272 -273 -274 275 -276 277 278 279\n", + "v 280 281 282 283 -284 285 -286 287 288 289 290 -291 292 -293 -294 295 -296\n", + "v 297 298 299 300 301 302 303 -304 -305 306 307 308 -309 310 -311 312 313 -314\n", + "v 315 316 -317 318 -319 320 321 322 -323 324 325 -326 327 328 329 -330 331 332\n", + "v 333 334 335 336 -337 -338 339 340 341 -342 -343 344 345 346 347 348 -349 350\n", + "v 351 352 353 354 -355 -356 -357 358 359 360 361 362 363 -364 365 -366 -367\n", + "v 368 369 370 -371 372 -373 374 375 376 -377 -378 379 380 381 -382 383 384\n", + "v -385 -386 -387 388 389 390 391 392 393 394 -395 396 397 -398 -399 400 401\n", + "v -402 -403 404 -405 406 407 408 409 -410 -411 412 413 414 415 -416 -417 418\n", + "v -419 420 -421 422 423 424 425 426 427 428 429 430 -431 432 433 434 435 436\n", + "v 437 438 439 -440 441 442 443 444 445 446 447 448 -449 450 -451 452 -453 454\n", + "v 455 456 457 -458 459 460 461 462 0\n", + "c\n", + "c ---- [ profiling ] ---------------------------------------------------------\n", + "c\n", + "c 0.00 43.12 % parse\n", + "c 0.00 42.30 % search\n", + "c 0.00 34.02 % focused\n", + "c 0.00 0.00 % simplify\n", + "c =============================================\n", + "c 0.00 100.00 % total\n", + "c\n", + "c ---- [ statistics ] --------------------------------------------------------\n", + "c\n", + "c conflicts: 31 17744.71 per second\n", + "c decisions: 224 7.23 per conflict\n", + "c jumped_reasons: 674 26 % propagations\n", + "c propagations: 2550 1459645 per second\n", + "c queue_decisions: 224 100 % decision\n", + "c random_decisions: 0 0 % decision\n", + "c random_sequences: 0 0 interval\n", + "c score_decisions: 0 0 % decision\n", + "c switched: 0 0 interval\n", + "c vivify_checks: 0 0 per vivify\n", + "c vivify_units: 0 0 % variables\n", + "c\n", + "c ---- [ resources ] ---------------------------------------------------------\n", + "c\n", + "c maximum-resident-set-size: 117702656 bytes 112 MB\n", + "c process-time: 0.00 seconds\n", + "c\n", + "c ---- [ shutting down ] -----------------------------------------------------\n", + "c\n", + "c exit 10\n", + "kissat SAT\n", + "Construct a Z3 SMT model and solve...\n", + "elapsed time: 0.020379s\n", + "Z3 SAT\n" + ] + } + ], + "source": [ + "result = lss.solve(\n", + " print_detail=True,\n", + " dimacs_file_name=\"./cnot.dimacs\",\n", + " sat_log_file_name=\"./cnot.sat\",\n", + " result_file_name=\"./cnot.json\",\n", + ")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You should see three new files in the same directory to this Jupyter notebook.\n", + "It would be nice to open up each one to get a sense of what they are.\n", + "Now, the result of the SAT solving is in a variable named `result`.\n", + "It is actually an object from a class `LatticeSurgerySubroutine` we also define in the package.\n", + "There are a few translation methods to generate more huamn-readable formats of our result.\n", + "\n", + "We can generate a 3D modelling file of the solution in `.gltf` format.\n", + "You can open it up online (search gltf viewer) or in other common 3D modelling software like Blender." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "result.generate_gltf(output_file_name=\"./cnot.gltf\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Maybe you have already noticed that our LSS is no other than a ZX-diagram with spiders on grid points.\n", + "There are three formats closely related to this fact.\n", + "The first one is a simple text figure for the LSS that spilits it up to slices in time.\n", + "The slices later in time is on top of the print out.\n", + "In each slice, time goes from bottom left to top right.\n", + "The slashes are pipes in the time (K) direction.\n", + "It's a good idea to compare the text figure with the 3d model rendered with the `.gltf` file now.\n", + "A T intersection with red faces drawing the T is an X-spider; if it's the blue faces that draw the T, it's a Z-spider.\n", + "If there are only two pipes at an intersectioni, then it doesn't matter if we lable it X or Z, because they are both identity." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " / \n", + " . H \n", + " / \n", + " \n", + " / \n", + " H . \n", + "/ \n", + " \n", + " \n", + " \n", + "\n", + "======================================\n", + " / \n", + " X---X \n", + "/ / \n", + " \n", + " / \n", + " X . \n", + "/ \n", + " \n", + " \n", + " \n", + "\n", + "======================================\n", + " / / \n", + " X H \n", + "/ / \n", + " \n", + " / \n", + " X . \n", + "/ \n", + " \n", + " \n", + " \n", + "\n", + "======================================\n", + " / / \n", + " X X \n", + " | / \n", + " | \n", + " |/ \n", + " Z . \n", + "/ \n", + " \n", + " \n", + " \n", + "\n", + "======================================\n", + " / \n", + " . X \n", + " / \n", + " \n", + " / \n", + " H . \n", + "/ \n", + " \n", + " \n", + " \n", + "\n", + "======================================\n", + " \n", + " . . \n", + " \n", + " \n", + " \n", + " . . \n", + " \n", + " \n", + " \n", + " \n", + "\n", + "======================================\n", + "\n" + ] + } + ], + "source": [ + "print(result.generate_textfig())" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A very similar format is a link to be opened with an online tool ZigXag.\n", + "We stitch the time slices together here.\n", + "With some rotation and reflection of the gltf, you should be able to spot the similarity of it and the ZigXag figure." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "https://algassert.com/zigxag#0,-4,O;0,-8,O;-1,-1,out;-1,-5,@;-1,-9,O;-1,-13,out;3,0,out;3,-4,O;3,-8,O;3,-12,out:0,-4,-1,-5,-;0,-4,0,-8,-;0,-8,3,-8,-;-1,-1,-1,-5,h;-1,-5,-1,-9,-;-1,-9,-1,-13,h;3,0,3,-4,-;3,-4,3,-8,h;3,-8,3,-12,h\n" + ] + } + ], + "source": [ + "print(result.generate_zigxag())" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The third format is an annotated NetworkX graph where the nodes are ZX spiders and edges are, well, just edges between them.\n", + "(You can use `generate_networkx` to get this `networkx.Graph`. We skip that here.)\n", + "The annotation follows the convention in [Stim ZX](https://github.com/quantumlib/Stim/tree/main/glue/zx), so we can easily derive the stabilizers of graph with stimzx.\n", + "Then, we can use stim to check whether this set of resulting stabilizers are the same with the stabiliers we specified previously.\n", + "(Both sets will be displayed if setting optional argument `print_stabilizers=True`.)\n", + "If so, we verified the correctness of our compiled result." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "specified:\n", + "+Z_Z_\n", + "+_ZZZ\n", + "+X_XX\n", + "+_X_X\n", + "==================================================================\n", + "resulting:\n", + "+X_XX\n", + "+Z_Z_\n", + "+_X_X\n", + "+_ZZZ\n", + "==================================================================\n", + "specified and resulting stabilizers are equivalent.\n" + ] + }, + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "result.verify_stabilizers_stimzx(print_stabilizers=True)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Sometimes, we'd like optimize a certain aspect of the LSS to the optimal value.\n", + "We provide an example to optimize the height of the LSS, which is, in turn, proportional to the depth of the circuit to actually run this LSS.\n", + "You can give a specific starting depth, and the `optimize_depth` method will try to solve the LSS with increased and decreased depth until it finds a solution with the optimal depth.\n", + "That is, decreasing the depth by 1 will make the problem unsatisfiable.\n", + "Note that in this method we assume that every port on the top floor will still be on the top floor when we increase or decrease the height." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "optimal depth of the LSS is 3\n" + ] + } + ], + "source": [ + "optimal_solution = lss.optimize_depth(2)\n", + "print(f\"optimal depth of the LSS is {optimal_solution.get_depth()}\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can also save more information on the optimization process.\n", + "Since the compiler may solve multiple problems with different height in the process, there are multiple sets of `.dimacs`, Kissat log, and solution files.\n", + "So the optional argument here are, e.g., `dimacs_file_name_prefix` instead of just the file name.\n", + "We'll append `_d=XX` in the file names to indicate the depth the file corresponds to.\n", + "Since we increased depth from 2 to 3 previously, we shall try to optimize from above the optimal value, starting from 4 this time." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "lss.optimize_depth(\n", + " 4,\n", + " dimacs_file_name_prefix='./cnot_dimacs',\n", + " sat_log_file_name_prefix='./cnot_sat',\n", + " result_file_name_prefix='./cnot_result',\n", + ").get_depth()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You should see a few new files poping up in the directory.\n", + "Notice that only the satisfiable problems will have the result file, while all problems have DIMACS and Kissat log.\n", + "In this example, the compiler finds that depth=4 and 3 are satisfiable, while depth=2 is not.\n", + "Thus, it concludes that the optimal depth is 3." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Sometimes, we'd like to try permuting some ports.\n", + "We also provides a method `try_all_permutations` to explore all permutations of a given set of ports.\n", + "To demonstrate this involves a more complex specificed in a file `./maj.json`.\n", + "We let the compiler explore permuting the ports 2, 4, and 6.\n", + "There are two new optional arguments to notice:\n", + "- `parallelism`: the number of parallel process the compiler can use\n", + "- `shuffle`: default to `True`, meaning the order of issueing the compilation jobs corresponding to different permutations is random.\n", + "\n", + "Note that here we're using Z3 to solve SAT because we do not set `solver=\"kissat\"` and it defaults to Z3." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(4, 2, 6): SAT\n", + "(2, 4, 6): SAT\n", + "(6, 2, 4): SAT\n", + "(4, 6, 2): SAT\n", + "(6, 4, 2): UNSAT\n", + "(2, 6, 4): UNSAT\n" + ] + }, + { + "data": { + "text/plain": [ + "{'SAT': [(4, 6, 2), (2, 4, 6), (6, 2, 4), (4, 2, 6)],\n", + " 'UNSAT': [(2, 6, 4), (6, 4, 2)]}" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import json\n", + "with open(\"./maj.json\", \"r\") as f:\n", + " data = json.load(f)\n", + "lss = LatticeSurgeryCompiler(specification=data)\n", + "lss.try_all_permutations([2, 4, 6], parallelism=6)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You should see that some permutation yields solutions while others are unsatisfiable.\n", + "Note that this method is to be used with caution.\n", + "When we permute the ports without changing the stabilizers (which is what we're doing here), our package does not check whether it's functionally equivalent to the original setting.\n", + "In fact, permuting the ports like above makes the LSS comething else than what specified in `./maj.json`.\n", + "(We just want to demonstrate this class method somehow.)\n", + "It's up to the user's judgement whether it makes sense to permute ports." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can also set values of variables to 'force' the solution in some ways.\n", + "For example, we notice that there is a pipe in the I direction from (0,0,2) to (1,0,2).\n", + "We can forbid it in two ways.\n", + "The first way is to provide a dictionary of arrays of values.\n", + "If we do not want to set that value, use -1 at the spot; otherwise use 0 or 1 to set the value.\n", + "Since we want to set an `ExistI` variable, the dimension of the array is 2x2x3 and we need to sat [0][0][2] element to 0.\n", + "With this method, we can set many variable values together.\n", + "\n", + "Also note that we can set the optional argument `specification` of `lss.solve()` to whatever problem we want to solve.\n", + "And since we're not initializing the `LatticeSurgeryCompiler` again, we're using Z3 for SAT still." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# reload the CNOT example\n", + "specification = pickle.loads(b'\\x80\\x04\\x95\\xea\\x00\\x00\\x00\\x00\\x00\\x00\\x00}\\x94(\\x8c\\x05max_i\\x94K\\x02\\x8c\\x05max_j\\x94K\\x02\\x8c\\x05max_k\\x94K\\x03\\x8c\\x05ports\\x94]\\x94(}\\x94(\\x8c\\x08location\\x94]\\x94(K\\x01K\\x00K\\x00e\\x8c\\tdirection\\x94\\x8c\\x02+K\\x94\\x8c\\x11z_basis_direction\\x94\\x8c\\x01J\\x94u}\\x94(h\\x07]\\x94(K\\x00K\\x01K\\x00eh\\th\\nh\\x0bh\\x0cu}\\x94(h\\x07]\\x94(K\\x01K\\x00K\\x03eh\\t\\x8c\\x02-K\\x94h\\x0bh\\x0cu}\\x94(h\\x07]\\x94(K\\x00K\\x01K\\x03eh\\th\\x11h\\x0bh\\x0cue\\x8c\\x0bstabilizers\\x94]\\x94(\\x8c\\x04Z.Z.\\x94\\x8c\\x04.ZZZ\\x94\\x8c\\x04X.XX\\x94\\x8c\\x04.X.X\\x94eu.')\n", + "\n", + "arr_vals = [\n", + " [[-1, -1, 0], [-1, -1, -1]],\n", + " [[-1, -1, -1], [-1, -1, -1]],\n", + "]\n", + "result = lss.solve(specification=specification, given_arrs={\"ExistI\": arr_vals})\n", + "result.generate_gltf(output_file_name=\"./cnot_forbid_arr.gltf\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Comparing the most recently generated gltf with `cnot.gltf`, we can see the difference of forbidding that pipe in the I direction: the 'bridge' between the two 'pillars' is flipped in a way.\n", + "We can also set individual values, instead of array of values.\n", + "We do so by specify a list of dictioinaries, each one contains 1) the name of the array, 2) indices in the array, and 3) value to sat (0 or 1).\n", + "If both `given_arrs` and `given_vals` are given, the latter will overwrite the former.\n", + "For example, let us forbid the pipe in the J direction from (0,0,2) to (0,1,2).\n", + "Inspect the output gltf, you should see a difference with `./cnot_forbid_arr.gltf`." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "result = lss.solve(specification=specification, given_vals=[\n", + " {\"array\": \"ExistJ\", \"indices\": [0,0,2], \"value\": 0},\n", + "])\n", + "result.generate_gltf(output_file_name=\"./cnot_forbid_val.gltf\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/glue/lattice_surgery/gltf_gen.py b/glue/lattice_surgery/gltf_gen.py deleted file mode 100644 index 52e159eaf..000000000 --- a/glue/lattice_surgery/gltf_gen.py +++ /dev/null @@ -1,214 +0,0 @@ -import codecs -import struct -import json - -SQ2 = 0.70710678118 - -def float_to_little_endian_hex(f): - # Pack the float into a binary string using the little-endian format - binary_data = struct.pack('0 and ExistX[x-1][y][z]: - exists['-x'] = 1 - if ExistX[x][y][z]: - exists['+x'] = 1 - if y>0 and ExistY[x][y-1][z]: - exists['-y'] = 1 - if ExistY[x][y][z]: - exists['+y'] = 1 - if z>0 and ExistZ[x][y][z-1]: - exists['-z'] = 1 - if ExistZ[x][y][z]: - exists['+z'] = 1 - - degree = sum([v for (k,v) in exists.items()]) - if degree == 1: - if NodeY[x][y][z]: - if exists['+z']: - gltf['nodes'].append({ - "name":f"InitY({x},{y},{z})", - "mesh": 4, - "translation": [SEP*x, SEP*z, -SEP*y] }) - if exists['-z']: - gltf['nodes'].append({ - "name":f"MeasY({x},{y},{z})", - "mesh": 4, - "rotation": [1, 0, 0, 0], - "translation": [SEP*x, SEP*z+1, -SEP*y-1] }) - else: - pass - elif degree == 2: - if NodeY[x][y][z]: - gltf['nodes'].append({ - "name":f"MeasInitY({x},{y},{z})", - "mesh": 6, - "translation": [SEP*x, SEP*z, -SEP*y] }) - else: - if exists['+z'] and exists['-z']: - if ColorZ[x][y][z]: - gltf['nodes'].append({ - "name":f"PassZ({x},{y},{z})-color1", - "mesh": 5, - "rotation": [0, SQ2, 0, SQ2], - "translation": [SEP*x+1, SEP*z, -SEP*y] }) - else: - gltf['nodes'].append({ - "name":f"PassZ({x},{y},{z})-color0", - "mesh": 5, - "translation": [SEP*x, SEP*z, -SEP*y] }) - - if exists['+y'] and exists['-y']: - if ColorY[x][y][z]: - gltf['nodes'].append({ - "name":f"PassY({x},{y},{z})", - "mesh": 5, - "rotation": [SQ2, 0, 0, SQ2], - "translation": [SEP*x, SEP*z, -SEP*y-1] }) - else: - gltf['nodes'].append({ - "name":f"PassY({x},{y},{z})", - "mesh": 5, - "rotation": [0.5, 0.5, 0.5, 0.5], - "translation": [SEP*x+1, SEP*z, -SEP*y-1] }) - - if exists['+x'] and exists['-x']: - if ColorX[x][y][z]: - gltf['nodes'].append({ - "name":f"PassX({x},{y},{z})", - "mesh": 5, - "rotation": [0, 0, SQ2, SQ2], - "translation": [SEP*x+1, SEP*z, -SEP*y] }) - else: - gltf['nodes'].append({ - "name":f"PassX({x},{y},{z})", - "mesh": 5, - "rotation": [0.5, -0.5, 0.5, 0.5], - "translation": [SEP*x+1, SEP*z, -SEP*y-1] }) - - if exists['-x'] and exists['+y']: - if ColorX[x-1][y][z]: - gltf['nodes'].append({ - "name":f"Turn-X&+Y({x},{y},{z})", - "mesh": 7, - "rotation": [-0.5, -0.5, 0.5, 0.5], - "translation": [SEP*x, SEP*z, -SEP*y] }) - else: - gltf['nodes'].append({ - "name":f"Turn-X&+Y({x},{y},{z})", - "mesh": 8, - "rotation": [-0.5, -0.5, 0.5, 0.5], - "translation": [SEP*x, SEP*z, -SEP*y] }) - - if exists['+x'] and exists['-y']: - if ColorX[x][y][z]: - gltf['nodes'].append({ - "name":f"Turn+X&-Y({x},{y},{z})", - "mesh": 7, - "rotation": [0, 0, -SQ2, SQ2], - "translation": [SEP*x, SEP*z+1, -SEP*y] }) - else: - gltf['nodes'].append({ - "name":f"Turn+X&-Y({x},{y},{z})", - "mesh": 8, - "rotation": [0, 0, -SQ2, SQ2], - "translation": [SEP*x, SEP*z+1, -SEP*y] }) - - if exists['+x'] and exists['+y']: - if ColorX[x][y][z]: - gltf['nodes'].append({ - "name":f"Turn+X&+Y({x},{y},{z})", - "mesh": 7, - "rotation": [-0.5, 0.5, -0.5, 0.5], - "translation": [SEP*x, SEP*z+1, -SEP*y] }) - else: - gltf['nodes'].append({ - "name":f"Turn+X&+Y({x},{y},{z})", - "mesh": 8, - "rotation": [-0.5, 0.5, -0.5, 0.5], - "translation": [SEP*x, SEP*z+1, -SEP*y] }) - - if exists['-x'] and exists['-y']: - if ColorX[x-1][y][z]: - gltf['nodes'].append({ - "name":f"Turn-X&-Y({x},{y},{z})", - "mesh": 7, - "rotation": [0.5, -0.5, -0.5, 0.5], - "translation": [SEP*x, SEP*z+1, -SEP*y-1] }) - else: - gltf['nodes'].append({ - "name":f"Turn-X&-Y({x},{y},{z})", - "mesh": 8, - "rotation": [0.5, -0.5, -0.5, 0.5], - "translation": [SEP*x, SEP*z+1, -SEP*y-1] }) - - if exists['-y'] and exists['+z']: - if ColorY[x][y-1][z]: - gltf['nodes'].append({ - "name":f"Turn-Y&+Z({x},{y},{z})", - "mesh": 7, - "rotation": [1, 0, 0, 0], - "translation": [SEP*x, SEP*z, -SEP*y] }) - else: - gltf['nodes'].append({ - "name":f"Turn-Y&+Z({x},{y},{z})", - "mesh": 8, - "rotation": [1, 0, 0, 0], - "translation": [SEP*x, SEP*z, -SEP*y] }) - - if exists['+y'] and exists['-z']: - if ColorY[x][y][z]: - gltf['nodes'].append({ - "name":f"Turn+Y&-Z({x},{y},{z})", - "mesh": 7, - "translation": [SEP*x, SEP*z+1, -SEP*y-1] }) - else: - gltf['nodes'].append({ - "name":f"Turn+Y&-Z({x},{y},{z})", - "mesh": 8, - "translation": [SEP*x, SEP*z+1, -SEP*y-1] }) - - if exists['+y'] and exists['+z']: - if ColorY[x][y][z]: - gltf['nodes'].append({ - "name":f"Turn+Y&+Z({x},{y},{z})", - "mesh": 7, - "rotation": [0, 1, 0, 0], - "translation": [SEP*x+1, SEP*z, -SEP*y-1] }) - else: - gltf['nodes'].append({ - "name":f"Turn+Y&+Z({x},{y},{z})", - "mesh": 8, - "rotation": [0, 1, 0, 0], - "translation": [SEP*x+1, SEP*z, -SEP*y-1] }) - - if exists['-y'] and exists['-z']: - if ColorY[x][y-1][z]: - gltf['nodes'].append({ - "name":f"Turn-Y&-Z({x},{y},{z})", - "mesh": 7, - "rotation": [SQ2, 0, 0, SQ2], - "translation": [SEP*x, SEP*z, -SEP*y-1] }) - else: - gltf['nodes'].append({ - "name":f"Turn-Y&-Z({x},{y},{z})", - "mesh": 8, - "rotation": [SQ2, 0, 0, SQ2], - "translation": [SEP*x, SEP*z, -SEP*y-1] }) - - if exists['+x'] and exists['+z']: - if ColorX[x][y][z]: - gltf['nodes'].append({ - "name":f"Turn+X&+Z({x},{y},{z})", - "mesh": 8, - "rotation": [0, SQ2, 0, SQ2], - "translation": [SEP*x+1, SEP*z, -SEP*y] }) - else: - gltf['nodes'].append({ - "name":f"Turn+X&+Z({x},{y},{z})", - "mesh": 7, - "rotation": [0, SQ2, 0, SQ2], - "translation": [SEP*x+1, SEP*z, -SEP*y] }) - - if exists['-x'] and exists['+z']: - if ColorX[x-1][y][z]: - gltf['nodes'].append({ - "name":f"Turn-X&+Z({x},{y},{z})", - "mesh": 8, - "rotation": [0, -SQ2, 0, SQ2], - "translation": [SEP*x, SEP*z, -SEP*y-1] }) - else: - gltf['nodes'].append({ - "name":f"Turn-X&+Z({x},{y},{z})", - "mesh": 7, - "rotation": [0, -SQ2, 0, SQ2], - "translation": [SEP*x, SEP*z, -SEP*y-1] }) - - if exists['+x'] and exists['-z']: - if ColorX[x][y][z]: - gltf['nodes'].append({ - "name":f"Turn+X&-Z({x},{y},{z})", - "mesh": 8, - "rotation": [0.5, 0.5, -0.5, 0.5], - "translation": [SEP*x, SEP*z, -SEP*y] }) - else: - gltf['nodes'].append({ - "name":f"Turn+X&-Z({x},{y},{z})", - "mesh": 7, - "rotation": [0.5, 0.5, -0.5, 0.5], - "translation": [SEP*x, SEP*z, -SEP*y] }) - - if exists['-x'] and exists['-z']: - if ColorX[x-1][y][z]: - gltf['nodes'].append({ - "name":f"Turn-X&-Z({x},{y},{z})", - "mesh": 8, - "rotation": [0.5, -0.5, 0.5, 0.5], - "translation": [SEP*x+1, SEP*z, -SEP*y-1] }) - else: - gltf['nodes'].append({ - "name":f"Turn-X&-Z({x},{y},{z})", - "mesh": 7, - "rotation": [0.5, -0.5, 0.5, 0.5], - "translation": [SEP*x+1, SEP*z, -SEP*y-1] }) - - elif degree == 3: - if exists['-y'] and exists['+y'] and exists['+z']: - if ColorY[x][y][z]: - gltf['nodes'].append({ - "name":f"JuncY&+Z({x},{y},{z})", - "mesh": 9, - "translation": [SEP*x, SEP*z, -SEP*y] }) - else: - gltf['nodes'].append({ - "name":f"JuncY&+Z({x},{y},{z})", - "mesh": 10, - "translation": [SEP*x, SEP*z, -SEP*y] }) - - if exists['-y'] and exists['+y'] and exists['-z']: - if ColorY[x][y][z]: - gltf['nodes'].append({ - "name":f"JuncY&-Z({x},{y},{z})", - "mesh": 9, - "rotation": [1, 0, 0, 0], - "translation": [SEP*x, SEP*z+1, -SEP*y-1] }) - else: - gltf['nodes'].append({ - "name":f"JuncY&+Z({x},{y},{z})", - "mesh": 10, - "translation": [SEP*x, SEP*z+1, -SEP*y-1] }) - - if exists['-z'] and exists['+z'] and exists['-y']: - if ColorY[x][y-1][z]: - gltf['nodes'].append({ - "name":f"JuncZ&-Y({x},{y},{z})", - "mesh": 9, - "rotation": [SQ2, 0, 0, SQ2], - "translation": [SEP*x, SEP*z, -SEP*y-1] }) - else: - gltf['nodes'].append({ - "name":f"JuncZ&-Y({x},{y},{z})", - "mesh": 10, - "rotation": [SQ2, 0, 0, SQ2], - "translation": [SEP*x, SEP*z, -SEP*y-1] }) - - if exists['-z'] and exists['+z'] and exists['+y']: - if ColorY[x][y][z]: - gltf['nodes'].append({ - "name":f"JuncZ&+Y({x},{y},{z})", - "mesh": 9, - "rotation": [-SQ2, 0, 0, SQ2], - "translation": [SEP*x, SEP*z+1, -SEP*y] }) - else: - gltf['nodes'].append({ - "name":f"JuncZ&+Y({x},{y},{z})", - "mesh": 10, - "rotation": [-SQ2, 0, 0, SQ2], - "translation": [SEP*x, SEP*z+1, -SEP*y] }) - - if exists['-y'] and exists['+y'] and exists['-x']: - if ColorX[x-1][y][z]: - gltf['nodes'].append({ - "name":f"JuncY&-X({x},{y},{z})", - "mesh": 9, - "rotation": [0, 0, SQ2, SQ2], - "translation": [SEP*x+1, SEP*z, -SEP*y] }) - else: - gltf['nodes'].append({ - "name":f"JuncY&-X({x},{y},{z})", - "mesh": 10, - "rotation": [0, 0, SQ2, SQ2], - "translation": [SEP*x+1, SEP*z, -SEP*y] }) - - if exists['-y'] and exists['+y'] and exists['+x']: - if ColorX[x][y][z]: - gltf['nodes'].append({ - "name":f"JuncY&+X({x},{y},{z})", - "mesh": 9, - "rotation": [0, 0, -SQ2, SQ2], - "translation": [SEP*x, SEP*z+1, -SEP*y] }) - else: - gltf['nodes'].append({ - "name":f"JuncY&+X({x},{y},{z})", - "mesh": 10, - "rotation": [0, 0, -SQ2, SQ2], - "translation": [SEP*x, SEP*z+1, -SEP*y] }) - - if exists['-x'] and exists['+x'] and exists['-y']: - if ColorX[x][y][z]: - gltf['nodes'].append({ - "name":f"JuncX&-Y({x},{y},{z})", - "mesh": 9, - "rotation": [0.5, 0.5, 0.5, 0.5], - "translation": [SEP*x+1, SEP*z, -SEP*y-1] }) - else: - gltf['nodes'].append({ - "name":f"JuncX&-Y({x},{y},{z})", - "mesh": 10, - "rotation": [0.5, 0.5, 0.5, 0.5], - "translation": [SEP*x+1, SEP*z, -SEP*y-1] }) - - if exists['-x'] and exists['+x'] and exists['+y']: - if ColorX[x][y][z]: - gltf['nodes'].append({ - "name":f"JuncX&+Y({x},{y},{z})", - "mesh": 9, - "rotation": [-0.5, 0.5, -0.5, 0.5], - "translation": [SEP*x+1, SEP*z+1, -SEP*y] }) - else: - gltf['nodes'].append({ - "name":f"JuncX&+Y({x},{y},{z})", - "mesh": 10, - "rotation": [-0.5, 0.5, -0.5, 0.5], - "translation": [SEP*x+1, SEP*z+1, -SEP*y] }) - - if exists['-x'] and exists['+x'] and exists['+z']: - if ColorX[x][y][z]: - gltf['nodes'].append({ - "name":f"JuncX&+Z({x},{y},{z})", - "mesh": 10, - "rotation": [0, SQ2, 0, SQ2], - "translation": [SEP*x+1, SEP*z, -SEP*y] }) - else: - gltf['nodes'].append({ - "name":f"JuncX&+Z({x},{y},{z})", - "mesh": 9, - "rotation": [0, SQ2, 0, SQ2], - "translation": [SEP*x+1, SEP*z, -SEP*y] }) - - if exists['-x'] and exists['+x'] and exists['-z']: - if ColorX[x][y][z]: - gltf['nodes'].append({ - "name":f"JuncX&-Z({x},{y},{z})", - "mesh": 10, - "rotation": [SQ2, 0, SQ2, 0], - "translation": [SEP*x+1, SEP*z+1, -SEP*y] }) - else: - gltf['nodes'].append({ - "name":f"JuncX&-Z({x},{y},{z})", - "mesh": 9, - "rotation": [SQ2, 0, SQ2, 0], - "translation": [SEP*x+1, SEP*z+1, -SEP*y] }) - - if exists['-z'] and exists['+z'] and exists['+x']: - if ColorX[x][y][z]: - gltf['nodes'].append({ - "name":f"JuncZ&+X({x},{y},{z})", - "mesh": 10, - "rotation": [0.5, 0.5, -0.5, 0.5], - "translation": [SEP*x, SEP*z, -SEP*y] }) - else: - gltf['nodes'].append({ - "name":f"JuncZ&+X({x},{y},{z})", - "mesh": 9, - "rotation": [0.5, 0.5, -0.5, 0.5], - "translation": [SEP*x, SEP*z, -SEP*y] }) - - if exists['-z'] and exists['+z'] and exists['-x']: - if ColorX[x-1][y][z]: - gltf['nodes'].append({ - "name":f"JuncZ&-X({x},{y},{z})", - "mesh": 10, - "rotation": [0.5, -0.5, 0.5, 0.5], - "translation": [SEP*x+1, SEP*z, -SEP*y-1] }) - else: - gltf['nodes'].append({ - "name":f"JuncZ&-X({x},{y},{z})", - "mesh": 9, - "rotation": [0.5, -0.5, 0.5, 0.5], - "translation": [SEP*x+1, SEP*z, -SEP*y-1] }) - - elif degree == 4: - if exists['-z'] and exists['+z'] and exists['-y'] and exists['+y']: - if ColorY[x][y][z]: - gltf['nodes'].append({ - "name":f"CrossYZ({x},{y},{z})", - "mesh": 11, - "translation": [SEP*x, SEP*z, -SEP*y] }) - else: - gltf['nodes'].append({ - "name":f"CrossYZ({x},{y},{z})", - "mesh": 12, - "translation": [SEP*x, SEP*z, -SEP*y] }) - - if exists['-x'] and exists['+x'] and exists['-y'] and exists['+y']: - if ColorX[x][y][z]: - gltf['nodes'].append({ - "name":f"CrossXY({x},{y},{z})", - "mesh": 11, - "translation": [SEP*x+1, SEP*z, -SEP*y] }) - else: - gltf['nodes'].append({ - "name":f"CrossXY({x},{y},{z})", - "mesh": 12, - "translation": [SEP*x+1, SEP*z, -SEP*y] }) - - if exists['-x'] and exists['+x'] and exists['-z'] and exists['+z']: - if ColorX[x][y][z]: - gltf['nodes'].append({ - "name":f"CrossXZ({x},{y},{z})", - "mesh": 12, - "translation": [SEP*x+1, SEP*z, -SEP*y] }) - else: - gltf['nodes'].append({ - "name":f"CrossXZ({x},{y},{z})", - "mesh": 11, - "translation": [SEP*x+1, SEP*z, -SEP*y] }) - - elif degree >= 5: - raise ValueError('Have 3D corner!') - -gltf['nodes'][0]['children'] = list(range(1, len(gltf['nodes']))) -with open(OLSCO_FILE_NAME.replace('.json', '.gltf'), 'w') as f: - json.dump(gltf, f) \ No newline at end of file diff --git a/glue/lattice_surgery/olssco/__init__.py b/glue/lattice_surgery/olssco/__init__.py new file mode 100644 index 000000000..42e9d2075 --- /dev/null +++ b/glue/lattice_surgery/olssco/__init__.py @@ -0,0 +1,2 @@ +from .lattice_surgery_compiler import LatticeSurgeryProblem +from .lattice_surgery_compiler import LatticeSurgerySolution diff --git a/glue/lattice_surgery/olssco/lattice_surgery_compiler.py b/glue/lattice_surgery/olssco/lattice_surgery_compiler.py new file mode 100644 index 000000000..80f604709 --- /dev/null +++ b/glue/lattice_surgery/olssco/lattice_surgery_compiler.py @@ -0,0 +1,460 @@ +"""Two wrapper classes fpr OLSSSol, rewrite passes, and translators.""" + +import functools +import itertools +import json +import multiprocessing +import random +from typing import Any, Literal, Mapping, Optional, Sequence +from olssco.rewrite_passes.attach_fixups import attach_fixups +from olssco.rewrite_passes.color_z import color_z +from olssco.rewrite_passes.remove_unconnected import remove_unconnected +from olssco.sat_lattice_surgery_solver import OptimalLatticeSurgerySubroutineSolver +from olssco.tools.verify_stabilizers import verify_stabilizers +from olssco.translators.gltf_generator import gltf_generator +from olssco.translators.networkx_generator import networkx_generator +from olssco.translators.textfig_generator import textfig_generator +from olssco.translators.zigxag_generator import zigxag_generator + + +class LatticeSurgerySolution: + """A class for the result of compilation lattice surgery subroutine (LSS). + + It internally saves an LaSSIR (Lattice Surgery Subroutine Intermediate + Representation) and we can apply rewrite passes to it, or use translators to + derive other formats of the LSS solution + """ + + def __init__( + self, + *, + lassir: Mapping[str, Any], + ) -> None: + """initialization for LatticeSurgerySubroutine + + Args: + lassir (Mapping[str, Any]): LaSSIR + """ + self.lassir = lassir + + def get_depth(self) -> int: + """get the depth/height of the LSS in LaSSIR. + + Returns: + int: depth/height of the LSS in LaSSIR + """ + return self.lassir["n_k"] + + def after_removing_disconnected_pieces(self): + """remove_unconnected.""" + return LatticeSurgerySolution(lassir=remove_unconnected(self.lassir)) + + def after_color_k_pipes(self): + """coloring K pipes.""" + return LatticeSurgerySolution(lassir=color_z(self.lassir)) + + def after_default_optimizations(self): + """default optimizations: remove unconnected, and then color K pipes.""" + solution = LatticeSurgerySolution(lassir=remove_unconnected(self.lassir)) + solution = LatticeSurgerySolution(lassir=color_z(solution.lassir)) + return solution + + def after_t_factory_default_optimizations(self): + """default optimization for T-factories.""" + solution = LatticeSurgerySolution(lassir=remove_unconnected(self.lassir)) + solution = LatticeSurgerySolution(lassir=color_z(solution.lassir)) + solution = LatticeSurgerySolution(lassir=attach_fixups(solution.lassir)) + return solution + + def save_lassir(self, file_name: str) -> None: + """save the current LaSSIR to a file. + + Args: + file_name (str): file to save the current LaSSIR + """ + with open(file_name, "w") as f: + json.dump(self.lassir, f) + + def to_3d_model_gltf( + self, + output_file_name: str, + stabilizer: int = -1, + tube_len: float = 2.0, + no_color_z: bool = False, + ) -> None: + """generate gltf file (for 3D modelling). + + Args: + output_file_name (str): + stabilizer (int, optional): Defaults to -1 meaning do not draw + correlation surfaces. If the value is in [0, n_s), the correlation + surfaces corresponding to that stabilizer are drawn and faces in one + of the directions are revealed to unveil the correlation surfaces. + tube_len (float, optional): Length of the pipe comapred to the cube. + Defaults to 2.0. + no_color_z (bool, optional): Do not color the K pipes. Defaults to + False. + """ + gltf_generator( + self.lassir, + output_file=output_file_name, + stabilizer=stabilizer, + tube_len=tube_len, + no_color_z=no_color_z, + ) + + def to_zigxag_url( + self, + io_spec: Optional[Sequence[str]] = None, + ) -> str: + """generate a link that leads to a ZigXag figure. + + Args: + io_spec (Optional[Sequence[str]], optional): Specify whether each port + is an input or an output. Length must be the same with the number of + ports. Defaults to None, which means all ports are outputs. + + Returns: + str: the ZigXag link + """ + return zigxag_generator(self.lassir, io_spec=io_spec) + + def to_text_diagram( + self, + ) -> str: + """generate the text figure of LSS time slices. + + Returns: + str: text figure of the LSS + """ + return textfig_generator(self.lassir) + + def generate_networkx(self): + """generate a annotated networkx.Graph correponding to the LSS. + + Returns: + networkx.Graph: + """ + return networkx_generator(self.lassir) + + def verify_stabilizers_stimzx(self, print_stabilizers: bool = False) -> bool: + """verify the stabilizer of the LSS. + + Use Stim ZX to deduce the stabilizers from the annotated networkx graph. + Then use Stim to ensure that this set of stabilizers and the set of + stabilizers specified in the input are equivalent. + + Args: + print_stabilizers (bool, optional): If True, print the two sets of + stabilizers. Defaults to False. + + Returns: + bool: True if the two sets are equivalent; otherwise False. + """ + paulistrings = [ + paulistring.replace(".", "_") + for paulistring in self.lassir["specification"]["stabilizers"] + ] + return verify_stabilizers( + paulistrings, + self.generate_networkx(), + print_stabilizers=print_stabilizers, + ) + + +class LatticeSurgeryProblem: + """A class to provide the input specification of LSS and solve it.""" + + def __init__( + self, + specification: Optional[Mapping[str, Any]] = None, + solver: Literal["kissat", "z3"] = "z3", + kissat_dir: Optional[str] = None, + ) -> None: + """initialize LatticeSurgeryCompiler. + + Args: + specification (Optional[Mapping[str, Any]], optional): the LSS + specification to solve. Defaults to None. + solver (Literal["kissat", "z3"], optional): the solver to use. Defaults + to "z3". "kissat" is recommended. + kissat_dir (Optional[str], optional): directory of the kissat + executable. Defaults to None. + """ + self.specification = specification + self.result = None + self.solver = solver + self.kissat_dir = kissat_dir + + def solve( + self, + specification: Optional[Mapping[str, Any]] = None, + given_arrs: Optional[Mapping[str, Any]] = None, + given_vals: Optional[Sequence[Mapping[str, Any]]] = None, + print_detail: bool = False, + dimacs_file_name: Optional[str] = None, + sat_log_file_name: Optional[str] = None, + ) -> Optional[LatticeSurgerySolution]: + """solve an LSS compilation problem. + + Args: + specification (Optional[Mapping[str, Any]], optional): the LSS + specification to solve. Defaults to None. + given_arrs (Optional[Mapping[str, Any]], optional): given array of known + values to plug in. Defaults to None. + given_vals (Optional[Sequence[Mapping[str, Any]]], optional): given + known values to plug in. Defaults to None. Format should be a sequence + of dicts. Each one contains three fields: 'array', the name of the + array, e.g., 'ExistI'; 'indices', a sequence of the indices, e.g., [0, + 0, 0]; and 'value', 0 or 1. + print_detail (bool, optional): whether to print details in SAT solving. + Defaults to False. + dimacs_file_name (Optional[str], optional): file to save the DIMACS. + Defaults to None. + sat_log_file_name (Optional[str], optional): file to save the SAT solver + log. Defaults to None. + + Returns: + Optional[LatticeSurgerySubroutine]: if the problem is unsatisfiable, + this is None; otherwise, an object initialized by the compiled result. + """ + olsssol = OptimalLatticeSurgerySubroutineSolver( + input_dict=specification if specification else self.specification, + given_arrs=given_arrs, + given_vals=given_vals, + ) + + if self.solver == "z3": + if_sat = olsssol.check_z3(print_progress=print_detail) + else: + if_sat = olsssol.check_external_solver( + dimacs_file_name=dimacs_file_name, + sat_log_file_name=sat_log_file_name, + print_progress=print_detail, + kissat_dir=self.kissat_dir, + ) + + if if_sat: + solver_result = olsssol.get_result() + self.result = LatticeSurgerySolution(lassir=solver_result) + return self.result + else: + return None + + def optimize_depth( + self, + start_depth: int, + print_detail: bool = False, + dimacs_file_name_prefix: Optional[str] = None, + sat_log_file_name_prefix: Optional[str] = None, + ) -> LatticeSurgerySolution: + """find the optimal solution in terms of depth/height of the LSS. + + Args: + start_depth (int): starting depth of the exploration + print_detail (bool, optional): whether to print details in SAT solving. + Defaults to False. + dimacs_file_name_prefix (Optional[str], optional): file prefix to save + the DIMACS. The full file name will contain the specific depth after + this prefix. Defaults to None. + sat_log_file_name_prefix (Optional[str], optional): file prefix to save + the SAT log. The full file name will contain the specific depth after + this prefix. Defaults to None. + result_file_name_prefix (Optional[str], optional): file prefix to save + the variable assignments. The full file name will contain the specific + depth after this prefix. Defaults to None. + post_optimization (str, optional): optimization to perform when + initializing the LatticeSurgerySubroutine object for the result. + Defaults to "default". + + Raises: + ValueError: starting depth is too low. + + Returns: + LatticeSurgerySubroutine: compiled result with the optimal depth. + """ + depth = int(start_depth) + if depth < 2: + raise ValueError("depth too low.") + + checked_depth = {} + while True: + # the ports on the top floor will still be on the top floor when we + # increase the height. This is an assumption. Adapt to your use cases. + for port in self.specification["ports"]: + if port["location"][2] == self.specification["max_k"]: + port["location"][2] = depth + self.specification["max_k"] = depth + + result = self.solve( + print_detail=print_detail, + dimacs_file_name=dimacs_file_name_prefix + f"_d={depth}" + if dimacs_file_name_prefix + else None, + sat_log_file_name=sat_log_file_name_prefix + f"_d={depth}" + if sat_log_file_name_prefix + else None, + ) + if result is None: + checked_depth[str(depth)] = "UNSAT" + if str(depth + 1) in checked_depth: + # since this depth leads to UNSAT, we need to increase the depth, + # but if depth+1 is already checked, we can stop + break + else: + depth += 1 + else: + checked_depth[str(depth)] = "SAT" + self.sat_result = LatticeSurgerySolution(lassir=result.lassir) + if str(depth - 1) in checked_depth: + # since this depth leads to SAT, we need to try decreasing the depth, + # but if depth-1 is already checked, we can stop + break + else: + depth -= 1 + + return self.sat_result + + def with_permuted_ports(self, perm): + # say permutation is [0,3,2], then original is in order, i.e., [0,2,3] + # the full permutation is 0,1,2,3 -> 0,1,3,2 + original = sorted(perm) + this_input = dict(self.specification) + new_ports = [] + for p, port in enumerate(self.specification["ports"]): + if p not in perm: + # the p-th port is not involved in the permutation, e.g., 1 is unchanged + new_ports.append(port) + + else: + # after the permutation, the index of the p-th port is the k-th port in + # `perm` where k is the place of p in `original`. In this example, when + # p=0 and 1, nothing changed. When p=2, we find `place` to be 1, and + # perm[place]=3, so we attach port_3. When p=3, we end up attach port_2 + place = original.index(p) + new_ports.append(self.specification["ports"][perm[place]]) + this_input["ports"] = new_ports + return LatticeSurgeryProblem(this_input) + + def try_one_permutation( + self, + perm: Sequence[int], + print_detail: bool = False, + dimacs_file_name_prefix: Optional[str] = None, + sat_log_file_name_prefix: Optional[str] = None, + result_file_name_prefix: Optional[str] = None, + ) -> Optional[LatticeSurgerySolution]: + """check after the given permutation of ports, if the problem is satisfiable. + + Args: + perm (Sequence[int]): the given permutation, which is an integer tuple + of length n (n being the number of ports permuted). + print_detail (bool, optional): whether to print details in SAT solving. + Defaults to False. + dimacs_file_name_prefix (Optional[str], optional): file prefix to save + the DIMACS. The full file name will contain the specific permutation + after this prefix. Defaults to None. + sat_log_file_name_prefix (Optional[str], optional): file prefix to save + the SAT log. The full file name will contain the specific permutation + after this prefix. Defaults to None. + result_file_name_prefix (Optional[str], optional): file prefix to save + the variable assignments. The full file name will contain the specific + permutation after this prefix. Defaults to None. + + Returns: + Optional[LatticeSurgerySubroutine]: if the problem is unsatisfiable, + this is None; otherwise, an object initialized by the compiled result. + """ + + # say permutation is [0,3,2], then original is in order, i.e., [0,2,3] + # the full permutation is 0,1,2,3 -> 0,1,3,2 + original = sorted(perm) + this_input = dict(self.specification) + new_ports = [] + for p, port in enumerate(self.specification["ports"]): + if p not in perm: + # the p-th port is not involved in the permutation, e.g., 1 is unchanged + new_ports.append(port) + + else: + # after the permutation, the index of the p-th port is the k-th port in + # `perm` where k is the place of p in `original`. In this example, when + # p=0 and 1, nothing changed. When p=2, we find `place` to be 1, and + # perm[place]=3, so we attach port_3. When p=3, we end up attach port_2 + place = original.index(p) + new_ports.append(self.specification["ports"][perm[place]]) + this_input["ports"] = new_ports + + result = self.solve( + specification=this_input, + print_detail=print_detail, + dimacs_file_name=dimacs_file_name_prefix + + "_" + + perm.__repr__().replace(" ", "") + if dimacs_file_name_prefix + else None, + sat_log_file_name=sat_log_file_name_prefix + + "_" + + perm.__repr__().replace(" ", "") + if sat_log_file_name_prefix + else None, + ) + print(f"{perm}: {'SAT' if result else 'UNSAT'}") + return result + + def solve_all_port_permutations( + self, + permute_ports: Sequence[int], + parallelism: int = 1, + shuffle: bool = True, + **kwargs, + ) -> Mapping[str, Sequence[Sequence[int]]]: + """try all the permutations of given ports to see which ones are satisfiable. + + Notice that we do not check that the LSS after permuting the ports (we do + not permute the stabilizers accordingly) is functionally equivalent. The + users should use this method based on their judgement. Also, the number of + permutations scales exponentially with the number of ports to permute, so + this method can easily take an immense amount of time. + + Args: + permute_ports (Sequence[int]): the indices of ports to permite + parallelism (int, optional): number of parallel process. Each one try + one permutation. A New proess starts when an old one finishes. + Defaults to 1. + shuffle (bool, optional): whether using a random order to start the + processes. Defaults to True. + **kwargs: + + Returns: + Mapping[str, Sequence[Sequence[int]]]: a dict with two keys. "SAT": [.] + a list containing all the satisfiable permutations; "UNSAT": [.] + all the unsatisfiable permutations + """ + perms = list(itertools.permutations(permute_ports)) + if shuffle: + random.shuffle(perms) + + pool = multiprocessing.Pool(parallelism) + # issue the job one by one (chuck=1) + results = pool.map( + functools.partial( + self.try_one_permutation, + **kwargs, + ), + perms, + chunksize=1, + ) + + sat_perms = [] + unsat_perms = [] + for p, result in enumerate(results): + if result is None: + unsat_perms.append(perms[p]) + else: + sat_perms.append(perms[p]) + + return { + "SAT": sat_perms, + "UNSAT": unsat_perms, + } diff --git a/glue/lattice_surgery/olssco/rewrite_passes/__init__.py b/glue/lattice_surgery/olssco/rewrite_passes/__init__.py new file mode 100644 index 000000000..e69de29bb diff --git a/glue/lattice_surgery/olssco/rewrite_passes/attach_fixups.py b/glue/lattice_surgery/olssco/rewrite_passes/attach_fixups.py new file mode 100644 index 000000000..770e410cb --- /dev/null +++ b/glue/lattice_surgery/olssco/rewrite_passes/attach_fixups.py @@ -0,0 +1,64 @@ +# assuming all T injections requiring fixup are on the top floor. The output is also on the top floor + + +def attach_fixups(lasir): + n_s = len(lasir['CorrIJ']) + n_i = lasir['n_i'] + n_j = lasir['n_j'] + n_k = lasir['n_k'] + + fixup_locs = [] + for p in lasir['optional']['top_fixups']: + fixup_locs.append((lasir['ports'][p]['i'], lasir['ports'][p]['j'])) + + for i in range(n_i): + for j in range(n_j): + if (i, j) in fixup_locs: + lasir['NodeY'][i][j].append(1) + lasir['ExistK'][i][j][n_k - 1] = 1 + else: + lasir['NodeY'][i][j].append(0) + lasir['ExistK'][i][j][n_k - 1] = 0 + lasir['NodeY'][i][j].append(0) + for arr in ['ExistI', 'ExistJ', 'ExistK']: + lasir[arr][i][j].append(0) + lasir[arr][i][j].append(0) + for arr in ['ColorI', 'ColorJ', 'ColorKM', 'ColorKP']: + lasir[arr][i][j].append(-1) + lasir[arr][i][j].append(-1) + for s in range(n_s): + for arr in ['CorrIJ', 'CorrIK', 'CorrJK', 'CorrJI', 'CorrKI', 'CorrKJ']: + lasir[arr][s][i][j].append(0) + lasir[arr][s][i][j].append(0) + + for port in lasir['ports']: + if 'f' in port and port['f'] == 'output': + ii, jj = port['i'], port['j'] + lasir['ExistK'][ii][jj][n_k - 1] = 1 + lasir['ExistK'][ii][jj][n_k] = 1 + lasir['ExistK'][ii][jj][n_k + 1] = 1 + lasir['ColorKM'][ii][jj][n_k] = lasir['ColorKP'][ii][jj][n_k - 1] + lasir['ColorKM'][ii][jj][n_k + 1] = lasir['ColorKM'][ii][jj][n_k] + lasir['ColorKP'][ii][jj][n_k] = lasir['ColorKM'][ii][jj][n_k] + lasir['ColorKP'][ii][jj][n_k + 1] = lasir['ColorKP'][ii][jj][n_k] + for s in range(n_s): + lasir['CorrKI'][s][ii][jj][n_k] = lasir['CorrKI'][s][ii][jj][n_k - 1] + lasir['CorrKI'][s][ii][jj][n_k + 1] = lasir['CorrKI'][s][ii][jj][n_k] + lasir['CorrKJ'][s][ii][jj][n_k] = lasir['CorrKJ'][s][ii][jj][n_k - 1] + lasir['CorrKJ'][s][ii][jj][n_k + 1] = lasir['CorrKJ'][s][ii][jj][n_k] + port['k'] += 2 + for c in lasir['port_cubes']: + if c[0] == port['i'] and c[1] == port['j']: + c[2] = port['k'] + 1 + + t_injections = [] + for port in lasir['ports']: + if port['f'] == 'T': + if port['e'] == '+': + t_injections.append([port['i'], port['j'], port['k'] + 1]) + else: + t_injections.append([port['i'], port['j'], port['k']]) + lasir['optional']['t_injections'] = t_injections + + lasir['n_k'] += 2 + return lasir diff --git a/glue/lattice_surgery/olssco/rewrite_passes/color_z.py b/glue/lattice_surgery/olssco/rewrite_passes/color_z.py new file mode 100644 index 000000000..ead83a445 --- /dev/null +++ b/glue/lattice_surgery/olssco/rewrite_passes/color_z.py @@ -0,0 +1,176 @@ +"""A one-line summary of the module or program, terminated by a period. + +Leave one blank line. The rest of this docstring should contain an +overall description of the module or program. Optionally, it may also +contain a brief description of exported classes and functions and/or usage +examples. + +Typical usage example: + + foo = ClassFoo() + bar = foo.FunctionBar() +""" + + +def if_uncolorK(n_i, n_j, n_k, ExistK, ColorKP, ColorKM): + for i in range(n_i): + for j in range(n_j): + for k in range(n_k): + if ExistK[i][j][k] and ( + ColorKP[i][j][k] == -1 or ColorKM[i][j][k] == -1 + ): + # print((i,j,k)) + return True + return False + + +def in_bound(n_i, n_j, n_k, i, j, k): + if i in range(n_i) and j in range(n_j) and k in range(n_k): + return True + return False + + +def propogate_IJcolor( + n_i, n_j, n_k, ExistI, ExistJ, ExistK, ColorI, ColorJ, ColorKP, ColorKM +): + for i in range(n_i): + for j in range(n_j): + for k in range(n_k): + if ExistK[i][j][k]: + if in_bound(n_i, n_j, n_k, i - 1, j, k) and ExistI[i - 1][j][k]: + ColorKM[i][j][k] = 1 - ColorI[i - 1][j][k] + if ExistI[i][j][k]: + ColorKM[i][j][k] = 1 - ColorI[i][j][k] + if in_bound(n_i, n_j, n_k, i, j - 1, k) and ExistJ[i][j - 1][k]: + ColorKM[i][j][k] = 1 - ColorJ[i][j - 1][k] + if ExistJ[i][j][k]: + ColorKM[i][j][k] = 1 - ColorJ[i][j][k] + + if ( + in_bound(n_i, n_j, n_k, i - 1, j, k + 1) + and ExistI[i - 1][j][k + 1] + ): + ColorKP[i][j][k] = 1 - ColorI[i - 1][j][k + 1] + if in_bound(n_i, n_j, n_k, i, j, k + 1) and ExistI[i][j][k + 1]: + ColorKP[i][j][k] = 1 - ColorI[i][j][k + 1] + if ( + in_bound(n_i, n_j, n_k, i, j - 1, k + 1) + and ExistJ[i][j - 1][k + 1] + ): + ColorKP[i][j][k] = 1 - ColorJ[i][j - 1][k + 1] + if in_bound(n_i, n_j, n_k, i, j, k + 1) and ExistJ[i][j][k + 1]: + ColorKP[i][j][k] = 1 - ColorJ[i][j][k + 1] + + +def propogate_Kcolor(n_i, n_j, n_k, ExistK, ColorKP, ColorKM, NodeY): + did_something = False + for i in range(n_i): + for j in range(n_j): + for k in range(n_k): + if ExistK[i][j][k]: + if in_bound(n_i, n_j, n_k, i, j, k - 1) and ExistK[i][j][k - 1]: + if ColorKP[i][j][k - 1] > -1 and ColorKM[i][j][k] == -1: + ColorKM[i][j][k] = ColorKP[i][j][k - 1] + did_something = True + if in_bound(n_i, n_j, n_k, i, j, k + 1) and ExistK[i][j][k + 1]: + if ColorKM[i][j][k + 1] > -1 and ColorKP[i][j][k] == -1: + ColorKP[i][j][k] = ColorKM[i][j][k + 1] + did_something = True + if ( + NodeY[i][j][k] + and ColorKM[i][j][k] == -1 + and ColorKP[i][j][k] > -1 + ): + ColorKM[i][j][k] = ColorKP[i][j][k] + did_something = True + if ( + in_bound(n_i, n_j, n_k, i, j, k + 1) + and NodeY[i][j][k + 1] + and ColorKM[i][j][k] > -1 + and ColorKP[i][j][k] == -1 + ): + ColorKP[i][j][k] = ColorKM[i][j][k] + did_something = True + return did_something + + +def assign_Kcolor(n_i, n_j, n_k, ExistK, ColorKP, ColorKM, NodeY): + for i in range(n_i): + for j in range(n_j): + for k in range(n_k): + if ExistK[i][j][k]: + if ColorKM[i][j][k] > -1 and ColorKP[i][j][k] == -1: + ColorKP[i][j][k] = ColorKM[i][j][k] + break + + for i in range(n_i): + for j in range(n_j): + for k in range(n_k): + if ExistK[i][j][k]: + if NodeY[i][j][k] and ColorKM[i][j][k] == -1: + ColorKM[i][j][k] = 0 + break + if ( + in_bound(n_i, n_j, n_k, i, j, k + 1) + and NodeY[i][j][k + 1] + and ColorKP[i][j][k] == -1 + ): + ColorKP[i][j][k] = 0 + break + + +def color_ports(ports, ColorKP, ColorKM): + for port in ports: + if port['d'] == 'K': + if port['e'] == '+': + ColorKP[port['i']][port['j']][port['k']] = port['c'] + else: + ColorKM[port['i']][port['j']][port['k']] = port['c'] + + +def colorZ( + n_i, + n_j, + n_k, + ExistI, + ExistJ, + ExistK, + ColorI, + ColorJ, + ports, + NodeY, + noPrune=False, +): + ColorKP = [[[-1 for _ in range(n_k)] for _ in range(n_j)] for _ in range(n_i)] + ColorKM = [[[-1 for _ in range(n_k)] for _ in range(n_j)] for _ in range(n_i)] + color_ports(ports, ColorKP, ColorKM) + propogate_IJcolor( + n_i, n_j, n_k, ExistI, ExistJ, ExistK, ColorI, ColorJ, ColorKP, ColorKM + ) + while (not noPrune) and if_uncolorK(n_i, n_j, n_k, ExistK, ColorKP, ColorKM): + if not propogate_Kcolor(n_i, n_j, n_k, ExistK, ColorKP, ColorKM, NodeY): + assign_Kcolor(n_i, n_j, n_k, ExistK, ColorKP, ColorKM, NodeY) + return ColorKP, ColorKM + + +def color_z(lasir: dict): + n_i, n_j, n_k, ExistK = ( + lasir['n_i'], + lasir['n_j'], + lasir['n_k'], + lasir['ExistK'], + ) + ExistI, ColorI, ExistJ, ColorJ = ( + lasir['ExistI'], + lasir['ColorI'], + lasir['ExistJ'], + lasir['ColorJ'], + ) + NodeY = lasir['NodeY'] + ports, port_cubes = lasir['ports'], lasir['port_cubes'] + + lasir['ColorKP'], lasir['ColorKM'] = colorZ( + n_i, n_j, n_k, ExistI, ExistJ, ExistK, ColorI, ColorJ, ports, NodeY + ) + # lasir['ColorKP'], lasir['ColorKM'] = [[[-1 for _ in range(n_k)] for _ in range(n_j)] for _ in range(n_i)], [[[-1 for _ in range(n_k)] for _ in range(n_j)] for _ in range(n_i)] + return lasir diff --git a/glue/lattice_surgery/olssco/rewrite_passes/remove_unconnected.py b/glue/lattice_surgery/olssco/rewrite_passes/remove_unconnected.py new file mode 100644 index 000000000..3af8695ac --- /dev/null +++ b/glue/lattice_surgery/olssco/rewrite_passes/remove_unconnected.py @@ -0,0 +1,134 @@ +"""A one-line summary of the module or program, terminated by a period. + +Leave one blank line. The rest of this docstring should contain an +overall description of the module or program. Optionally, it may also +contain a brief description of exported classes and functions and/or usage +examples. + +Typical usage example: + + foo = ClassFoo() + bar = foo.FunctionBar() +""" + + +def check_connect(n_i, n_j, n_k, ExistI, ExistJ, ExistK, ports, NodeY): + y_nodes = [ + i * n_j * n_k + j * n_k + k + for i in range(n_i) + for j in range(n_j) + for k in range(n_k) + if NodeY[i][j][k] + ] + Connect = [[[0 for _ in range(n_k)] for _ in range(n_j)] for _ in range(n_i)] + vips = [p['i'] * n_j * n_k + p['j'] * n_k + p['k'] for p in ports] + mat = [[0 for _ in range(n_i * n_j * n_k)] for _ in range(n_i * n_j * n_k)] + adj = [[] for _ in range(n_i * n_j * n_k)] + for i in range(n_i): + for j in range(n_j): + for k in range(n_k): + if ExistI[i][j][k] and i + 1 < n_i: + adj[i * n_j * n_k + j * n_k + k].append( + (i + 1) * n_j * n_k + j * n_k + k + ) + adj[(i + 1) * n_j * n_k + j * n_k + k].append( + i * n_j * n_k + j * n_k + k + ) + if ExistJ[i][j][k] and j + 1 < n_j: + adj[i * n_j * n_k + j * n_k + k].append( + i * n_j * n_k + (j + 1) * n_k + k + ) + adj[i * n_j * n_k + (j + 1) * n_k + k].append( + i * n_j * n_k + j * n_k + k + ) + if ExistK[i][j][k] and k + 1 < n_k: + adj[i * n_j * n_k + j * n_k + k].append( + i * n_j * n_k + j * n_k + k + 1 + ) + adj[i * n_j * n_k + j * n_k + k + 1].append( + i * n_j * n_k + j * n_k + k + ) + for i in range(n_i): + for j in range(n_j): + for k in range(n_k): + queue = [ + i * n_j * n_k + j * n_k + k, + ] + if i * n_j * n_k + j * n_k + k in y_nodes: + continue + visited = [0 for _ in range(n_i * n_j * n_k)] + while len(queue) > 0: + if queue[0] in vips: + Connect[i][j][k] = 1 + break + visited[queue[0]] = 1 + for v in adj[queue[0]]: + if not visited[v] and v not in y_nodes: + queue.append(v) + queue.pop(0) + + return Connect + + +def array3DAnd(arr0, arr1): + a = len(arr0) + b = len(arr0[0]) + c = len(arr0[0][0]) + arrAnd = [[[0 for _ in range(c)] for _ in range(b)] for _ in range(a)] + for i in range(a): + for j in range(b): + for k in range(c): + if arr0[i][j][k] == 1 and arr1[i][j][k] == 1: + arrAnd[i][j][k] = 1 + return arrAnd + + +def check_edge(n_i, n_j, n_k, ExistI, ExistJ, ExistK, Connect): + EffectI = [[[0 for _ in range(n_k)] for _ in range(n_j)] for _ in range(n_i)] + EffectJ = [[[0 for _ in range(n_k)] for _ in range(n_j)] for _ in range(n_i)] + EffectK = [[[0 for _ in range(n_k)] for _ in range(n_j)] for _ in range(n_i)] + for i in range(n_i): + for j in range(n_j): + for k in range(n_k): + if ExistI[i][j][k] and ( + Connect[i][j][k] or (i + 1 < n_i and Connect[i + 1][j][k]) + ): + EffectI[i][j][k] = 1 + if ExistJ[i][j][k] and ( + Connect[i][j][k] or (j + 1 < n_j and Connect[i][j + 1][k]) + ): + EffectJ[i][j][k] = 1 + if ExistK[i][j][k] and ( + Connect[i][j][k] or (k + 1 < n_k and Connect[i][j][k + 1]) + ): + EffectK[i][j][k] = 1 + return EffectI, EffectJ, EffectK + + +def remove_unconnected(lasir: dict): + n_i, n_j, n_k, ExistK = ( + lasir['n_i'], + lasir['n_j'], + lasir['n_k'], + lasir['ExistK'], + ) + ExistI, ColorI, ExistJ, ColorJ = ( + lasir['ExistI'], + lasir['ColorI'], + lasir['ExistJ'], + lasir['ColorJ'], + ) + NodeY = lasir['NodeY'] + ports, port_cubes = lasir['ports'], lasir['port_cubes'] + Connect = check_connect(n_i, n_j, n_k, ExistI, ExistJ, ExistK, ports, NodeY) + EffectI, EffectJ, EffectK = check_edge( + n_i, n_j, n_k, ExistI, ExistJ, ExistK, Connect + ) + ExistI, ExistJ, ExistK = ( + array3DAnd(ExistI, EffectI), + array3DAnd(ExistJ, EffectJ), + array3DAnd(ExistK, EffectK), + ) + lasir['ExistI'], lasir['ExistJ'], lasir['ExistK'] = ExistI, ExistJ, ExistK + + return lasir diff --git a/glue/lattice_surgery/olssco/sat_lattice_surgery_solver.py b/glue/lattice_surgery/olssco/sat_lattice_surgery_solver.py new file mode 100644 index 000000000..f8c294175 --- /dev/null +++ b/glue/lattice_surgery/olssco/sat_lattice_surgery_solver.py @@ -0,0 +1,1805 @@ +"""OLSSSol: Optimal Lattice Surgery Subroutine Solver + +It encodes a lattice surgery problem to SAT/SMT and checks whether there is a +solution. In this compilation problem, we are given certain spacetime volume, +certain ports, and certain stabilizers. OLSSSol encodes the constraints on +LaSSIR variables such that the resulting variable assignments consist of a valid +lattice surgery procedure with the correct functionality (satisfies all the +given stabilizers). OLSSSol finds the solution with a SAT/SMT solver. +""" + +import os +import subprocess +import sys +import tempfile +import time +from typing import Any, Mapping, Optional, Sequence +import z3 + + +def var_given( + data: dict[ + str, + Any, + ], + arr: str, + i: int, + j: int, + k: int, + l: int | None = None, +) -> bool: + """Check whether data[arr][i][j][k]([l]) is given. + + If the given indices are not found, or the number is neither 0 nor 1, return + False; otherwise return True. + + Args: + data (dict[ str, Any, ]): contain arrays + arr (str): ExistI, etc. + i (int): first index + j (int): second index + k (int): third index + l (int | None, optional): optional fourth index. Defaults to None. + + Returns: + bool: whether the variable value is given + """ + + if arr not in data: + return False + if i not in range(len(data[arr])): + return False + if j not in range(len(data[arr][i])): + return False + if k not in range(len(data[arr][i][j])): + return False + if l is None: + if data[arr][i][j][k] != 0 and data[arr][i][j][k] != 1: + return False + return True + # l is not None, then + if l not in range(len(data[arr][i][j][k])): + return False + if data[arr][i][j][k][l] != 0 and data[arr][i][j][k][l] != 1: + return False + return True + + +def port_incident_edges( + port: Mapping[str, str | int], n_i: int, n_j: int, n_k: int +) -> tuple[Sequence[str], Sequence[tuple[int, int, int]]]: + """Compute the edges incident to a port. + + A port is an edge with a dangling end. The incident edges of a port are the + five other edges connecting to that end. However, some of these edges can be + out of bound, we just want to compute those that are in bound. + + Args: + port (Mapping[str, str | int]): the port to consider + n_i (int): spatial bound on I direction + n_j (int): spatial bound on J direction + n_k (int): spatial bound on K direction + + Returns: + tuple[Sequence[str], Sequence[tuple[int, int, int]]]: + Two lists of the same length [0,6): (dirs, coords) + dirs: the direction of the incident edges, can be 'I', 'J', or 'K' + coords: the coordinates of the incident edges, each one is (i,j,k) + """ + coords = [] + dirs = [] + + # first, just consider adjancency without caring about out-of-bound + if port['d'] == 'I': + adj_dirs = ['I', 'J', 'J', 'K', 'K'] + if port['e'] == '-': # empty cube is (i,j,k) + adj_coords = [ + (port['i'] - 1, port['j'], port['k']), # (i-1,j,k)---(i,j,k) + (port['i'], port['j'] - 1, port['k']), # (i,j-1,k)---(i,j,k) + (port['i'], port['j'], port['k']), # (i,j,k)---(i+1,j,k) + (port['i'], port['j'], port['k'] - 1), # (i,j,k-1)---(i,j,k) + (port['i'], port['j'], port['k']), # (i,j,k)---(i,j,k+1) + ] + elif port['e'] == '+': # empty cube is (i+1,j,k) + adj_coords = [ + (port['i'] + 1, port['j'], port['k']), # (i+1,j,k)---(i+2,j,k) + (port['i'] + 1, port['j'] - 1, port['k']), # (i+1,j-1,k)---(i+1,j,k) + (port['i'] + 1, port['j'], port['k']), # (i+1,j,k)---(i+1,j+1,k) + (port['i'] + 1, port['j'], port['k'] - 1), # (i+1,j,k-1)---(i+1,j,k) + (port['i'] + 1, port['j'], port['k']), # (i+1,j,k)---(i+1,j,k+1) + ] + + if port['d'] == 'J': + adj_dirs = ['J', 'K', 'K', 'I', 'I'] + if port['e'] == '-': + adj_coords = [ + (port['i'], port['j'] - 1, port['k']), + (port['i'], port['j'], port['k'] - 1), + (port['i'], port['j'], port['k']), + (port['i'] - 1, port['j'], port['k']), + (port['i'], port['j'], port['k']), + ] + elif port['e'] == '+': + adj_coords = [ + (port['i'], port['j'] + 1, port['k']), + (port['i'], port['j'] + 1, port['k'] - 1), + (port['i'], port['j'] + 1, port['k']), + (port['i'] - 1, port['j'] + 1, port['k']), + (port['i'], port['j'] + 1, port['k']), + ] + + if port['d'] == 'K': + adj_dirs = ['K', 'I', 'I', 'J', 'J'] + if port['e'] == '-': + adj_coords = [ + (port['i'], port['j'], port['k'] - 1), + (port['i'] - 1, port['j'], port['k']), + (port['i'], port['j'], port['k']), + (port['i'], port['j'] - 1, port['k']), + (port['i'], port['j'], port['k']), + ] + elif port['e'] == '+': + adj_coords = [ + (port['i'], port['j'], port['k'] + 1), + (port['i'] - 1, port['j'], port['k'] + 1), + (port['i'], port['j'], port['k'] + 1), + (port['i'], port['j'] - 1, port['k'] + 1), + (port['i'], port['j'], port['k'] + 1), + ] + + # only keep the edges in bound + for i, coord in enumerate(adj_coords): + if ( + (coord[0] in range(n_i)) + and (coord[1] in range(n_j)) + and (coord[2] in range(n_k)) + ): + coords.append(adj_coords[i]) + dirs.append(adj_dirs[i]) + + return dirs, coords + + +def cnf_even_parity_upto4(eles: Sequence[Any]) -> Any: + """Compute the CNF format of parity of up to four Z3 binary variables. + + Args: + eles (Sequence[Any]): the binary variables + + Returns: + (Any) the Z3 constraint meaning the parity of the inputs is even. + """ + + if len(eles) == 1: # 1 var even parity -> this var is false + return z3.Not(eles[0]) + if len(eles) == 2: # 2 vars even pairty -> both True or both False + return z3.Or( + z3.And(z3.Not(eles[0]), z3.Not(eles[1])), z3.And(eles[0], eles[1]) + ) + if len(eles) == 3: # 3 vars even parity -> all False, or 2 True and 1 False + return z3.Or( + z3.And(z3.Not(eles[0]), z3.Not(eles[1]), z3.Not(eles[2])), + z3.And(eles[0], eles[1], z3.Not(eles[2])), + z3.And(eles[0], z3.Not(eles[1]), eles[2]), + z3.And(z3.Not(eles[0]), eles[1], eles[2]), + ) + if len(eles) == 4: # 4 vars even parity -> 0, 2, or 4 vars are True + return z3.Or( + z3.And( + z3.Not(eles[0]), z3.Not(eles[1]), z3.Not(eles[2]), z3.Not(eles[3]) + ), + z3.And(z3.Not(eles[0]), z3.Not(eles[1]), eles[2], eles[3]), + z3.And(z3.Not(eles[0]), eles[1], z3.Not(eles[2]), eles[3]), + z3.And(z3.Not(eles[0]), eles[1], eles[2], z3.Not(eles[3])), + z3.And(eles[0], z3.Not(eles[1]), z3.Not(eles[2]), eles[3]), + z3.And(eles[0], z3.Not(eles[1]), eles[2], z3.Not(eles[3])), + z3.And(eles[0], eles[1], z3.Not(eles[2]), z3.Not(eles[3])), + z3.And(eles[0], eles[1], eles[2], eles[3]), + ) + + +class OptimalLatticeSurgerySubroutineSolver: + """class of compiling LaSSIR using Z3 SMT solver.""" + + def __init__( + self, + input_dict: Mapping[str, Any], + given_arrs: Mapping[str, Any] | None = None, + given_vals: Sequence[Mapping[str, Any]] | None = None, + color_ij: bool = True, + ) -> None: + """initialization of OLSSSol objects. + + Args: + input_dict (Mapping[str, Any]): specification of LSS + given_arrs (Mapping[str, Any], optional): Arrays of values to plug in. + Defaults to None. + given_vals (Sequence[Mapping[str, Any]], optional): Values to plug in. + Defaults to None. + color_ij (bool, optional): if the color matching constraints of I and J + edges are imposed. Defaults to False. + """ + self.input_dict = input_dict + self.color_ij = color_ij + self.goal = z3.Goal() + self.process_input(input_dict) + self.build_smt_model( + given_arrs=given_arrs, given_vals=given_vals, color_ij=color_ij + ) + + def process_input(self, input_dict: Mapping[str, Any]) -> None: + """read input file, mainly translating the info of the ports. + + Args: + input_dict (Mapping[str, Any]): + + Raises: + ValueError: no input specification given + ValueError: missing key in input + ValueError: some spatial bound <= 0 + ValueError: more stabilizers than ports + ValueError: stabilizer length is not the same as the number of ports + ValueError: stabilizer contain things other than I, X, Y, or Z + ValueError: missing key in port + ValueError: port location is not a 3-tuple + ValueError: port direction is not 2-string + ValueError: port sign (which end is dangling) is not - or + + ValueError: port axis is not I, J, or K + ValueError: port Z basis direction is not I, J, or K, and not the same + with the edge + """ + data = input_dict + + if not input_dict: + raise ValueError('no input specification given.') + + for key in ['max_i', 'max_j', 'max_k', 'ports', 'stabilizers']: + if key not in data: + raise ValueError(f'missing key {key} in input.') + + # load spatial bound, check > 0 + self.n_i = data['max_i'] + self.n_j = data['max_j'] + self.n_k = data['max_k'] + if min([self.n_i, self.n_j, self.n_k]) <= 0: + raise ValueError('max_i or _j or _k <= 0.') + + self.n_p = len(data['ports']) + self.n_s = len(data['stabilizers']) + # there's at most as many stabilizers as ports + if self.n_s > self.n_p: + raise ValueError('Too many stabilizers compated to ports.') + + # stabilizers should be paulistrings of length #ports + self.paulistings = [s.replace('.', 'I') for s in data['stabilizers']] + for s in self.paulistings: + if len(s) != self.n_p: + raise ValueError(f'invalid stabilizer length {s}.') + for i in range(len(s)): + if s[i] not in ['I', 'X', 'Y', 'Z']: + raise ValueError(f'invalid stabilizer pauli {s}.') + + # transform port data + self.ports = [] + for port in data['ports']: + my_port = {} + + for key in ['location', 'direction', 'z_basis_direction']: + if key not in port: + raise ValueError(f'missing key {key} in port {port}') + + if len(port['location']) != 3: + raise ValueError(f'port with invalid location {port}.') + my_port['i'], my_port['j'], my_port['k'] = port['location'] + + if len(port['direction']) != 2: + raise ValueError(f'port with invalid direction {port}.') + if port['direction'][0] not in ['+', '-']: + raise ValueError(f'port with invalid sign {port}.') + if port['direction'][1] not in ['I', 'J', 'K']: + raise ValueError(f'port with invalid axis {port}.') + my_port['e'] = '-' if port['direction'][0] == '+' else '+' + my_port['d'] = port['direction'][1] + if my_port['e'] == '+': + # the corresponding coordinate should -1, e.g., if axis is K and + # it's minus direction, then edge should be (i,j,k-1)-(i,j,k) + my_port[my_port['d'].lower()] -= 1 + + z_dir = port['z_basis_direction'] + if z_dir not in ['I', 'J', 'K'] or z_dir == my_port['d']: + raise ValueError(f'port with invalid Z basis direction {port}.') + if my_port['d'] == 'I': + my_port['c'] = 0 if z_dir == 'J' else 1 + if my_port['d'] == 'J': + my_port['c'] = 0 if z_dir == 'K' else 1 + if my_port['d'] == 'K': + my_port['c'] = 0 if z_dir == 'I' else 1 + + if 'function' in port: + my_port['f'] = port['function'] + + self.ports.append(my_port) + + # from paulistrings to correlation surfaces + self.stabs = self.derive_corr_boundary(self.paulistings) + + self.optional = {} + self.forbidden_cubes = [] + if 'optional' in data: + self.optional = data['optional'] + + if 'forbidden_cubes' in data['optional']: + for cube in data['optional']['forbidden_cubes']: + if len(cube) != 3: + raise ValueError(f'forbid cube invalid {cube}.') + if ( + cube[0] not in range(self.n_i) + or cube[1] not in range(self.n_j) + or cube[2] not in range(self.n_k) + ): + continue + self.forbidden_cubes.append(cube) + + self.get_port_cubes() + + def derive_corr_boundary( + self, paulistrings: Sequence[str] + ) -> list[list[Mapping[str, int]]]: + """derive the boundary correlation surface variable values. + + From the color orientation of the ports and the stabilizers, we can derive + which correlation surface variables evaluates to True and which to False at + the ports for each stabilizer. + + Args: + paulistrings (Sequence[str]): stabilizers as a list of Pauli strings. + + Returns: + list[list[Mapping[str, int]]]: Outer layer list is the list of + stabilizers. Inner layer list is the situation at each port for one + specifeic stabilizer. Each port is specified with a dictionary of 2 bits + for the 2 correaltion surfaces. + """ + stabs = [] + for paulistring in paulistrings: + corr = [] + for p in range(self.n_p): + if paulistring[p] == 'I': # I -> no corr surf should be present + if self.ports[p]['d'] == 'I': + corr.append({'IJ': 0, 'IK': 0}) + if self.ports[p]['d'] == 'J': + corr.append({'JI': 0, 'JK': 0}) + if self.ports[p]['d'] == 'K': + corr.append({'KI': 0, 'KJ': 0}) + + if paulistring[p] == 'Y': # Y -> both corr surf should be present + if self.ports[p]['d'] == 'I': + corr.append({'IJ': 1, 'IK': 1}) + if self.ports[p]['d'] == 'J': + corr.append({'JI': 1, 'JK': 1}) + if self.ports[p]['d'] == 'K': + corr.append({'KI': 1, 'KJ': 1}) + + if paulistring[p] == 'X': # X -> only corr surf touching red faces + if self.ports[p]['d'] == 'I': + if self.ports[p]['c']: + corr.append({'IJ': 1, 'IK': 0}) + else: + corr.append({'IJ': 0, 'IK': 1}) + if self.ports[p]['d'] == 'J': + if self.ports[p]['c']: + corr.append({'JI': 0, 'JK': 1}) + else: + corr.append({'JI': 1, 'JK': 0}) + if self.ports[p]['d'] == 'K': + if self.ports[p]['c']: + corr.append({'KI': 1, 'KJ': 0}) + else: + corr.append({'KI': 0, 'KJ': 1}) + + if paulistring[p] == 'Z': # Z -> only corr surf touching blue faces + if self.ports[p]['d'] == 'I': + if not self.ports[p]['c']: + corr.append({'IJ': 1, 'IK': 0}) + else: + corr.append({'IJ': 0, 'IK': 1}) + if self.ports[p]['d'] == 'J': + if not self.ports[p]['c']: + corr.append({'JI': 0, 'JK': 1}) + else: + corr.append({'JI': 1, 'JK': 0}) + if self.ports[p]['d'] == 'K': + if not self.ports[p]['c']: + corr.append({'KI': 1, 'KJ': 0}) + else: + corr.append({'KI': 0, 'KJ': 1}) + stabs.append(corr) + return stabs + + def define_vars(self, color_ij: bool = True) -> None: + """define the variables in Z3 into self.vars. + + Args: + color_ij (bool, optional): if the color matching constraints of I and J + edges are imposed. Defaults to True. + """ + self.vars = { + 'ExistI': [ + [ + [z3.Bool(f'ExistI({i},{j},{k})') for k in range(self.n_k)] + for j in range(self.n_j) + ] + for i in range(self.n_i) + ], + 'ExistJ': [ + [ + [z3.Bool(f'ExistJ({i},{j},{k})') for k in range(self.n_k)] + for j in range(self.n_j) + ] + for i in range(self.n_i) + ], + 'ExistK': [ + [ + [z3.Bool(f'ExistK({i},{j},{k})') for k in range(self.n_k)] + for j in range(self.n_j) + ] + for i in range(self.n_i) + ], + 'NodeY': [ + [ + [z3.Bool(f'NodeY({i},{j},{k})') for k in range(self.n_k)] + for j in range(self.n_j) + ] + for i in range(self.n_i) + ], + 'CorrIJ': [ + [ + [ + [ + z3.Bool(f'CorrIJ({s},{i},{j},{k})') + for k in range(self.n_k) + ] + for j in range(self.n_j) + ] + for i in range(self.n_i) + ] + for s in range(self.n_s) + ], + 'CorrIK': [ + [ + [ + [ + z3.Bool(f'CorrIK({s},{i},{j},{k})') + for k in range(self.n_k) + ] + for j in range(self.n_j) + ] + for i in range(self.n_i) + ] + for s in range(self.n_s) + ], + 'CorrJK': [ + [ + [ + [ + z3.Bool(f'CorrJK({s},{i},{j},{k})') + for k in range(self.n_k) + ] + for j in range(self.n_j) + ] + for i in range(self.n_i) + ] + for s in range(self.n_s) + ], + 'CorrJI': [ + [ + [ + [ + z3.Bool(f'CorrJI({s},{i},{j},{k})') + for k in range(self.n_k) + ] + for j in range(self.n_j) + ] + for i in range(self.n_i) + ] + for s in range(self.n_s) + ], + 'CorrKI': [ + [ + [ + [ + z3.Bool(f'CorrKI({s},{i},{j},{k})') + for k in range(self.n_k) + ] + for j in range(self.n_j) + ] + for i in range(self.n_i) + ] + for s in range(self.n_s) + ], + 'CorrKJ': [ + [ + [ + [ + z3.Bool(f'CorrKJ({s},{i},{j},{k})') + for k in range(self.n_k) + ] + for j in range(self.n_j) + ] + for i in range(self.n_i) + ] + for s in range(self.n_s) + ], + } + + if color_ij: + self.vars['ColorI'] = [ + [ + [z3.Bool(f'ColorI({i},{j},{k})') for k in range(self.n_k)] + for j in range(self.n_j) + ] + for i in range(self.n_i) + ] + self.vars['ColorJ'] = [ + [ + [z3.Bool(f'ColorJ({i},{j},{k})') for k in range(self.n_k)] + for j in range(self.n_j) + ] + for i in range(self.n_i) + ] + + def plugin_arrs(self, data: Mapping[str, Any], color_ij: bool = True) -> None: + """plug in the given arrays of values. + + Args: + data (Mapping[str, Any]): contains gieven values + color_ij (bool, optional): if the color matching constraints of I and J + edges are imposed. Defaults to True. + """ + arrs = [ + 'NodeY', + 'ExistI', + 'ExistJ', + 'ExistK', + ] + if color_ij: + arrs += ['ColorI', 'ColorJ'] + + for s in range(self.n_s): + for i in range(self.n_i): + for j in range(self.n_j): + for k in range(self.n_k): + if s == 0: # Exist, Node, and Color vars + for arr in arrs: + if var_given(data, arr, i, j, k): + self.goal.add( + self.vars[arr][i][j][k] + if data[arr][i][j][k] == 1 + else z3.Not(self.vars[arr][i][j][k]) + ) + # Corr vars + for arr in [ + 'CorrIJ', + 'CorrIK', + 'CorrJI', + 'CorrJK', + 'CorrKI', + 'CorrKJ', + ]: + if var_given(data, arr, s, i, j, k): + self.goal.add( + self.vars[arr][s][i][j][k] + if data[arr][s][i][j][k] + else z3.Not(self.vars[arr][s][i][j][k]) + ) + + def plugin_vals(self, data_set: Sequence[Mapping[str, Any]]): + """plug in the given values + + Args: + data (Sequence[Mapping[str, Any]]): given values as a sequence of dicts. + Each one contains three fields: 'array', the name of the array, e.g., + 'ExistI'; 'indices', a sequence of the indices; and 'value'. + """ + for data in data_set: + (arr, idx) = data['array'], data['indices'] + if arr.startswith('Corr'): + s, i, j, k = idx + if data['value']: + self.goal.add(self.vars[arr][s][i][j][k]) + else: + self.goal.add(z3.Not(self.vars[arr][s][i][j][k])) + else: + i, j, k = idx + if data['value']: + self.goal.add(self.vars[arr][i][j][k]) + else: + self.goal.add(z3.Not(self.vars[arr][i][j][k])) + + def get_port_cubes(self) -> None: + """calculate which cubes are empty serving as ports.""" + self.port_cubes = [] + for p in self.ports: + # if e=-, (i,j,k); otherwise, +1 in the proper direction + if p['e'] == '-': + self.port_cubes.append((p['i'], p['j'], p['k'])) + elif p['d'] == 'I': + self.port_cubes.append((p['i'] + 1, p['j'], p['k'])) + elif p['d'] == 'J': + self.port_cubes.append((p['i'], p['j'] + 1, p['k'])) + elif p['d'] == 'K': + self.port_cubes.append((p['i'], p['j'], p['k'] + 1)) + + def constraint_forbid_cube(self) -> None: + """forbid a list of cubes.""" + for cube in self.forbidden_cubes: + (i, j, k) = cube[0], cube[1], cube[2] + if ( + len(cube) != 3 + or i not in range(self.n_i) + or j not in range(self.n_j) + or k not in range(self.n_k) + ): + continue + self.goal.add(z3.Not(self.vars['NodeY'][i][j][k])) + if i > 0: + self.goal.add(z3.Not(self.vars['ExistI'][i - 1][j][k])) + self.goal.add(z3.Not(self.vars['ExistI'][i][j][k])) + if j > 0: + self.goal.add(z3.Not(self.vars['ExistJ'][i][j - 1][k])) + self.goal.add(z3.Not(self.vars['ExistJ'][i][j][k])) + # if k > 0: + # self.model.add(z3.Not(self.vars['ExistK'][i][j][k - 1])) + # self.model.add(z3.Not(self.vars['ExistK'][i][j][k])) + + def constraint_port(self, color_ij: bool = True) -> None: + """structural constraints at ports: some edges must exist and some must not. + + Args: + color_ij (bool, optional): if the color matching constraints of I and J + edges are imposed. Defaults to True. + """ + for port in self.ports: + # the edge specified by the port exists + self.goal.add( + self.vars[f'Exist{port["d"]}'][port['i']][port['j']][port['k']] + ) + # if I- or J-edge exist, set the color value too to the given one + if color_ij: + if port['d'] != 'K': + if port['c'] == 1: + self.goal.add( + self.vars[f'Color{port["d"]}'][port['i']][port['j']][port['k']] + ) + else: + self.goal.add( + z3.Not( + self.vars[f'Color{port["d"]}'][port['i']][port['j']][ + port['k'] + ] + ) + ) + + # collect the edges touching the port to forbid them + dirs, coords = port_incident_edges(port, self.n_i, self.n_j, self.n_k) + for i, coord in enumerate(coords): + self.goal.add( + z3.Not(self.vars[f'Exist{dirs[i]}'][coord[0]][coord[1]][coord[2]]) + ) + + def constraint_connect_outside(self) -> None: + """no edge should cross the spatial bound except for ports.""" + for i in range(self.n_i): + for j in range(self.n_j): + # consider K-edges crossing K-bound and not a port + if (i, j, self.n_k) not in self.port_cubes: + self.goal.add(z3.Not(self.vars['ExistK'][i][j][self.n_k - 1])) + for i in range(self.n_i): + for k in range(self.n_k): + if (i, self.n_j, k) not in self.port_cubes: + self.goal.add(z3.Not(self.vars['ExistJ'][i][self.n_j - 1][k])) + for j in range(self.n_j): + for k in range(self.n_k): + if (self.n_i, j, k) not in self.port_cubes: + self.goal.add(z3.Not(self.vars['ExistI'][self.n_i - 1][j][k])) + + def constraint_timelike_y(self) -> None: + """Y-spiders must be timelike, i.e., forbid all I- and J- edges to them.""" + for i in range(self.n_i): + for j in range(self.n_j): + for k in range(self.n_k): + if (i, j, k) not in self.port_cubes: + self.goal.add( + z3.Implies( + self.vars['NodeY'][i][j][k], + z3.Not(self.vars['ExistI'][i][j][k]), + ) + ) + self.goal.add( + z3.Implies( + self.vars['NodeY'][i][j][k], + z3.Not(self.vars['ExistJ'][i][j][k]), + ) + ) + if i - 1 >= 0: + self.goal.add( + z3.Implies( + self.vars['NodeY'][i][j][k], + z3.Not(self.vars['ExistI'][i - 1][j][k]), + ) + ) + if j - 1 >= 0: + self.goal.add( + z3.Implies( + self.vars['NodeY'][i][j][k], + z3.Not(self.vars['ExistJ'][i][j - 1][k]), + ) + ) + + def constraint_no_deg1(self) -> None: + """forbid degree-1 X or Z spiders by considering incident edges.""" + for i in range(self.n_i): + for j in range(self.n_j): + for k in range(self.n_k): + for d in ['I', 'J', 'K']: + for e in ['-', '+']: + cube = {'I': i, 'J': j, 'K': k} + cube[d] += 1 if e == '+' else 0 + + # construct fake ports to get incident edges + p0 = {'i': i, 'j': j, 'k': k, 'd': d, 'e': e, 'c': 0} + found_p0 = False + for port in self.ports: + if ( + i == port['i'] + and j == port['j'] + and k == port['k'] + and d == port['d'] + ): + found_p0 = True + + # only non-port edges need to consider + if ( + not found_p0 + and cube['I'] < self.n_i + and cube['J'] < self.n_j + and cube['K'] < self.n_k + ): + # only cubes inside bound need to consider + dirs, coords = port_incident_edges( + p0, self.n_i, self.n_j, self.n_k + ) + edges = [ + self.vars[f'Exist{dirs[l]}'][coord[0]][coord[1]][coord[2]] + for l, coord in enumerate(coords) + ] + # if the cube is not Y and the edge exist, then + # at least one of its incident edges exists. + self.goal.add( + z3.Implies( + z3.And( + z3.Not( + self.vars['NodeY'][cube['I']][cube['J']][ + cube['K'] + ] + ), + self.vars[f'Exist{d}'][i][j][k], + ), + z3.Or(edges), + ) + ) + + def constraint_ij_color(self) -> None: + """color matching for I- and J-edges.""" + for i in range(self.n_i): + for j in range(self.n_j): + for k in range(self.n_k): + if i >= 1 and j >= 1: + # (i-1,j,k)-(i,j,k) and (i,j-1,k)-(i,j,k) + self.goal.add( + z3.Implies( + z3.And( + self.vars['ExistI'][i - 1][j][k], + self.vars['ExistJ'][i][j - 1][k], + ), + z3.Or( + z3.And( + self.vars['ColorI'][i - 1][j][k], + z3.Not(self.vars['ColorJ'][i][j - 1][k]), + ), + z3.And( + z3.Not(self.vars['ColorI'][i - 1][j][k]), + self.vars['ColorJ'][i][j - 1][k], + ), + ), + ) + ) + + if i >= 1: + # (i-1,j,k)-(i,j,k) and (i,j,k)-(i,j+1,k) + self.goal.add( + z3.Implies( + z3.And( + self.vars['ExistI'][i - 1][j][k], + self.vars['ExistJ'][i][j][k], + ), + z3.Or( + z3.And( + self.vars['ColorI'][i - 1][j][k], + z3.Not(self.vars['ColorJ'][i][j][k]), + ), + z3.And( + z3.Not(self.vars['ColorI'][i - 1][j][k]), + self.vars['ColorJ'][i][j][k], + ), + ), + ) + ) + # (i-1,j,k)-(i,j,k) and (i,j,k)-(i+1,j,k) + self.goal.add( + z3.Implies( + z3.And( + self.vars['ExistI'][i - 1][j][k], + self.vars['ExistI'][i][j][k], + ), + z3.Or( + z3.And( + self.vars['ColorI'][i - 1][j][k], + self.vars['ColorI'][i][j][k], + ), + z3.And( + z3.Not(self.vars['ColorI'][i - 1][j][k]), + z3.Not(self.vars['ColorI'][i][j][k]), + ), + ), + ) + ) + + if j >= 1: + # (i,j,k)-(i+1,j,k) and (i,j-1,k)-(i,j,k) + self.goal.add( + z3.Implies( + z3.And( + self.vars['ExistI'][i][j][k], + self.vars['ExistJ'][i][j - 1][k], + ), + z3.Or( + z3.And( + self.vars['ColorI'][i][j][k], + z3.Not(self.vars['ColorJ'][i][j - 1][k]), + ), + z3.And( + z3.Not(self.vars['ColorI'][i][j][k]), + self.vars['ColorJ'][i][j - 1][k], + ), + ), + ) + ) + # (i,j-1,k)-(i,j,k) and (i,j,k)-(i,j+1,k) + self.goal.add( + z3.Implies( + z3.And( + self.vars['ExistJ'][i][j - 1][k], + self.vars['ExistJ'][i][j][k], + ), + z3.Or( + z3.And( + self.vars['ColorJ'][i][j - 1][k], + self.vars['ColorJ'][i][j][k], + ), + z3.And( + z3.Not(self.vars['ColorJ'][i][j - 1][k]), + z3.Not(self.vars['ColorJ'][i][j][k]), + ), + ), + ) + ) + + # (i,j,k)-(i+1,j,k) and (i,j,k)-(i,j+1,k) + self.goal.add( + z3.Implies( + z3.And( + self.vars['ExistI'][i][j][k], self.vars['ExistJ'][i][j][k] + ), + z3.Or( + z3.And( + self.vars['ColorI'][i][j][k], + z3.Not(self.vars['ColorJ'][i][j][k]), + ), + z3.And( + z3.Not(self.vars['ColorI'][i][j][k]), + self.vars['ColorJ'][i][j][k], + ), + ), + ) + ) + + def constraint_3d_corner(self) -> None: + """forbid 3D corners by saying at least in one direction, both edges nonexist.""" + for i in range(self.n_i): + for j in range(self.n_j): + for k in range(self.n_k): + i_edges = [ + self.vars['ExistI'][i][j][k], + ] + if i - 1 >= 0: + i_edges.append(self.vars['ExistI'][i - 1][j][k]) + j_edges = [ + self.vars['ExistJ'][i][j][k], + ] + if j - 1 >= 0: + j_edges.append(self.vars['ExistJ'][i][j - 1][k]) + k_edges = [ + self.vars['ExistK'][i][j][k], + ] + if k - 1 >= 0: + k_edges.append(self.vars['ExistK'][i][j][k - 1]) + + # at least one of the three terms is true. The first term is that + # both I-edges connecting to (i,j,k) do not exist + self.goal.add( + z3.Or( + z3.Not(z3.Or(i_edges)), + z3.Not(z3.Or(j_edges)), + z3.Not(z3.Or(k_edges)), + ) + ) + + def constraint_corr_ports(self) -> None: + """plug in the correlation surface values at the ports.""" + for s, stab in enumerate(self.stabs): + for p, corrs in enumerate(stab): + for k, v in corrs.items(): + if v == 1: + self.goal.add( + self.vars[f'Corr{k}'][s][self.ports[p]['i']][ + self.ports[p]['j'] + ][self.ports[p]['k']] + ) + else: + self.goal.add( + z3.Not( + self.vars[f'Corr{k}'][s][self.ports[p]['i']][ + self.ports[p]['j'] + ][self.ports[p]['k']] + ) + ) + + def constraint_corr_y(self) -> None: + """correlation surfaces at Y-spider should both exist or nonexist.""" + for s in range(self.n_s): + for i in range(self.n_i): + for j in range(self.n_j): + for k in range(self.n_k): + self.goal.add( + z3.Or( + z3.Not(self.vars['NodeY'][i][j][k]), + z3.Or( + z3.And( + self.vars['CorrKI'][s][i][j][k], + self.vars['CorrKJ'][s][i][j][k], + ), + z3.And( + z3.Not(self.vars['CorrKI'][s][i][j][k]), + z3.Not(self.vars['CorrKJ'][s][i][j][k]), + ), + ), + ) + ) + if k - 1 >= 0: + self.goal.add( + z3.Or( + z3.Not(self.vars['NodeY'][i][j][k]), + z3.Or( + z3.And( + self.vars['CorrKI'][s][i][j][k - 1], + self.vars['CorrKJ'][s][i][j][k - 1], + ), + z3.And( + z3.Not(self.vars['CorrKI'][s][i][j][k - 1]), + z3.Not(self.vars['CorrKJ'][s][i][j][k - 1]), + ), + ), + ) + ) + + def constraint_corr_perp(self) -> None: + """for corr surf perpendicular to normal vector, all exist or nonexist.""" + for s in range(self.n_s): + for i in range(self.n_i): + for j in range(self.n_j): + for k in range(self.n_k): + if (i, j, k) not in self.port_cubes: # only internal spider + # only consider X or Z spider + # if normal is K meaning meaning both (i,j,k)-(i,j,k+1) and + # (i,j,k)-(i,j,k-1) are out of range, or in range but nonexistent + normal = z3.And( + z3.Not(self.vars['NodeY'][i][j][k]), + z3.Not(self.vars['ExistK'][i][j][k]), + ) + if k - 1 >= 0: + normal = z3.And( + normal, z3.Not(self.vars['ExistK'][i][j][k - 1]) + ) + + # for other edges, need to build intermediate expression + # for (i,j,k)-(i+1,j,k) and (i,j,k)-(i,j+1,k), build expression + # meaning the edge is nonexistent or exist and has the correlation + # surface perpendicular to the normal vector in them. + no_edge_or_with_corr = [ + z3.Or( + z3.Not(self.vars['ExistI'][i][j][k]), + self.vars['CorrIJ'][s][i][j][k], + ), + z3.Or( + z3.Not(self.vars['ExistJ'][i][j][k]), + self.vars['CorrJI'][s][i][j][k], + ), + ] + + # for (i,j,k)-(i+1,j,k) and (i,j,k)-(i,j+1,k), build expression + # meaning the edge is nonexistent or exist and does not have the + # correlation surface perpendicular to the normal vector in them. + no_edge_or_no_corr = [ + z3.Or( + z3.Not(self.vars['ExistI'][i][j][k]), + z3.Not(self.vars['CorrIJ'][s][i][j][k]), + ), + z3.Or( + z3.Not(self.vars['ExistJ'][i][j][k]), + z3.Not(self.vars['CorrJI'][s][i][j][k]), + ), + ] + + if i - 1 >= 0: + # build intermediate expression for (i-1,j,k)-(i,j,k) + no_edge_or_with_corr.append( + z3.Or( + z3.Not(self.vars['ExistI'][i - 1][j][k]), + self.vars['CorrIJ'][s][i - 1][j][k], + ) + ) + no_edge_or_no_corr.append( + z3.Or( + z3.Not(self.vars['ExistI'][i - 1][j][k]), + z3.Not(self.vars['CorrIJ'][s][i - 1][j][k]), + ) + ) + + if j - 1 >= 0: + # build intermediate expression for (i,j-1,k)-(i,j,k) + no_edge_or_with_corr.append( + z3.Or( + z3.Not(self.vars['ExistJ'][i][j - 1][k]), + self.vars['CorrJI'][s][i][j - 1][k], + ) + ) + no_edge_or_no_corr.append( + z3.Or( + z3.Not(self.vars['ExistJ'][i][j - 1][k]), + z3.Not(self.vars['CorrJI'][s][i][j - 1][k]), + ) + ) + + # if normal vector is K, then in all its incident edges that exist + # all correlation surface in I-J plane exist or nonexist + self.goal.add( + z3.Implies( + normal, + z3.Or( + z3.And(no_edge_or_with_corr), + z3.And(no_edge_or_no_corr), + ), + ) + ) + + # if normal is I + normal = z3.And( + z3.Not(self.vars['NodeY'][i][j][k]), + z3.Not(self.vars['ExistI'][i][j][k]), + ) + if i - 1 >= 0: + normal = z3.And( + normal, z3.Not(self.vars['ExistI'][i - 1][j][k]) + ) + no_edge_or_with_corr = [ + z3.Or( + z3.Not(self.vars['ExistJ'][i][j][k]), + self.vars['CorrJK'][s][i][j][k], + ), + z3.Or( + z3.Not(self.vars['ExistK'][i][j][k]), + self.vars['CorrKJ'][s][i][j][k], + ), + ] + no_edge_or_no_corr = [ + z3.Or( + z3.Not(self.vars['ExistJ'][i][j][k]), + z3.Not(self.vars['CorrJK'][s][i][j][k]), + ), + z3.Or( + z3.Not(self.vars['ExistK'][i][j][k]), + z3.Not(self.vars['CorrKJ'][s][i][j][k]), + ), + ] + if j - 1 >= 0: + no_edge_or_with_corr.append( + z3.Or( + z3.Not(self.vars['ExistJ'][i][j - 1][k]), + self.vars['CorrJK'][s][i][j - 1][k], + ) + ) + no_edge_or_no_corr.append( + z3.Or( + z3.Not(self.vars['ExistJ'][i][j - 1][k]), + z3.Not(self.vars['CorrJK'][s][i][j - 1][k]), + ) + ) + if k - 1 >= 0: + no_edge_or_with_corr.append( + z3.Or( + z3.Not(self.vars['ExistK'][i][j][k - 1]), + self.vars['CorrKJ'][s][i][j][k - 1], + ) + ) + no_edge_or_no_corr.append( + z3.Or( + z3.Not(self.vars['ExistK'][i][j][k - 1]), + z3.Not(self.vars['CorrKJ'][s][i][j][k - 1]), + ) + ) + self.goal.add( + z3.Implies( + normal, + z3.Or( + z3.And(no_edge_or_with_corr), + z3.And(no_edge_or_no_corr), + ), + ) + ) + + # if normal is J + normal = z3.And( + z3.Not(self.vars['NodeY'][i][j][k]), + z3.Not(self.vars['ExistJ'][i][j][k]), + ) + if j - 1 >= 0: + normal = z3.And( + normal, z3.Not(self.vars['ExistJ'][i][j - 1][k]) + ) + no_edge_or_with_corr = [ + z3.Or( + z3.Not(self.vars['ExistI'][i][j][k]), + self.vars['CorrIK'][s][i][j][k], + ), + z3.Or( + z3.Not(self.vars['ExistK'][i][j][k]), + self.vars['CorrKI'][s][i][j][k], + ), + ] + no_edge_or_no_corr = [ + z3.Or( + z3.Not(self.vars['ExistI'][i][j][k]), + z3.Not(self.vars['CorrIK'][s][i][j][k]), + ), + z3.Or( + z3.Not(self.vars['ExistK'][i][j][k]), + z3.Not(self.vars['CorrKI'][s][i][j][k]), + ), + ] + if i - 1 >= 0: + no_edge_or_with_corr.append( + z3.Or( + z3.Not(self.vars['ExistI'][i - 1][j][k]), + self.vars['CorrIK'][s][i - 1][j][k], + ) + ) + no_edge_or_no_corr.append( + z3.Or( + z3.Not(self.vars['ExistI'][i - 1][j][k]), + z3.Not(self.vars['CorrIK'][s][i - 1][j][k]), + ) + ) + if k - 1 >= 0: + no_edge_or_with_corr.append( + z3.Or( + z3.Not(self.vars['ExistK'][i][j][k - 1]), + self.vars['CorrKI'][s][i][j][k - 1], + ) + ) + no_edge_or_no_corr.append( + z3.Or( + z3.Not(self.vars['ExistK'][i][j][k - 1]), + z3.Not(self.vars['CorrKI'][s][i][j][k - 1]), + ) + ) + self.goal.add( + z3.Implies( + normal, + z3.Or( + z3.And(no_edge_or_with_corr), + z3.And(no_edge_or_no_corr), + ), + ) + ) + + def constraint_corr_para(self) -> None: + """for corr surf parallel to the normal vector, even number of them exist.""" + for s in range(self.n_s): + for i in range(self.n_i): + for j in range(self.n_j): + for k in range(self.n_k): + if (i, j, k) not in self.port_cubes: # only internal spiders + # only X or Z spiders, if normal is K + normal = z3.And( + z3.Not(self.vars['NodeY'][i][j][k]), + z3.Not(self.vars['ExistK'][i][j][k]), + ) + if k - 1 >= 0: + normal = z3.And( + normal, z3.Not(self.vars['ExistK'][i][j][k - 1]) + ) + + # unlike in constraint_corr_perp, we only care about the cases + # where the edge exists and the correlation surface parallel to + # K also is present, so we build intermediate expressions as below + edge_with_corr = [ + z3.And( + self.vars['ExistI'][i][j][k], + self.vars['CorrIK'][s][i][j][k], + ), + z3.And( + self.vars['ExistJ'][i][j][k], + self.vars['CorrJK'][s][i][j][k], + ), + ] + + # build the intermediate expression for (i-1,j,k)-(i,j,k) + if i - 1 >= 0: + edge_with_corr.append( + z3.And( + self.vars['ExistI'][i - 1][j][k], + self.vars['CorrIK'][s][i - 1][j][k], + ) + ) + + # build the intermediate expression for (i,j-1,k)-(i,j,k) + if j - 1 >= 0: + edge_with_corr.append( + z3.And( + self.vars['ExistJ'][i][j - 1][k], + self.vars['CorrJK'][s][i][j - 1][k], + ) + ) + + # the parity of the intermediate expressions must be even + self.goal.add( + z3.Implies(normal, cnf_even_parity_upto4(edge_with_corr)) + ) + + # if normal is I + normal = z3.And( + z3.Not(self.vars['NodeY'][i][j][k]), + z3.Not(self.vars['ExistI'][i][j][k]), + ) + if i - 1 >= 0: + normal = z3.And( + normal, z3.Not(self.vars['ExistI'][i - 1][j][k]) + ) + edge_with_corr = [ + z3.And( + self.vars['ExistJ'][i][j][k], + self.vars['CorrJI'][s][i][j][k], + ), + z3.And( + self.vars['ExistK'][i][j][k], + self.vars['CorrKI'][s][i][j][k], + ), + ] + if j - 1 >= 0: + edge_with_corr.append( + z3.And( + self.vars['ExistJ'][i][j - 1][k], + self.vars['CorrJI'][s][i][j - 1][k], + ) + ) + if k - 1 >= 0: + edge_with_corr.append( + z3.And( + self.vars['ExistK'][i][j][k - 1], + self.vars['CorrKI'][s][i][j][k - 1], + ) + ) + self.goal.add( + z3.Implies(normal, cnf_even_parity_upto4(edge_with_corr)) + ) + + # if normal is J + normal = z3.And( + z3.Not(self.vars['NodeY'][i][j][k]), + z3.Not(self.vars['ExistJ'][i][j][k]), + ) + if j - 1 >= 0: + normal = z3.And( + normal, z3.Not(self.vars['ExistJ'][i][j - 1][k]) + ) + edge_with_corr = [ + z3.And( + self.vars['ExistI'][i][j][k], + self.vars['CorrIJ'][s][i][j][k], + ), + z3.And( + self.vars['ExistK'][i][j][k], + self.vars['CorrKJ'][s][i][j][k], + ), + ] + if i - 1 >= 0: + edge_with_corr.append( + z3.And( + self.vars['ExistI'][i - 1][j][k], + self.vars['CorrIJ'][s][i - 1][j][k], + ) + ) + if k - 1 >= 0: + edge_with_corr.append( + z3.And( + self.vars['ExistK'][i][j][k - 1], + self.vars['CorrKJ'][s][i][j][k - 1], + ) + ) + self.goal.add( + z3.Implies(normal, cnf_even_parity_upto4(edge_with_corr)) + ) + + def build_smt_model( + self, + given_arrs: Mapping[str, Any] = None, + given_vals: Sequence[Mapping[str, Any]] = None, + color_ij: bool = True, + ) -> None: + """build the SMT model with variables and constraints. + + Args: + given_arrs (Mapping[str, Any], optional): given arrays of values to plug + in. Defaults to None. + given_vals (Sequence[Mapping[str, Any]], optional): given values to plug + in. Defaults to None. + color_ij (bool, optional): if the color matching constraints of I and J + edges are imposed. Defaults to True. + """ + self.define_vars(color_ij=color_ij) + if given_arrs: + self.plugin_arrs(given_arrs, color_ij=color_ij) + if given_vals: + self.plugin_vals(given_vals) + + # baseline order + self.constraint_forbid_cube() + self.constraint_port(color_ij=color_ij) + self.constraint_connect_outside() + self.constraint_timelike_y() + self.constraint_no_deg1() + if color_ij: + self.constraint_ij_color() + self.constraint_3d_corner() + + self.constraint_corr_ports() + self.constraint_corr_y() + self.constraint_corr_perp() + self.constraint_corr_para() + + def check_z3(self, print_progress: bool = True) -> bool: + """check whether the built goal in self.goal is satisfiable. + + Args: + print_progress (bool, optional): if print out the progress made. + + Returns: + bool: True if SAT, False if UNSAT + """ + if print_progress: + print('Construct a Z3 SMT model and solve...') + start_time = time.time() + self.solver = z3.Solver() + self.solver.add(self.goal) + ifsat = self.solver.check() + elapsed = time.time() - start_time + if print_progress: + print('elapsed time: {:2f}s'.format(elapsed)) + if ifsat == z3.sat: + if print_progress: + print('Z3 SAT') + return True + else: + if print_progress: + print('Z3 UNSAT') + return False + + def get_result(self) -> Mapping[str, Any]: + """get the variable values. + + Returns: + Mapping[str, Any]: output in the LaSSIR format + """ + model = self.solver.model() + data = { + 'specification': self.input_dict, + 'n_i': self.n_i, + 'n_j': self.n_j, + 'n_k': self.n_k, + 'n_p': self.n_p, + 'n_s': self.n_s, + 'ports': self.ports, + 'stabs': self.stabs, + 'port_cubes': self.port_cubes, + 'optional': self.optional, + 'ExistI': [ + [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i) + ], + 'ExistJ': [ + [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i) + ], + 'ExistK': [ + [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i) + ], + 'ColorI': [ + [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i) + ], + 'ColorJ': [ + [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i) + ], + 'NodeY': [ + [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i) + ], + 'CorrIJ': [ + [ + [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i) + ] + for _ in range(self.n_s) + ], + 'CorrIK': [ + [ + [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i) + ] + for _ in range(self.n_s) + ], + 'CorrJK': [ + [ + [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i) + ] + for _ in range(self.n_s) + ], + 'CorrJI': [ + [ + [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i) + ] + for _ in range(self.n_s) + ], + 'CorrKI': [ + [ + [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i) + ] + for _ in range(self.n_s) + ], + 'CorrKJ': [ + [ + [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i) + ] + for _ in range(self.n_s) + ], + } + arrs = [ + 'NodeY', + 'ExistI', + 'ExistJ', + 'ExistK', + ] + if self.color_ij: + arrs += [ + 'ColorI', + 'ColorJ', + ] + for s in range(self.n_s): + for i in range(self.n_i): + for j in range(self.n_j): + for k in range(self.n_k): + if s == 0: # Exist, Node, and Color vars + for arr in arrs: + data[arr][i][j][k] = 1 if model[self.vars[arr][i][j][k]] else 0 + + # Corr vars + for arr in [ + 'CorrIJ', + 'CorrIK', + 'CorrJI', + 'CorrJK', + 'CorrKI', + 'CorrKJ', + ]: + data[arr][s][i][j][k] = ( + 1 if model[self.vars[arr][s][i][j][k]] else 0 + ) + return data + + def write_cnf(self, output_file_name: str) -> bool: + """generate CNF for the problem. + + Args: + output_file_name (str): file to write CNF. + + Returns: + bool: False if the CNF is trivial, True otherwise + """ + simplified = z3.Tactic('simplify')(self.goal)[0] + simplified = z3.Tactic('propagate-values')(simplified)[0] + cnf = z3.Tactic('tseitin-cnf')(simplified)[0] + dimacs = cnf.dimacs() + + with open(output_file_name, 'w') as output_f: + output_f.write(cnf.dimacs()) + if dimacs.startswith('p cnf 1 1'): + print( + 'Generated CNF is trivial meaning z3 concludes the instance UNSAT' + ' during simplification.' + ) + return False + else: + return True + + def read_external_result( + self, dimacs_file: str, result_file: str + ) -> Mapping[str, Any]: + """read result from external SAT solver + + Args: + dimacs_file (str): + result_file (str): log, e.g., from Kissat containing SAT assignments + + Raises: + ValueError: in the dimacs file, the last lines are comments that records + the mapping from SAT variable indices to the variable names in Z3. If + the coordinates in this name is incorrect, this error is raised. + + Returns: + Mapping[str, Any]: variable assignment in arrays. All the one with a + corresponding SAT variable are read off from the SAT log. The others + are left with -1. + """ + results = { + 'ExistI': [ + [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i) + ], + 'ExistJ': [ + [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i) + ], + 'ExistK': [ + [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i) + ], + 'ColorI': [ + [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i) + ], + 'ColorJ': [ + [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i) + ], + 'NodeY': [ + [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i) + ], + 'CorrIJ': [ + [ + [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i) + ] + for _ in range(self.n_s) + ], + 'CorrIK': [ + [ + [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i) + ] + for _ in range(self.n_s) + ], + 'CorrJK': [ + [ + [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i) + ] + for _ in range(self.n_s) + ], + 'CorrJI': [ + [ + [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i) + ] + for _ in range(self.n_s) + ], + 'CorrKI': [ + [ + [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i) + ] + for _ in range(self.n_s) + ], + 'CorrKJ': [ + [ + [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i) + ] + for _ in range(self.n_s) + ], + } + + # in this file, the assigments are lines starting with 'v' like + # v -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 ... + # the vars starts from 1 and - means it's False; otherwise, it's True + # we scan through all these lines, and save the assignments to `sat` + with open(result_file, 'r') as f: + sat_output = f.readlines() + sat = {} + for line in sat_output: + if line.startswith('v'): + assignments = line[1:].strip().split(' ') + for assignment in assignments: + tmp = int(assignment) + if tmp < 0: + sat[str(-tmp)] = 0 + elif tmp > 0: + sat[str(tmp)] = 1 + + # in the dimacs generated by Z3, there are lines starting with 'c' like + # c 8804 CorrIJ(1,0,3,4) or c 60053 k!44404 + # which records the mapping from our variables to variables in dimacs + # the ones starting with k! are added in the translation, we don't care + with open(dimacs_file, 'r') as f: + dimacs = f.readlines() + for line in dimacs: + if line.startswith('c'): + _, index, name = line.strip().split(' ') + if name.startswith(( + 'NodeY', + 'ExistI', + 'ExistJ', + 'ExistK', + 'ColorI', + 'ColorJ', + 'CorrIJ', + 'CorrIK', + 'CorrJI', + 'CorrJK', + 'CorrKI', + 'CorrKJ', + )): + arr, tmp = name[:-1].split('(') + coords = [int(num) for num in tmp.split(',')] + if len(coords) == 3: + results[arr][coords[0]][coords[1]][coords[2]] = sat[index] + elif len(coords) == 4: + results[arr][coords[0]][coords[1]][coords[2]][coords[3]] = sat[ + index + ] + else: + raise ValueError('number of coord should be 3 or 4!') + + return results + + def check_external_solver( + self, + kissat_dir: str, + dimacs_file_name: Optional[str] = None, + sat_log_file_name: Optional[str] = None, + print_progress: bool = True, + ) -> bool: + """check whether there is a solution with an external solver, e.g., Kissat + + Args: + kissat_dir (str): directory containing an executable named kissat + dimacs_file_name (Optional[str], optional): Defaults to None. Then, the + dimacs file is in a tmp directory. If specified, the dimacs will be + saved to that path. + sat_log_file_name (Optional[str], optional): Defaults to None. Then, the + sat log file is in a tmp directory. If specified, the dimacs will be + saved to that path. + print_progress (bool, optional): whether print the SAT solving process + on screen. Defaults to True. + + Raises: + ValueError: kissat_dir is not a directory + ValueError: there is no executable kissat in kissat_dir + ValueError: the return code to kissat is neither SAT (10) nor UNSAT (20) + + Returns: + bool: True if SAT, False if UNSAT + """ + if not os.path.isdir(kissat_dir): + raise ValueError(f'{kissat_dir} is not a directory.') + if kissat_dir.endswith('/'): + solver_cmd = kissat_dir + 'kissat' + else: + solver_cmd = kissat_dir + '/kissat' + if not os.path.isfile(solver_cmd): + raise ValueError(f'There is no kissat in {kissat_dir}.') + + if_solved = False + with tempfile.TemporaryDirectory() as tmp_dir: + # open a tmp directory as workspace + + # dimacs and sat log are either in the tmp directory, or as user specified + tmp_dimacs_file_name = ( + dimacs_file_name if dimacs_file_name else tmp_dir + '/tmp.dimacs' + ) + tmp_sat_log_file_name = ( + sat_log_file_name if sat_log_file_name else tmp_dir + '/tmp.sat' + ) + + if self.write_cnf(tmp_dimacs_file_name): + # continue if the CNF is non-trivial. Otherwise, we conclude it's UNSAT + + with open(tmp_sat_log_file_name, 'w') as log: + # use tmp_sat_log_file_name to record stdout of kissat + + kissat_return_code = -100 + # -100 if the return code is not updated later on. + + with subprocess.Popen( + [solver_cmd, tmp_dimacs_file_name], + stdout=subprocess.PIPE, + bufsize=1, + universal_newlines=True, + ) as run_kissat: + for line in run_kissat.stdout: + log.write(line) + if print_progress: + sys.stdout.write(line) + get_return_code = run_kissat.communicate()[0] + kissat_return_code = run_kissat.returncode + + if kissat_return_code == 10: + # 10 means SAT in Kissat + if_solved = True + if print_progress: + print('kissat SAT') + + # we read the Kissat solution from the SAT log, then, plug those into + # the Z3 model and solved inside Z3 again. The reason is that Z3 did + # some simplification of the problem so not every variable appear in + # the DIMACS given to Kissat. We still need to know their value. + result = self.read_external_result( + tmp_dimacs_file_name, + tmp_sat_log_file_name, + ) + self.plugin_arrs(result, self.color_ij) + self.check_z3(print_progress) + + elif kissat_return_code == 20: + if print_progress: + print(f'{solver_cmd} UNSAT') + + elif kissat_return_code == -100: + print('Did not get Kissat return code.') + + else: + raise ValueError( + f'Kissat return code {kissat_return_code} is neither SAT nor' + ' UNSAT. Maybe you should add print_process=True to enable the' + ' Kissat printout message to see what is going on.' + ) + # closing the tmp directory, the files and itself are removed + + return if_solved diff --git a/glue/lattice_surgery/olssco/tools/__init__.py b/glue/lattice_surgery/olssco/tools/__init__.py new file mode 100644 index 000000000..e69de29bb diff --git a/glue/lattice_surgery/olssco/tools/verify_stabilizers.py b/glue/lattice_surgery/olssco/tools/verify_stabilizers.py new file mode 100644 index 000000000..87a0f15b9 --- /dev/null +++ b/glue/lattice_surgery/olssco/tools/verify_stabilizers.py @@ -0,0 +1,40 @@ +from typing import Sequence +import stim +import stimzx + + +def verify_stabilizers( + specified_paulistrings: Sequence[str], + result_networkx, + print_stabilizers: bool = False, +) -> bool: + result_stabilizers = [ + stab.output + for stab in stimzx.zx_graph_to_external_stabilizers(result_networkx) + ] + specified_stabilizers = [ + stim.PauliString(paulistring) for paulistring in specified_paulistrings + ] + if print_stabilizers: + print("specified:") + for s in specified_stabilizers: + print(s) + print("==================================================================") + print("resulting:") + for s in result_stabilizers: + print(s) + print("==================================================================") + + for s in result_stabilizers: + for ss in specified_stabilizers: + if not ss.commutes(s): + print( + f"result stabilizer {s} not commuting with specified stabilizer" + f" {ss}" + ) + if print_stabilizers: + print("specified and resulting stabilizers are not equivalent.") + return False + if print_stabilizers: + print("specified and resulting stabilizers are equivalent.") + return True diff --git a/glue/lattice_surgery/olssco/translators/__init__.py b/glue/lattice_surgery/olssco/translators/__init__.py new file mode 100644 index 000000000..dbe918638 --- /dev/null +++ b/glue/lattice_surgery/olssco/translators/__init__.py @@ -0,0 +1 @@ +from olssco.translators.zx_grid_graph import ZXGridGraph diff --git a/glue/lattice_surgery/olssco/translators/gltf_generator.py b/glue/lattice_surgery/olssco/translators/gltf_generator.py new file mode 100644 index 000000000..a40ff227d --- /dev/null +++ b/glue/lattice_surgery/olssco/translators/gltf_generator.py @@ -0,0 +1,1582 @@ +"""A one-line summary of the module or program, terminated by a period. + +Leave one blank line. The rest of this docstring should contain an +overall description of the module or program. Optionally, it may also +contain a brief description of exported classes and functions and/or usage +examples. + +Typical usage example: + + foo = ClassFoo() + bar = foo.FunctionBar() +""" + +import json +from typing import Any, Mapping, Optional, Sequence + +SQ2 = 0.707106769085 +BASE_GLTF = { + "asset": {"generator": "LaSIR CodeGen", "version": "2.0"}, + "scene": 0, + "scenes": [{"name": "Scene", "nodes": [0]}], + "nodes": [{"name": "try", "children": []}], +} + + +def float_to_little_endian_hex(f): + from struct import pack + + # Pack the float into a binary string using the little-endian format + binary_data = pack(" -1: + rectangles = [rect for rect in rectangles if rm_dir not in rect["name"]] + else: + rectangles = [rect for rect in rectangles if "Corr" not in rect["name"]] + return rectangles + + +def cube_gen( + SEP, + loc, + exists, + colors, + stabilizer, + corr, + noColor, + rm_dir: str = ":+J", +): + squares = [] + for face in ["-K", "+K"]: + if exists[face] == 0: + squares.append({ + "name": f"spider{loc}:{face}", + "mesh": 2, + "translation": [ + SEP * loc[0], + (1 if face == "+K" else 0) + SEP * loc[2], + -SEP * loc[1], + ], + }) + for dir in ["+I", "-I", "+J", "-J"]: + if exists[dir]: + if dir == "+I" or dir == "-I": + if colors[dir] == 1: + squares[-1]["mesh"] = 0 + else: + squares[-1]["mesh"] = 1 + else: + if colors[dir] == 0: + squares[-1]["mesh"] = 0 + else: + squares[-1]["mesh"] = 1 + break + for face in ["-I", "+I"]: + if exists[face] == 0: + squares.append({ + "name": f"spider{loc}:{face}", + "mesh": 2, + "translation": [ + (1 if face == "+I" else 0) + SEP * loc[0], + SEP * loc[2], + -SEP * loc[1], + ], + "rotation": [0, 0, SQ2, SQ2], + }) + for dir in ["+J", "-J", "+K", "-K"]: + if exists[dir]: + if dir == "+J" or dir == "-J": + if colors[dir] == 1: + squares[-1]["mesh"] = 0 + else: + squares[-1]["mesh"] = 1 + elif not noColor: + if colors[dir] == 1: + squares[-1]["mesh"] = 1 + elif colors[dir] == 0: + squares[-1]["mesh"] = 0 + for face in ["-J", "+J"]: + if exists[face] == 0: + squares.append({ + "name": f"spider{loc}:{face}", + "mesh": 2, + "translation": [ + 1 + SEP * loc[0], + SEP * loc[2], + (-1 if face == "+J" else 0) - SEP * loc[1], + ], + "rotation": [0.5, 0.5, 0.5, 0.5], + }) + for dir in ["+I", "-I", "+K", "-K"]: + if exists[dir]: + if dir == "+I" or dir == "-I": + if colors[dir] == 0: + squares[-1]["mesh"] = 0 + else: + squares[-1]["mesh"] = 1 + elif not noColor: + if colors[dir] == 1: + squares[-1]["mesh"] = 0 + elif colors[dir] == 0: + squares[-1]["mesh"] = 1 + + degree = sum([v for (k, v) in exists.items()]) + normal = {"I": 0, "J": 0, "K": 0} + if exists["-I"] == 0 and exists["+I"] == 0: + normal["I"] = 1 + if exists["-J"] == 0 and exists["+J"] == 0: + normal["J"] = 1 + if exists["-K"] == 0 and exists["+K"] == 0: + normal["K"] = 1 + if degree > 1: + if ( + exists["-I"] + and exists["+I"] + and exists["-J"] == 0 + and exists["+J"] == 0 + and exists["-K"] == 0 + and exists["+K"] == 0 + ): + if corr["-I"][0]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 9, + "translation": [ + SEP * loc[0], + 0.5 + SEP * loc[2], + -SEP * loc[1], + ], + }) + if corr["-I"][1]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 9, + "translation": [ + 1 + SEP * loc[0], + SEP * loc[2], + -0.5 - SEP * loc[1], + ], + "rotation": [0.5, 0.5, 0.5, 0.5], + }) + elif ( + exists["-I"] == 0 + and exists["+I"] == 0 + and exists["-J"] + and exists["+J"] + and exists["-K"] == 0 + and exists["+K"] == 0 + ): + if corr["-J"][0]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 9, + "translation": [ + 0.5 + SEP * loc[0], + SEP * loc[2], + -SEP * loc[1], + ], + "rotation": [0, 0, SQ2, SQ2], + }) + if corr["-J"][1]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 9, + "translation": [ + SEP * loc[0], + 0.5 + SEP * loc[2], + -SEP * loc[1], + ], + }) + elif ( + exists["-I"] == 0 + and exists["+I"] == 0 + and exists["-J"] == 0 + and exists["+J"] == 0 + and exists["-K"] + and exists["+K"] + ): + if corr["-K"][0]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 9, + "translation": [ + 1 + SEP * loc[0], + SEP * loc[2], + -0.5 - SEP * loc[1], + ], + "rotation": [0.5, 0.5, 0.5, 0.5], + }) + if corr["-K"][1]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 9, + "translation": [ + 0.5 + SEP * loc[0], + SEP * loc[2], + -SEP * loc[1], + ], + "rotation": [0, 0, SQ2, SQ2], + }) + else: + if normal["I"]: + if corr["-J"][0] or corr["+J"][0] or corr["-K"][1] or corr["+K"][1]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 9, + "translation": [ + 0.5 + SEP * loc[0], + SEP * loc[2], + -SEP * loc[1], + ], + "rotation": [0, 0, SQ2, SQ2], + }) + + if corr["-J"][1] and corr["+J"][1] and corr["-K"][0] and corr["+K"][0]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 11, + "translation": [ + SEP * loc[0], + SEP * loc[2], + -1 - SEP * loc[1], + ], + "rotation": [0, -SQ2, 0, SQ2], + }) + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 11, + "translation": [ + SEP * loc[0], + 0.5 + SEP * loc[2], + -0.5 - SEP * loc[1], + ], + "rotation": [0, -SQ2, 0, SQ2], + }) + elif corr["-J"][1] and corr["+J"][1]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 9, + "translation": [ + SEP * loc[0], + 0.5 + SEP * loc[2], + -SEP * loc[1], + ], + }) + elif corr["-K"][0] and corr["+K"][0]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 9, + "translation": [ + 1 + SEP * loc[0], + SEP * loc[2], + -0.5 - SEP * loc[1], + ], + "rotation": [0.5, 0.5, 0.5, 0.5], + }) + elif corr["-J"][1] and corr["-K"][0]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 11, + "translation": [ + 1 + SEP * loc[0], + SEP * loc[2], + -SEP * loc[1], + ], + "rotation": [0, SQ2, 0, SQ2], + }) + elif corr["+J"][1] and corr["+K"][0]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 11, + "translation": [ + 1 + SEP * loc[0], + 0.5 + SEP * loc[2], + -0.5 - SEP * loc[1], + ], + "rotation": [0, SQ2, 0, SQ2], + }) + elif corr["+J"][1] and corr["-K"][0]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 11, + "translation": [ + SEP * loc[0], + SEP * loc[2], + -1 - SEP * loc[1], + ], + "rotation": [0, -SQ2, 0, SQ2], + }) + elif corr["-J"][1] and corr["+K"][0]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 11, + "translation": [ + SEP * loc[0], + 0.5 + SEP * loc[2], + -0.5 - SEP * loc[1], + ], + "rotation": [0, -SQ2, 0, SQ2], + }) + elif normal["J"]: + if corr["-K"][0] or corr["+K"][0] or corr["-I"][1] or corr["+I"][1]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 9, + "translation": [ + 1 + SEP * loc[0], + SEP * loc[2], + -0.5 - SEP * loc[1], + ], + "rotation": [0.5, 0.5, 0.5, 0.5], + }) + + if corr["-K"][1] and corr["+K"][1] and corr["-I"][0] and corr["+I"][0]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 11, + "translation": [ + 0.5 + SEP * loc[0], + 0.5 + SEP * loc[2], + -SEP * loc[1], + ], + "rotation": [0, 0, SQ2, SQ2], + }) + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 11, + "translation": [ + 1 + SEP * loc[0], + SEP * loc[2], + -SEP * loc[1], + ], + "rotation": [0, 0, SQ2, SQ2], + }) + elif corr["-K"][1] and corr["+K"][1]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 9, + "translation": [ + 0.5 + SEP * loc[0], + SEP * loc[2], + -SEP * loc[1], + ], + "rotation": [0, 0, SQ2, SQ2], + }) + elif corr["-I"][0] and corr["+I"][0]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 9, + "translation": [ + SEP * loc[0], + 0.5 + SEP * loc[2], + -SEP * loc[1], + ], + }) + elif corr["-K"][1] and corr["-I"][0]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 11, + "translation": [SEP * loc[0], SEP * loc[2], -SEP * loc[1]], + }) + elif corr["+K"][1] and corr["+I"][0]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 11, + "translation": [ + 0.5 + SEP * loc[0], + 0.5 + SEP * loc[2], + -SEP * loc[1], + ], + }) + elif corr["+K"][1] and corr["-I"][0]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 11, + "translation": [ + 0.5 + SEP * loc[0], + 0.5 + SEP * loc[2], + -SEP * loc[1], + ], + "rotation": [0, 0, SQ2, SQ2], + }) + elif corr["-K"][1] and corr["+I"][0]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 11, + "translation": [ + 1 + SEP * loc[0], + SEP * loc[2], + -SEP * loc[1], + ], + "rotation": [0, 0, SQ2, SQ2], + }) + else: + if corr["-I"][0] or corr["+I"][0] or corr["-J"][1] or corr["+J"][1]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 9, + "translation": [ + SEP * loc[0], + 0.5 + SEP * loc[2], + -SEP * loc[1], + ], + }) + + if corr["-I"][1] and corr["+I"][1] and corr["-J"][0] and corr["+J"][0]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 11, + "translation": [ + 0.5 + SEP * loc[0], + SEP * loc[2], + -0.5 - SEP * loc[1], + ], + "rotation": [SQ2, 0, 0, SQ2], + }) + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 11, + "translation": [ + SEP * loc[0], + SEP * loc[2], + -1 - SEP * loc[1], + ], + "rotation": [SQ2, 0, 0, SQ2], + }) + elif corr["-I"][1] and corr["+I"][1]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 9, + "translation": [ + 1 + SEP * loc[0], + SEP * loc[2], + -0.5 - SEP * loc[1], + ], + "rotation": [0.5, 0.5, 0.5, 0.5], + }) + elif corr["-J"][0] and corr["+J"][0]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 9, + "translation": [ + 0.5 + SEP * loc[0], + SEP * loc[2], + -SEP * loc[1], + ], + "rotation": [0, 0, SQ2, SQ2], + }) + elif corr["-I"][1] and corr["-J"][0]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 11, + "translation": [ + SEP * loc[0], + 1 + SEP * loc[2], + -SEP * loc[1], + ], + "rotation": [-SQ2, 0, 0, SQ2], + }) + elif corr["+I"][1] and corr["+J"][0]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 11, + "translation": [ + 0.5 + SEP * loc[0], + 1 + SEP * loc[2], + -0.5 - SEP * loc[1], + ], + "rotation": [-SQ2, 0, 0, SQ2], + }) + elif corr["+I"][1] and corr["-J"][0]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 11, + "translation": [ + 0.5 + SEP * loc[0], + SEP * loc[2], + -0.5 - SEP * loc[1], + ], + "rotation": [SQ2, 0, 0, SQ2], + }) + elif corr["-I"][1] and corr["+J"][0]: + squares.append({ + "name": f"spider{loc}:Corr", + "mesh": 11, + "translation": [ + SEP * loc[0], + SEP * loc[2], + -1 - SEP * loc[1], + ], + "rotation": [SQ2, 0, 0, SQ2], + }) + + if stabilizer > -1: + squares = [sqar for sqar in squares if rm_dir not in sqar["name"]] + else: + squares = [sqar for sqar in squares if "Corr" not in sqar["name"]] + return squares + + +def special_gen( + SEP, + loc, + exists, + type, + stabilizer, + rm_dir: str = ":+J", +): + if type == "Y": + square_mesh = 3 + half_dist_mesh = 12 + elif type == "T": + square_mesh = 13 + half_dist_mesh = 14 + else: + square_mesh = -1 + half_dist_mesh = -1 + + shapes = [] + if exists["+K"]: + # need connect to top + shapes.append({ + "name": f"spider{loc}:top:-K", + "mesh": square_mesh, + "translation": [ + SEP * loc[0], + 0.55 + SEP * loc[2], + -SEP * loc[1], + ], + }) + shapes.append({ + "name": f"spider{loc}:top:-I", + "mesh": half_dist_mesh, + "rotation": [0, 0, SQ2, SQ2], + "translation": [SEP * loc[0], 0.55 + SEP * loc[2], -SEP * loc[1]], + }) + shapes.append({ + "name": f"spider{loc}:top:+I", + "mesh": half_dist_mesh, + "rotation": [0, 0, SQ2, SQ2], + "translation": [1 + SEP * loc[0], 0.55 + SEP * loc[2], -SEP * loc[1]], + }) + shapes.append({ + "name": f"spider{loc}:top:-J", + "mesh": half_dist_mesh, + "rotation": [0.5, 0.5, 0.5, 0.5], + "translation": [1 + SEP * loc[0], 0.55 + SEP * loc[2], -SEP * loc[1]], + }) + shapes.append({ + "name": f"spider{loc}:top:+J", + "mesh": half_dist_mesh, + "rotation": [0.5, 0.5, 0.5, 0.5], + "translation": [ + 1 + SEP * loc[0], + 0.55 + SEP * loc[2], + -SEP * loc[1] - 1, + ], + }) + + if exists["-K"]: + # need connect to bottom + shapes.append({ + "name": f"spider{loc}:bottom:+K", + "mesh": square_mesh, + "translation": [ + SEP * loc[0], + 0.45 + SEP * loc[2], + -SEP * loc[1], + ], + }) + shapes.append({ + "name": f"spider{loc}:bottom:-I", + "mesh": half_dist_mesh, + "rotation": [0, 0, SQ2, SQ2], + "translation": [SEP * loc[0], SEP * loc[2], -SEP * loc[1]], + }) + shapes.append({ + "name": f"spider{loc}:bottom:+I", + "mesh": half_dist_mesh, + "rotation": [0, 0, SQ2, SQ2], + "translation": [1 + SEP * loc[0], SEP * loc[2], -SEP * loc[1]], + }) + shapes.append({ + "name": f"spider{loc}:bottom:-J", + "mesh": half_dist_mesh, + "rotation": [0.5, 0.5, 0.5, 0.5], + "translation": [1 + SEP * loc[0], SEP * loc[2], -SEP * loc[1]], + }) + shapes.append({ + "name": f"spider{loc}:bottom:+J", + "mesh": half_dist_mesh, + "rotation": [0.5, 0.5, 0.5, 0.5], + "translation": [ + 1 + SEP * loc[0], + SEP * loc[2], + -SEP * loc[1] - 1, + ], + }) + + if stabilizer > -1: + shapes = [shp for shp in shapes if rm_dir not in shp["name"]] + return shapes + + +def gltf_generator( + lasir: Mapping[str, Any], + output_file: Optional[str] = "", + stabilizer: Optional[int] = -1, + tube_len: Optional[float] = 2.0, + no_color_z: Optional[bool] = False, +) -> Mapping[str, Any]: + gltf_file, s, tubelen, noColor = ( + output_file, + stabilizer, + tube_len, + no_color_z, + ) + rm_dir = ":+J" + + gltf = base_gen(BASE_GLTF, tubelen) + + gltf["nodes"] = [ + {"name": "smaple"}, + ] + i_bound = lasir["n_i"] + j_bound = lasir["n_j"] + k_bound = lasir["n_k"] + NodeY = lasir["NodeY"] + ExistI = lasir["ExistI"] + ColorI = lasir["ColorI"] + ExistJ = lasir["ExistJ"] + ColorJ = lasir["ColorJ"] + ExistK = lasir["ExistK"] + CorrIJ = lasir["CorrIJ"] + CorrIK = lasir["CorrIK"] + CorrJI = lasir["CorrJI"] + CorrJK = lasir["CorrJK"] + CorrKI = lasir["CorrKI"] + CorrKJ = lasir["CorrKJ"] + if "ColorKP" not in lasir: + ColorKP = [ + [[-1 for _ in range(k_bound)] for _ in range(j_bound)] + for _ in range(i_bound) + ] + else: + ColorKP = lasir["ColorKP"] + if "ColorKM" not in lasir: + ColorKM = [ + [[-1 for _ in range(k_bound)] for _ in range(j_bound)] + for _ in range(i_bound) + ] + else: + ColorKM = lasir["ColorKM"] + port_cubes = lasir["port_cubes"] + t_injections = ( + lasir["optional"]["t_injections"] + if "t_injections" in lasir["optional"] + else [] + ) + + if s >= len(CorrIJ) or s < -1: + raise ValueError(f"No such stabilizer {s}.") + for i in range(i_bound): + for j in range(j_bound): + for k in range(k_bound): + if ExistI[i][j][k]: + gltf["nodes"] += tube_gen( + tubelen + 1.0, + (i, j, k), + "I", + ColorI[i][j][k], + s, + (CorrIJ[s][i][j][k], CorrIK[s][i][j][k]), + noColor, + rm_dir, + ) + if ExistJ[i][j][k]: + gltf["nodes"] += tube_gen( + tubelen + 1.0, + (i, j, k), + "J", + ColorJ[i][j][k], + s, + (CorrJK[s][i][j][k], CorrJI[s][i][j][k]), + noColor, + rm_dir, + ) + if ExistK[i][j][k]: + gltf["nodes"] += tube_gen( + tubelen + 1.0, + (i, j, k), + "K", + 7 * ColorKM[i][j][k] + ColorKP[i][j][k], + s, + (CorrKI[s][i][j][k], CorrKJ[s][i][j][k]), + noColor, + rm_dir, + ) + + for i in range(i_bound): + for j in range(j_bound): + for k in range(k_bound): + exists = {"-I": 0, "+I": 0, "-K": 0, "+K": 0, "-J": 0, "+J": 0} + colors = {} + corr = { + "-I": (0, 0), + "+I": (0, 0), + "-J": (0, 0), + "+J": (0, 0), + "-K": (0, 0), + "+K": (0, 0), + } + if i > 0 and ExistI[i - 1][j][k]: + exists["-I"] = 1 + colors["-I"] = ColorI[i - 1][j][k] + corr["-I"] = (CorrIJ[s][i - 1][j][k], CorrIK[s][i - 1][j][k]) + if ExistI[i][j][k]: + exists["+I"] = 1 + colors["+I"] = ColorI[i][j][k] + corr["+I"] = (CorrIJ[s][i][j][k], CorrIK[s][i][j][k]) + if j > 0 and ExistJ[i][j - 1][k]: + exists["-J"] = 1 + colors["-J"] = ColorJ[i][j - 1][k] + corr["-J"] = (CorrJK[s][i][j - 1][k], CorrJI[s][i][j - 1][k]) + if ExistJ[i][j][k]: + exists["+J"] = 1 + colors["+J"] = ColorJ[i][j][k] + corr["+J"] = (CorrJK[s][i][j][k], CorrJI[s][i][j][k]) + if k > 0 and ExistK[i][j][k - 1]: + exists["-K"] = 1 + colors["-K"] = ColorKP[i][j][k - 1] + corr["-K"] = (CorrKI[s][i][j][k - 1], CorrKJ[s][i][j][k - 1]) + if ExistK[i][j][k]: + exists["+K"] = 1 + colors["+K"] = ColorKM[i][j][k] + corr["+K"] = (CorrKI[s][i][j][k], CorrKJ[s][i][j][k]) + if sum([v for (k, v) in exists.items()]) > 0: + if [i, j, k] not in port_cubes: + if NodeY[i][j][k]: + gltf["nodes"] += special_gen( + tubelen + 1.0, + (i, j, k), + exists, + "Y", + s, + rm_dir, + ) + else: + gltf["nodes"] += cube_gen( + tubelen + 1.0, + (i, j, k), + exists, + colors, + s, + corr, + noColor, + rm_dir, + ) + elif [i, j, k] in t_injections: + gltf["nodes"] += special_gen( + tubelen + 1.0, + (i, j, k), + exists, + "T", + s, + rm_dir, + ) + + gltf["nodes"][0]["children"] = list(range(1, len(gltf["nodes"]))) + with open(gltf_file, "w") as f: + json.dump(gltf, f) + + return gltf diff --git a/glue/lattice_surgery/olssco/translators/networkx_generator.py b/glue/lattice_surgery/olssco/translators/networkx_generator.py new file mode 100644 index 000000000..0481bd9e0 --- /dev/null +++ b/glue/lattice_surgery/olssco/translators/networkx_generator.py @@ -0,0 +1,250 @@ +import argparse +import json +from networkx import Graph +import stimzx + + +class ZXNode: + + def __init__(self, coord3, n_j): + self.type = 'N' + i, j, k = coord3 + self.yTailP = False + self.yTailM = False + self.node_id = -1 + + self.y = -(n_j + 1) * i + j + self.x = k * (n_j + 2) + j + + def getCoord2(self): + return (self.x, self.y) + + def computeType(self, exists, colors): + deg = sum([v for (k, v) in exists.items()]) + if deg == 0: + self.type = 'N' + return + elif deg == 1: + raise ValueError('There should not be deg-1 Z or X spiders.') + elif deg == 2: + self.type = 'I' + elif deg >= 5: + raise ValueError('deg > 4: 3D corner exists') + else: + if exists['-I'] == 0 and exists['+I'] == 0: + if exists['-J']: + if colors['-J'] == 0: + self.type = 'X' + else: + self.type = 'Z' + else: # must exist +J + if colors['+J'] == 0: + self.type = 'X' + else: + self.type = 'Z' + + if exists['-J'] == 0 and exists['+J'] == 0: + if exists['-I']: + if colors['-I'] == 0: + self.type = 'Z' + else: + self.type = 'X' + else: # must exist +I + if colors['+I'] == 0: + self.type = 'Z' + else: + self.type = 'X' + + if exists['-K'] == 0 and exists['+K'] == 0: + if exists['-I']: + if colors['-I'] == 0: + self.type = 'X' + else: + self.type = 'Z' + else: # must exist +I + if colors['+I'] == 0: + self.type = 'X' + else: + self.type = 'Z' + + def emit(self): + zigxag = { + 'Z': '@', + 'X': 'O', + 'S': 's', + 'W': 'w', + 'I': 'O', + 'Pi': 'in', + 'Po': 'out', + } + # return str(self.x) + ',' + str(self.y) + ',' + str(zigxag[self.type]) + return str(-self.y) + ',' + str(self.x) + ',' + str(zigxag[self.type]) + + +class ZXEdge: + + def __init__(self, ifH, nodea: ZXNode, nodeb: ZXNode): + self.type = '-' + if ifH: + self.type = 'h' + self.nodea = nodea + self.nodeb = nodeb + + def emit(self): + # return ( + # str(self.xa) + # + ',' + # + str(self.ya) + # + ',' + # + str(self.xb) + # + ',' + # + str(self.yb) + # + ',' + # + self.type + # ) + + return ( + str(-self.ya) + + ',' + + str(self.xa) + + ',' + + str(-self.yb) + + ',' + + str(self.xb) + + ',' + + self.type + ) + + +def networkx_generator(lasir: dict): + n_i = lasir['n_i'] + n_j = lasir['n_j'] + n_k = lasir['n_k'] + NodeY = lasir['NodeY'] + ExistI = lasir['ExistI'] + ColorI = lasir['ColorI'] + ExistJ = lasir['ExistJ'] + ColorJ = lasir['ColorJ'] + ExistK = lasir['ExistK'] + ColorKP = lasir['ColorKP'] + ColorKM = lasir['ColorKM'] + port_cubes = lasir['port_cubes'] + + nodes = [ + [[ZXNode((i, j, k), n_j) for k in range(n_k + 1)] for j in range(n_j + 1)] + for i in range(n_i + 1) + ] + + # Y spiders + for i in range(n_i): + for j in range(n_j): + for k in range(n_k): + if NodeY[i][j][k]: + if k - 1 >= 0 and ExistK[i][j][k - 1] and (not NodeY[i][j][k - 1]): + nodes[i][j][k - 1].yTailP = True + if k + 1 < n_k and ExistK[i][j][k] and (not NodeY[i][j][k + 1]): + nodes[i][j][k + 1].yTailM = True + + # Z/X Spiders + for i in range(n_i): + for j in range(n_j): + for k in range(n_k): + if (i, j, k) not in port_cubes and NodeY[i][j][k] == 0: + exists = {'-I': 0, '+I': 0, '-K': 0, '+K': 0, '-J': 0, '+J': 0} + colors = {} + if i > 0 and ExistI[i - 1][j][k]: + exists['-I'] = 1 + colors['-I'] = ColorI[i - 1][j][k] + if ExistI[i][j][k]: + exists['+I'] = 1 + colors['+I'] = ColorI[i][j][k] + if j > 0 and ExistJ[i][j - 1][k]: + exists['-J'] = 1 + colors['-J'] = ColorJ[i][j - 1][k] + if ExistJ[i][j][k]: + exists['+J'] = 1 + colors['+J'] = ColorJ[i][j][k] + if k > 0 and ExistK[i][j][k - 1]: + exists['-K'] = 1 + colors['-K'] = ColorKP[i][j][k - 1] + if ExistK[i][j][k]: + exists['+K'] = 1 + colors['+K'] = ColorKM[i][j][k] + nodes[i][j][k].computeType(exists, colors) + + for i, j, k in port_cubes: + nodes[i][j][k].type = 'Po' + + # edges + edges = [] + # anc_nodes = [] + valid_types = ['Z', 'X', 'S', 'W', 'I', 'Pi', 'Po'] + for i in range(n_i): + for j in range(n_j): + for k in range(n_k): + if ( + ExistI[i][j][k] == 1 + and nodes[i][j][k].type in valid_types + and nodes[i + 1][j][k].type in valid_types + ): + edges.append(ZXEdge(0, nodes[i][j][k], nodes[i + 1][j][k])) + + if ( + ExistJ[i][j][k] == 1 + and nodes[i][j][k].type in valid_types + and nodes[i][j + 1][k].type in valid_types + ): + # anc_nodes.append( (nodes[i][j][k].x+1, nodes[i][j][k].y) ) + # edges.append(ZXEdge(0, nodes[i][j][k].getCoord2(), anc_nodes[-1])) + # edges.append(ZXEdge(0, anc_nodes[-1], nodes[i][j+1][k].getCoord2())) + edges.append(ZXEdge(0, nodes[i][j][k], nodes[i][j + 1][k])) + + if ( + ExistK[i][j][k] == 1 + and nodes[i][j][k].type in valid_types + and nodes[i][j][k + 1].type in valid_types + ): + edges.append( + ZXEdge( + abs(ColorKM[i][j][k] - ColorKP[i][j][k]), + nodes[i][j][k], + nodes[i][j][k + 1], + ) + ) + + zx_graph = Graph() + type_to_str = {'X': 'X', 'Z': 'Z', 'Pi': 'in', 'Po': 'out', 'I': 'X'} + cnt = 0 + for i, j, k in port_cubes: + node = nodes[i][j][k] + zx_graph.add_node(cnt, value=stimzx.ZxType(type_to_str[node.type])) + node.node_id = cnt + cnt += 1 + + for i in range(n_i + 1): + for j in range(n_j + 1): + for k in range(n_k + 1): + node = nodes[i][j][k] + if node.type not in ['N', 'Po', 'Pi']: + zx_graph.add_node(cnt, value=stimzx.ZxType(type_to_str[node.type])) + node.node_id = cnt + cnt += 1 + if node.yTailM: + zx_graph.add_node(cnt, value=stimzx.ZxType('Z', 1)) + zx_graph.add_edge(node.node_id, cnt) + cnt += 1 + if node.yTailP: + zx_graph.add_node(cnt, value=stimzx.ZxType('Z', 3)) + zx_graph.add_edge(node.node_id, cnt) + cnt += 1 + + for edge in edges: + if edge.type != 'h': + zx_graph.add_edge(edge.nodea.node_id, edge.nodeb.node_id) + else: + zx_graph.add_node(cnt, value=stimzx.ZxType('H')) + zx_graph.add_edge(cnt, edge.nodea.node_id) + zx_graph.add_edge(cnt, edge.nodeb.node_id) + cnt += 1 + + return zx_graph diff --git a/glue/lattice_surgery/olssco/translators/textfig_generator.py b/glue/lattice_surgery/olssco/translators/textfig_generator.py new file mode 100644 index 000000000..a2e7b8ac9 --- /dev/null +++ b/glue/lattice_surgery/olssco/translators/textfig_generator.py @@ -0,0 +1,184 @@ +"""A one-line summary of the module or program, terminated by a period. + +Leave one blank line. The rest of this docstring should contain an +overall description of the module or program. Optionally, it may also +contain a brief description of exported classes and functions and/or usage +examples. + +Typical usage example: + + foo = ClassFoo() + bar = foo.FunctionBar() +""" + +import argparse +import json +from typing import Any, Mapping, Sequence + +from olssco.translators import ZXGridGraph + + +class TextLayer: + pad_i = 1 + pad_j = 1 + sep_i = 4 + sep_j = 4 + + def __init__(self, zx_graph: ZXGridGraph, k: int, if_middle: bool) -> None: + self.n_i, self.n_j, self.n_k = ( + zx_graph.n_i, + zx_graph.n_j, + zx_graph.n_k, + ) + self.chars = [ + [ + " " + for _ in range( + 2 * TextLayer.pad_i + (self.n_i - 1) * TextLayer.sep_i + 1 + ) + ] + + ["\n"] + for _ in range( + 2 * TextLayer.pad_j + (self.n_j - 1) * TextLayer.sep_j + 1 + ) + ] + if if_middle: + self.compute_middle(zx_graph, k) + else: + self.compute_normal(zx_graph, k) + + def set_char(self, j: int, i: int, character): + self.chars[j][i] = character + + def compute_middle(self, zx_graph: ZXGridGraph, k: int): + for i in range(self.n_i): + for j in range(self.n_j): + self.set_char( + TextLayer.pad_j + j * TextLayer.sep_j, + TextLayer.pad_i + i * TextLayer.sep_i, + ".", + ) + spider = zx_graph.spiders[i][j][k] + color_sum = -1 + if k == self.n_k - 1: + try: + for port in zx_graph.lasir["ports"]: + if (port["i"], port["j"], port["k"]) == (i, j, k): + color_sum = port["c"] + spider.colors["+K"] + break + except ValueError: + print(f"KPipe({i},{j},{k}) connecting outside but not port.") + else: + upper_spider = zx_graph.spiders[i][j][k + 1] + if spider.exists["+K"] == 1 and upper_spider.exists["-K"] == 1: + color_sum = spider.colors["+K"] + upper_spider.colors["-K"] + if spider.exists["+K"] == 0 and upper_spider.exists["-K"] == 1: + try: + for port in zx_graph.lasir["ports"]: + if (port["i"], port["j"], port["k"]) == (i, j, k): + color_sum = port["c"] + upper_spider.colors["-K"] + break + except ValueError: + print(f"KPipe({i},{j},{k})- should be a port.") + if spider.exists["+K"] == 1 and upper_spider.exists["-K"] == 0: + try: + for port in zx_graph.lasir["ports"]: + if (port["i"], port["j"], port["k"]) == (i, j, k + 1): + color_sum = port["c"] + spider.colors["+K"] + break + except ValueError: + print(f"KPipe({i},{j},{k + 1})- should be a port") + + if color_sum != -1: + self.set_char( + TextLayer.pad_j + j * TextLayer.sep_j - 1, + TextLayer.pad_i + i * TextLayer.sep_i + 1, + "/", + ) + self.set_char( + TextLayer.pad_j + j * TextLayer.sep_j + 1, + TextLayer.pad_i + i * TextLayer.sep_i - 1, + "/", + ) + if color_sum == 1: + self.set_char( + TextLayer.pad_j + j * TextLayer.sep_j, + TextLayer.pad_i + i * TextLayer.sep_i, + "H", + ) + else: + self.set_char( + TextLayer.pad_j + j * TextLayer.sep_j, + TextLayer.pad_i + i * TextLayer.sep_i, + "X", + ) + + def compute_normal(self, zx_graph: ZXGridGraph, k: int): + for i in range(self.n_i): + for j in range(self.n_j): + spider = zx_graph.spiders[i][j][k] + + if spider.type == "N": + self.set_char( + TextLayer.pad_j + j * TextLayer.sep_j, + TextLayer.pad_i + i * TextLayer.sep_i, + ".", + ) + continue + else: + self.set_char( + TextLayer.pad_j + j * TextLayer.sep_j, + TextLayer.pad_i + i * TextLayer.sep_i, + spider.type, + ) + + # I pipes + if spider.exists["+I"]: + for offset in range(1, TextLayer.sep_i): + self.set_char( + TextLayer.pad_j + j * TextLayer.sep_j, + TextLayer.pad_i + i * TextLayer.sep_i + offset, + "-", + ) + + # J pipes + if spider.exists["+J"]: + for offset in range(1, TextLayer.sep_i): + self.set_char( + TextLayer.pad_j + j * TextLayer.sep_j + offset, + TextLayer.pad_i + i * TextLayer.sep_i, + "|", + ) + + # K pipes + if spider.exists["+K"]: + self.set_char( + TextLayer.pad_j + j * TextLayer.sep_j - 1, + TextLayer.pad_i + i * TextLayer.sep_i + 1, + "/", + ) + if spider.exists["-K"]: + self.set_char( + TextLayer.pad_j + j * TextLayer.sep_j + 1, + TextLayer.pad_i + i * TextLayer.sep_i - 1, + "/", + ) + + def get_text(self): + text = "" + for j in range(2 * TextLayer.pad_j + (self.n_j - 1) * TextLayer.sep_j): + for i in range(2 * TextLayer.pad_i + (self.n_i - 1) * TextLayer.sep_i): + text += self.chars[j][i] + text += "\n" + return text + + +def textfig_generator(lasir: dict): + text = "" + zx_graph = ZXGridGraph(lasir) + for k in range(lasir["n_k"] - 1, -1, -1): + text += TextLayer(zx_graph, k, True).get_text() + text += "\n======================================\n" + text += TextLayer(zx_graph, k, False).get_text() + text += "\n======================================\n" + return text diff --git a/glue/lattice_surgery/olssco/translators/zigxag_generator.py b/glue/lattice_surgery/olssco/translators/zigxag_generator.py new file mode 100644 index 000000000..12085f4c0 --- /dev/null +++ b/glue/lattice_surgery/olssco/translators/zigxag_generator.py @@ -0,0 +1,301 @@ +"""A one-line summary of the module or program, terminated by a period. + +Leave one blank line. The rest of this docstring should contain an +overall description of the module or program. Optionally, it may also +contain a brief description of exported classes and functions and/or usage +examples. + +Typical usage example: + + foo = ClassFoo() + bar = foo.FunctionBar() +""" + +from typing import Sequence + + +class ZXNode: + + def __init__(self, coord3, n_j): + self.type = 'N' + i, j, k = coord3 + self.yTailP = False + self.yTailM = False + + self.y = -(n_j + 1) * i + j + self.x = k * (n_j + 2) + j + + def getCoord2(self): + return (self.x, self.y) + + def computeType(self, exists, colors): + deg = sum([v for (k, v) in exists.items()]) + if deg == 0: + self.type = 'N' + return + elif deg == 1: + raise ValueError('There should not be deg-1 Z or X spiders.') + elif deg == 2: + self.type = 'I' + elif deg >= 5: + raise ValueError('deg > 4: 3D corner exists') + else: + if exists['-I'] == 0 and exists['+I'] == 0: + if exists['-J']: + if colors['-J'] == 0: + self.type = 'X' + else: + self.type = 'Z' + else: # must exist +J + if colors['+J'] == 0: + self.type = 'X' + else: + self.type = 'Z' + + if exists['-J'] == 0 and exists['+J'] == 0: + if exists['-I']: + if colors['-I'] == 0: + self.type = 'Z' + else: + self.type = 'X' + else: # must exist +I + if colors['+I'] == 0: + self.type = 'Z' + else: + self.type = 'X' + + if exists['-K'] == 0 and exists['+K'] == 0: + if exists['-I']: + if colors['-I'] == 0: + self.type = 'X' + else: + self.type = 'Z' + else: # must exist +I + if colors['+I'] == 0: + self.type = 'X' + else: + self.type = 'Z' + + def emit(self): + zigxag = { + 'Z': '@', + 'X': 'O', + 'S': 's', + 'W': 'w', + 'I': 'O', + 'Pi': 'in', + 'Po': 'out', + } + # return str(self.x) + ',' + str(self.y) + ',' + str(zigxag[self.type]) + return str(-self.y) + ',' + str(-self.x) + ',' + str(zigxag[self.type]) + + +class ZXEdge: + + def __init__(self, ifH, coord2a, coord2b): + self.xa, self.ya = coord2a + self.xb, self.yb = coord2b + self.type = '-' + if ifH: + self.type = 'h' + + def emit(self): + # return ( + # str(self.xa) + # + ',' + # + str(self.ya) + # + ',' + # + str(self.xb) + # + ',' + # + str(self.yb) + # + ',' + # + self.type + # ) + + return ( + str(-self.ya) + + ',' + + str(-self.xa) + + ',' + + str(-self.yb) + + ',' + + str(-self.xb) + + ',' + + self.type + ) + + +def zigxag_generator(lasir: dict, io_spec: Sequence[str] = None): + n_i = lasir['n_i'] + n_j = lasir['n_j'] + n_k = lasir['n_k'] + NodeY = lasir['NodeY'] + ExistI = lasir['ExistI'] + ColorI = lasir['ColorI'] + ExistJ = lasir['ExistJ'] + ColorJ = lasir['ColorJ'] + ExistK = lasir['ExistK'] + ColorKP = lasir['ColorKP'] + ColorKM = lasir['ColorKM'] + port_cubes = lasir['port_cubes'] + + nodes = [ + [[ZXNode((i, j, k), n_j) for k in range(n_k + 1)] for j in range(n_j + 1)] + for i in range(n_i + 1) + ] + + # ports + for [i, j, k] in port_cubes: + nodes[i][j][k].type = 'Po' + if io_spec: + if len(io_spec) != len(port_cubes): + raise ValueError('io_spec should be of same length as port_cubes') + for w, [i, j, k] in enumerate(port_cubes): + nodes[i][j][k].type = io_spec[w] + + # Y spiders + for i in range(n_i): + for j in range(n_j): + for k in range(n_k): + if NodeY[i][j][k]: + if k - 1 >= 0 and ExistK[i][j][k - 1] and (not NodeY[i][j][k - 1]): + nodes[i][j][k - 1].yTailP = True + if k + 1 < n_k and ExistK[i][j][k] and (not NodeY[i][j][k + 1]): + nodes[i][j][k + 1].yTailM = True + + # Z/X Spiders + for i in range(n_i): + for j in range(n_j): + for k in range(n_k): + if (i, j, k) not in port_cubes and NodeY[i][j][k] == 0: + exists = {'-I': 0, '+I': 0, '-K': 0, '+K': 0, '-J': 0, '+J': 0} + colors = {} + if i > 0 and ExistI[i - 1][j][k]: + exists['-I'] = 1 + colors['-I'] = ColorI[i - 1][j][k] + if ExistI[i][j][k]: + exists['+I'] = 1 + colors['+I'] = ColorI[i][j][k] + if j > 0 and ExistJ[i][j - 1][k]: + exists['-J'] = 1 + colors['-J'] = ColorJ[i][j - 1][k] + if ExistJ[i][j][k]: + exists['+J'] = 1 + colors['+J'] = ColorJ[i][j][k] + if k > 0 and ExistK[i][j][k - 1]: + exists['-K'] = 1 + colors['-K'] = ColorKP[i][j][k - 1] + if ExistK[i][j][k]: + exists['+K'] = 1 + colors['+K'] = ColorKM[i][j][k] + nodes[i][j][k].computeType(exists, colors) + + # edges + edges = [] + # anc_nodes = [] + valid_types = ['Z', 'X', 'S', 'W', 'I', 'Pi', 'Po'] + for i in range(n_i): + for j in range(n_j): + for k in range(n_k): + if ( + ExistI[i][j][k] == 1 + and nodes[i][j][k].type in valid_types + and nodes[i + 1][j][k].type in valid_types + ): + edges.append( + ZXEdge( + 0, nodes[i][j][k].getCoord2(), nodes[i + 1][j][k].getCoord2() + ) + ) + + if ( + ExistJ[i][j][k] == 1 + and nodes[i][j][k].type in valid_types + and nodes[i][j + 1][k].type in valid_types + ): + # anc_nodes.append( (nodes[i][j][k].x+1, nodes[i][j][k].y) ) + # edges.append(ZXEdge(0, nodes[i][j][k].getCoord2(), anc_nodes[-1])) + # edges.append(ZXEdge(0, anc_nodes[-1], nodes[i][j+1][k].getCoord2())) + edges.append( + ZXEdge( + 0, nodes[i][j][k].getCoord2(), nodes[i][j + 1][k].getCoord2() + ) + ) + + if ( + ExistK[i][j][k] == 1 + and nodes[i][j][k].type in valid_types + and nodes[i][j][k + 1].type in valid_types + ): + edges.append( + ZXEdge( + abs(ColorKM[i][j][k] - ColorKP[i][j][k]), + nodes[i][j][k].getCoord2(), + nodes[i][j][k + 1].getCoord2(), + ) + ) + + nodes_str = '' + first = True + for i in range(n_i + 1): + for j in range(n_j + 1): + for k in range(n_k + 1): + if nodes[i][j][k].type in valid_types: + if not first: + nodes_str += ';' + nodes_str += nodes[i][j][k].emit() + first = False + + # for (x,y) in anc_nodes: + # zigxag_str += ';' + str(x) + ',' + str(y) + '+' + + edges_str = '' + for i, edge in enumerate(edges): + if i > 0: + edges_str += ';' + edges_str += edge.emit() + + for i in range(n_i): + for j in range(n_j): + for k in range(n_k): + if nodes[i][j][k].yTailP: + nodes_str += ( + ';' + + str(nodes[i][j][k].x + n_j - j) + + ',' + + str(nodes[i][j][k].y) + + ',s' + ) + edges_str += ( + ';' + + str(nodes[i][j][k].x + n_j - j) + + ',' + + str(nodes[i][j][k].y) + + ',' + + str(nodes[i][j][k].x) + + ',' + + str(nodes[i][j][k].y) + + ',-' + ) + if nodes[i][j][k].yTailM: + nodes_str += ( + ';' + + str(nodes[i][j][k].x - j - 1) + + ',' + + str(nodes[i][j][k].y) + + ',s' + ) + edges_str += ( + ';' + + str(nodes[i][j][k].x - j - 1) + + ',' + + str(nodes[i][j][k].y) + + ',' + + str(nodes[i][j][k].x) + + ',' + + str(nodes[i][j][k].y) + + ',-' + ) + + zigxag_str = 'https://algassert.com/zigxag#' + nodes_str + ':' + edges_str + return zigxag_str diff --git a/glue/lattice_surgery/olssco/translators/zx_grid_graph.py b/glue/lattice_surgery/olssco/translators/zx_grid_graph.py new file mode 100644 index 000000000..bd2349970 --- /dev/null +++ b/glue/lattice_surgery/olssco/translators/zx_grid_graph.py @@ -0,0 +1,157 @@ +"""A one-line summary of the module or program, terminated by a period. + +Leave one blank line. The rest of this docstring should contain an +overall description of the module or program. Optionally, it may also +contain a brief description of exported classes and functions and/or usage +examples. + +Typical usage example: + + foo = ClassFoo() + bar = foo.FunctionBar() +""" + + +from typing import Any, Mapping, Sequence + + +class ZXEdge: + + def __init__(self, if_h: bool, spider0, spider1): + self.spider0, self.spider1 = spider0, spider1 + self.type = "h" if if_h else "-" + + +class ZXSpider: + + def __init__(self, coord3): + self.type = "N" + self.i, self.j, self.k = coord3 + self.y_tail_plus = False + self.y_tail_minus = False + self.exists = {"-I": 0, "+I": 0, "-K": 0, "+K": 0, "-J": 0, "+J": 0} + self.colors = {"-I": -1, "+I": -1, "-K": -1, "+K": -1, "-J": -1, "+J": -1} + + def compute_type(self, exists: dict, colors: dict): + self.exists, self.colors = exists, colors + deg = sum([v for (k, v) in exists.items()]) + if deg == 0: + self.type = "N" + return + elif deg == 1: + raise ValueError("There should not be deg-1 Z or X spiders.") + elif deg == 2: + self.type = "X" + elif deg >= 5: + raise ValueError("deg > 4: 3D corner exists") + else: + if exists["-I"] == 0 and exists["+I"] == 0: + if exists["-J"]: + if colors["-J"] == 0: + self.type = "X" + else: + self.type = "Z" + else: # must exist +J + if colors["+J"] == 0: + self.type = "X" + else: + self.type = "Z" + + if exists["-J"] == 0 and exists["+J"] == 0: + if exists["-I"]: + if colors["-I"] == 0: + self.type = "Z" + else: + self.type = "X" + else: # must exist +I + if colors["+I"] == 0: + self.type = "Z" + else: + self.type = "X" + + if exists["-K"] == 0 and exists["+K"] == 0: + if exists["-I"]: + if colors["-I"] == 0: + self.type = "X" + else: + self.type = "Z" + else: # must exist +I + if colors["+I"] == 0: + self.type = "X" + else: + self.type = "Z" + + +class ZXGridGraph: + + def __init__(self, lasir: dict) -> None: + self.lasir = lasir + self.n_i, self.n_j, self.n_k = ( + lasir["n_i"], + lasir["n_j"], + lasir["n_k"], + ) + self.spiders = [ + [ + [ZXSpider((i, j, k)) for k in range(self.n_k + 1)] + for j in range(self.n_j + 1) + ] + for i in range(self.n_i + 1) + ] + self.edges = [] + self.append_y_tails() + self.compute_spiders_type() + + def append_y_tails(self): + for i in range(self.n_i): + for j in range(self.n_j): + for k in range(self.n_k): + if self.lasir["NodeY"][i][j][k]: + if ( + k - 1 >= 0 + and self.lasir["ExistK"][i][j][k - 1] + and (not self.lasir["NodeY"][i][j][k - 1]) + ): + self.spiders[i][j][k - 1].y_tail_plus = True + if ( + k + 1 < self.n_k + and self.lasir["ExistK"][i][j][k] + and (not self.lasir["NodeY"][i][j][k + 1]) + ): + self.spiders[i][j][k + 1].y_tail_minus = True + + def compute_spiders_type(self): + for i in range(self.n_i): + for j in range(self.n_j): + for k in range(self.n_k): + if ((i, j, k) not in self.lasir["port_cubes"]) and ( + self.lasir["NodeY"][i][j][k] == 0 + ): + exists = {"-I": 0, "+I": 0, "-K": 0, "+K": 0, "-J": 0, "+J": 0} + colors = { + "-I": -1, + "+I": -1, + "-K": -1, + "+K": -1, + "-J": -1, + "+J": -1, + } + if i > 0 and self.lasir["ExistI"][i - 1][j][k]: + exists["-I"] = 1 + colors["-I"] = self.lasir["ColorI"][i - 1][j][k] + if self.lasir["ExistI"][i][j][k]: + exists["+I"] = 1 + colors["+I"] = self.lasir["ColorI"][i][j][k] + if j > 0 and self.lasir["ExistJ"][i][j - 1][k]: + exists["-J"] = 1 + colors["-J"] = self.lasir["ColorJ"][i][j - 1][k] + if self.lasir["ExistJ"][i][j][k]: + exists["+J"] = 1 + colors["+J"] = self.lasir["ColorJ"][i][j][k] + if k > 0 and self.lasir["ExistK"][i][j][k - 1]: + exists["-K"] = 1 + colors["-K"] = self.lasir["ColorKP"][i][j][k - 1] + if self.lasir["ExistK"][i][j][k]: + exists["+K"] = 1 + colors["+K"] = self.lasir["ColorKM"][i][j][k] + self.spiders[i][j][k].compute_type(exists, colors) diff --git a/glue/lattice_surgery/paper/graph_state_olssco.py b/glue/lattice_surgery/paper/graph_state_olssco.py new file mode 100644 index 000000000..e6d053e85 --- /dev/null +++ b/glue/lattice_surgery/paper/graph_state_olssco.py @@ -0,0 +1,111 @@ +import json +import multiprocessing +import sys +from olssco import OptimalLatticeSurgerySubroutineCompiler + + +def graph_state_olssco( + edges, seed, layout, wdir, starting_depth, if_print: bool = True +): + n_q = 8 + # dimensions depending on the qubit layout + if layout == "1row": + data = { + "max_i": n_q, + "max_j": 2, + } + elif layout == "2rows": + data = { + "max_i": n_q // 2, + "max_j": 3, + } + else: + raise ValueError("layout not supported! ") + + # should not be too low, avoids being trivially proved UNSAT by Z3 + depth = starting_depth + + checked_depth = {} + while True: + data["max_k"] = depth + + # get the outgoing ports + if layout == "1row": + data["ports"] = [ + { + "location": [i, 0, depth], + "direction": "-K", + "z_basis_direction": "I", + } + for i in range(n_q) + ] + elif layout == "2rows": + data["ports"] = [ + { + "location": [i, 0, depth], + "direction": "-K", + "z_basis_direction": "I", + } + for i in range(n_q // 2) + ] + [ + { + "location": [i - (n_q // 2), 2, depth], + "direction": "-K", + "z_basis_direction": "I", + } + for i in range(n_q // 2, n_q) + ] + + # stabilizers are X on qubit and Z on all its neighbors + data["stabilizers"] = [] + for i in range(n_q): + stab = "." * i + "X" + "." * (n_q - i - 1) + for edge in edges: + if edge[0] == i: + stab = stab[: edge[1]] + "Z" + stab[edge[1] + 1 :] + if edge[1] == i: + stab = stab[: edge[0]] + "Z" + stab[edge[0] + 1 :] + data["stabilizers"].append(stab) + + olssco = OptimalLatticeSurgerySubroutineCompiler(data, color_ij=True) + + if olssco.check_external_solver( + f"{wdir}graph_n{n_q}_s{seed}", print_progress=if_print + ): + checked_depth[str(depth)] = "SAT" + with open(f"{wdir}graph_n{n_q}_s{seed}.json", "w") as f: + json.dump(data, f) + if str(depth - 1) in checked_depth: + break + else: + depth -= 1 + else: + checked_depth[str(depth)] = "UNSAT" + if str(depth + 1) in checked_depth: + break + else: + depth += 1 + + with open(f"{wdir}graph_n{n_q}_s{seed}.json", "r") as f: + opt_data = json.load(f) + + with open(wdir + "olsco_stats", "a") as f: + f.write(f"{n_q}, {seed}, {opt_data['max_k']}\n") + + +if __name__ == "__main__": + n_core = int(sys.argv[1]) + layout = sys.argv[2] + wdir = sys.argv[3] + starting_depth = int(sys.argv[4]) + + def f(s): + # read the edges from the graph library + with open("graphs8.json", "r") as f: + graphs = json.load(f) + edges = graphs["8"][s] + return graph_state_olssco(edges, s, "1row", wdir, 3, if_print=False) + + pool = multiprocessing.Pool(n_core) + + outputs = pool.map(f, range(101), chunksize=1) diff --git a/glue/lattice_surgery/paper/graphs8.json b/glue/lattice_surgery/paper/graphs8.json new file mode 100644 index 000000000..838af862e --- /dev/null +++ b/glue/lattice_surgery/paper/graphs8.json @@ -0,0 +1,106 @@ +{ + "8":[ + [[0,7],[1,7],[2,7],[3,7],[4,7],[5,7],[6,7]], + [[0,7],[5,6],[1,7],[2,7],[3,7],[4,7],[6,7]], + [[0,7],[4,6],[1,7],[5,6],[2,7],[3,7],[6,7]], + [[0,7],[5,6],[1,7],[4,6],[2,7],[3,7],[5,7]], + [[0,6],[1,7],[2,7],[4,6],[3,7],[5,6],[6,7]], + [[0,7],[5,6],[1,7],[3,6],[2,7],[4,6],[5,7]], + [[0,7],[3,5],[4,6],[1,7],[2,7],[5,7],[6,7]], + [[0,7],[5,6],[1,7],[3,5],[4,6],[2,7],[6,7]], + [[0,7],[3,5],[4,6],[1,7],[5,6],[2,7],[4,7]], + [[0,7],[2,5],[3,6],[1,7],[4,6],[5,7],[6,7]], + [[0,7],[3,5],[4,6],[1,7],[2,6],[4,7],[5,7]], + [[0,7],[1,5],[2,6],[3,6],[5,7],[4,5],[6,7]], + [[0,6],[2,7],[4,5],[1,6],[5,7],[3,7],[4,6]], + [[0,7],[3,4],[5,6],[1,6],[4,7],[2,6],[5,7]], + 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+} \ No newline at end of file diff --git a/glue/lattice_surgery/paper/rand_graph_baseline_opt.py b/glue/lattice_surgery/paper/rand_graph_baseline_opt.py new file mode 100644 index 000000000..333263c7c --- /dev/null +++ b/glue/lattice_surgery/paper/rand_graph_baseline_opt.py @@ -0,0 +1,103 @@ +import json +import random +import sys + + +def split_map_i(i, lorr, n_col): + if i == 0: + return 0 + elif i == n_col - 1: + return 2 * n_col - 3 + else: + if lorr == "L": + return 2 * i + elif lorr == "R": + return 2 * i - 1 + else: + raise ValueError() + + +def split_map_back_i(i, n_col): + if i == 0: + return 0 + elif i == n_col - 1: + return i // 2 + else: + return (i + 1) // 2 + + +def split_map_edge(edge, n_col): + if len(edge) != 2: + raise ValueError() + left = min(edge) + right = max(edge) + return (split_map_i(left, "L", n_col), split_map_i(right, "R", n_col)) + + +def depth_baseline(edges, n_col, layout): + # sort according to the smaller col involved (beginning of interval) + edges.sort(key=lambda x: x[0]) + + original_edges = edges + split_edges = [split_map_edge(edge, n_col) for edge in edges] + edges = split_edges + n_col = 2 * (n_col - 1) + + # calculate number of layers + n_layer = 0 + for c in range(n_col): + cnt = 0 + for edge in edges: + if c >= edge[0] and c <= edge[1]: + cnt += 1 + n_layer = max(n_layer, cnt) + + layer = [-1 for _ in edges] + for i, edge in enumerate(edges): + used = [] + for j in range(i): + if edges[j][1] >= edge[0]: + used.append(layer[j]) + for l in range(n_layer): + if l not in used: + layer[i] = l + break + + # for l in range(n_layer): + # info = f"layer {l}:" + # for i, edge in enumerate(edges): + # if layer[i] == l: + # info += f" {edge}" + # print(info) + + # for l in range(n_layer): + # info = f"layer {l}:" + # for i, edge in enumerate(original_edges): + # if layer[i] == l: + # info += f" {edge}" + # print(info) + + return 2 * n_layer + + +if __name__ == "__main__": + n_q = int(sys.argv[1]) + layout = sys.argv[2] + wdir = sys.argv[3] + graph_lib = sys.argv[4] + + # read the edges from the graph library + with open(graph_lib, "r") as f: + graphs = json.load(f) + if str(n_q) not in graphs: # all n_q should be even + raise ValueError("n_q not found in graph library!") + with open(wdir + "baseline_stats", "w") as f: + f.write("n_q, ratio, s, n_layer\n") + + for r in range(1, 5): + for s in range(len(graphs[str(n_q)][r])): + edges = graphs[str(n_q)][r][s] + with open(wdir + "baseline_stats", "a") as f: + f.write( + f"{n_q}, {(r+1)/10}, {s}, {2*depth_baseline(edges, n_q, layout)}\n" + ) diff --git a/glue/lattice_surgery/paper/rand_graph_olsco_hier.py b/glue/lattice_surgery/paper/rand_graph_olsco_hier.py new file mode 100644 index 000000000..efa74a489 --- /dev/null +++ b/glue/lattice_surgery/paper/rand_graph_olsco_hier.py @@ -0,0 +1,193 @@ +import json +import math +import subprocess +import sys +from olsco_compiler import OLSCo +from rand_graph.rand_graph_baseline_opt import depth_baseline + + +def solve_sub( + edges, ratioX10_1, seed, layout, wdir, starting_depth, if_print, note, n_q=8 +): + # dimensions depending on the qubit layout + if layout == "1row": + data = { + "max_i": n_q, + "max_j": 2, + } + elif layout == "2rows": + data = { + "max_i": n_q // 2, + "max_j": 3, + } + else: + raise ValueError("layout not supported! ") + + # should not be too low, avoids being trivially proved UNSAT by Z3 + depth = starting_depth + + checked_depth = {} + while True: + data["max_k"] = depth + + # get the outgoing ports + if layout == "1row": + data["ports"] = [ + { + "location": [i, 0, 0], + "direction": "+K", + "z_basis_direction": "I", + } + for i in range(n_q) + ] + [ + { + "location": [i, 0, depth], + "direction": "-K", + "z_basis_direction": "I", + } + for i in range(n_q) + ] + elif layout == "2rows": + data["ports"] = [ + { + "location": [i, 0, depth], + "direction": "-K", + "z_basis_direction": "I", + } + for i in range(n_q // 2) + ] + [ + { + "location": [i - (n_q // 2), 2, depth], + "direction": "-K", + "z_basis_direction": "I", + } + for i in range(n_q // 2, n_q) + ] + + # stabilizers are X on qubit and Z on all its neighbors + data["stabilizers"] = [ + ("." * i + "Z" + "." * (n_q - i - 1)) * 2 for i in range(n_q) + ] + for i in range(n_q): + stab = ("." * i + "X" + "." * (n_q - i - 1)) * 2 + for edge in edges: + if edge[0] == i: + stab = stab[: n_q + edge[1]] + "Z" + stab[n_q + edge[1] + 1 :] + if edge[1] == i: + stab = stab[: n_q + edge[0]] + "Z" + stab[n_q + edge[0] + 1 :] + data["stabilizers"].append(stab) + + olsco = OLSCo(data, cnf=True, color_ij=True) + olsco.write_cnf(f"{wdir}graph_n{n_q}_r{ratioX10_1}_s{seed}{note}.dimacs") + + subprocess.run( + f"kissat {wdir}graph_n{n_q}_r{ratioX10_1}_s{seed}{note}.dimacs" + + ( + f" | tee {wdir}graph_n{n_q}_r{ratioX10_1}_s{seed}{note}.sat" + if if_print + else f" > {wdir}graph_n{n_q}_r{ratioX10_1}_s{seed}{note}.sat" + ), + capture_output=False, + check=False, + shell=True, + ) + + with open(f"{wdir}graph_n{n_q}_r{ratioX10_1}_s{seed}{note}.sat", "r") as f: + sat_output = f.readlines() + + if "exit 10" in sat_output[-1]: # found SAT + checked_depth[str(depth)] = "SAT" + with open( + f"{wdir}graph_n{n_q}_r{ratioX10_1}_s{seed}{note}.json", "w" + ) as f: + json.dump(data, f) + if str(depth - 1) in checked_depth or depth <= 2: + break + else: + depth -= 1 + else: + checked_depth[str(depth)] = "UNSAT" + if str(depth + 1) in checked_depth: + break + else: + depth += 1 + + with open(f"{wdir}graph_n{n_q}_r{ratioX10_1}_s{seed}{note}.json", "r") as f: + opt_data = json.load(f) + + return opt_data["max_k"] + + +if __name__ == "__main__": + n_q = int(sys.argv[1]) + ratioX10_1 = int(sys.argv[2]) + seed = int(sys.argv[3]) + layout = sys.argv[4] + wdir = sys.argv[5] + graph_lib = sys.argv[6] + starting_depth = int(sys.argv[7]) + if_print = int(sys.argv[8]) + + max_q = 8 + + # read the edges from the graph library + with open(graph_lib, "r") as f: + graphs = json.load(f) + if str(n_q) not in graphs: # all n_q should be even + raise ValueError("n_q not found in graph library!") + if ratioX10_1 not in range(10): + raise ValueError("invalid ratio x 10 - 1!") + ratio = (1 + ratioX10_1) / 10 + if seed not in range(10): + raise ValueError("invalid random seed!") + edges = graphs[str(n_q)][ratioX10_1][seed] + + total_cycle = 0 + n_stretch = int(math.log(n_q // max_q, 2)) + 1 + for t in range(n_stretch): + for l in range(2**t): + n_partition = n_q // (max_q * (2**t)) + max_cycle = 0 + for p in range(n_partition): + if not edges: + continue + subset = [] + others = [] + i_start = max_q * (2**t) * p + l + i_end = i_start + (2**t) * max_q + for edge in edges: + if (edge[0] in range(i_start, i_end, 2**t)) and ( + edge[1] in range(i_start, i_end, 2**t) + ): + subset.append([ + (edge[0] - i_start) // (2**t), + (edge[1] - i_start) // (2**t), + ]) + else: + others.append(edge) + edges = others + + max_cycle = max( + max_cycle, + solve_sub( + subset, + ratioX10_1, + seed, + layout, + wdir, + starting_depth, + if_print, + f"_t{t}_l{l}_p{p}", + n_q=max_q, + ), + ) + + total_cycle += max_cycle + + if edges: + total_cycle += depth_baseline(edges, n_q, layout) + + by_gate_d = depth_baseline(graphs[str(n_q)][ratioX10_1][seed], n_q, layout) + # print(f"baseline:{by_gate_d} vs partially-compiled:{total_cycle-1}") + with open(wdir + "hybrid_stats", "a") as f: + f.write(f"{n_q}, {ratio}, {seed}, {total_cycle}\n") diff --git a/glue/lattice_surgery/sample.gltf b/glue/lattice_surgery/sample.gltf deleted file mode 100644 index d6af77309..000000000 --- a/glue/lattice_surgery/sample.gltf +++ /dev/null @@ -1 +0,0 @@ -{"accessors": [{"bufferView": 0, "componentType": 5126, "count": 4, "max": [1, 0, 0], "min": [0, 0, -1], "type": "VEC3"}, {"bufferView": 1, "componentType": 5126, "count": 4, "max": [2, 0, 0], "min": [0, 0, -1], "type": "VEC3"}, {"bufferView": 2, "componentType": 5126, "count": 4, "type": "VEC3"}, {"bufferView": 3, "componentType": 5123, "count": 6, "type": "SCALAR"}, {"bufferView": 4, "componentType": 5126, "count": 7, "max": [2, 0, 0], "min": [0, 0, -1], "type": "VEC3"}, {"bufferView": 5, "componentType": 5126, "count": 7, "type": "VEC3"}, {"bufferView": 6, "componentType": 5123, "count": 9, "type": "SCALAR"}, {"bufferView": 7, "componentType": 5123, "count": 9, "type": "SCALAR"}], "asset": {"generator": 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0]], [[1, 1, 1, 0, 0], [0, 0, 0, 0, 0]], [[1, 1, 0, 1, 0], [0, 0, 0, 0, 0]], [[0, 0, 0, 1, 0], [0, 0, 0, 0, 0]]], "ExistK": [[[1, 1, 1, 1, 0], [0, 0, 0, 0, 0]], [[1, 1, 1, 1, 0], [0, 0, 0, 0, 0]], [[1, 1, 1, 0, 0], [0, 0, 0, 0, 0]], [[1, 1, 1, 1, 0], [0, 0, 0, 0, 0]], [[0, 0, 0, 1, 0], [1, 1, 0, 0, 0]]], "CorrIK": [[[[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], [[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], [[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], [[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]]], "CorrIJ": [[[[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], [[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], [[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], [[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]]], "CorrJK": [[[[1, 0, 1, 1, 0], [0, 0, 0, 0, 0]], [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]]], "CorrJI": [[[[1, 0, 1, 1, 0], [0, 0, 0, 0, 0]], [[0, 0, 1, 1, 0], [0, 0, 0, 0, 0]], [[1, 0, 1, 0, 0], [0, 0, 0, 0, 0]], [[1, 0, 0, 1, 0], [0, 0, 0, 0, 0]], [[0, 0, 0, 1, 0], [0, 0, 0, 0, 0]]]], "CorrKJ": [[[[1, 1, 1, 1, 0], [0, 0, 0, 0, 0]], [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], [[0, 0, 0, 0, 1], [1, 1, 0, 0, 0]]]], "CorrKI": [[[[1, 1, 0, 1, 0], [0, 0, 0, 0, 0]], [[0, 0, 1, 0, 0], [0, 0, 0, 0, 0]], [[1, 1, 0, 0, 0], [0, 0, 0, 0, 0]], [[1, 1, 1, 0, 0], [0, 0, 0, 0, 0]], [[0, 0, 0, 1, 0], [1, 1, 0, 0, 0]]]]} \ No newline at end of file diff --git a/glue/lattice_surgery/sample.olsco b/glue/lattice_surgery/sample.olsco deleted file mode 100644 index c8c4a3013..000000000 --- a/glue/lattice_surgery/sample.olsco +++ /dev/null @@ -1,103 +0,0 @@ -{ - "i_bound": 5, - "j_bound": 2, - "k_bound": 5, - "ports": [[0, 0, 4, 5]], - "stabilizer": ["Y"], - "NodeY": [ - [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], - [[1, 0, 0, 0, 1], [0, 0, 0, 0, 0]], - [[0, 0, 0, 1, 0], [0, 0, 0, 0, 0]], - [[0, 0, 0, 0, 1], [0, 0, 0, 0, 0]], - [[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]] - ], - "ExistI": [ - [[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], - [[0, 0, 0, 0, 0], [1, 1, 1, 1, 0]], - [[0, 0, 0, 0, 0], [1, 1, 1, 1, 0]], - [[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], - [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]] - ], - "ColorI": [ - [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], - [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], - [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], - [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], - [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]] - ], - "ExistJ": [ - [[1, 0, 1, 1, 0], [0, 0, 0, 0, 0]], - [[0, 1, 1, 1, 0], [0, 0, 0, 0, 0]], - [[1, 1, 1, 0, 0], [0, 0, 0, 0, 0]], - [[1, 1, 0, 1, 0], [0, 0, 0, 0, 0]], - [[0, 0, 0, 1, 0], [0, 0, 0, 0, 0]] - ], - "ColorJ": [ - [[1, 0, 1, 1, 0], [0, 0, 0, 0, 0]], - [[0, 1, 1, 1, 0], [0, 0, 0, 0, 0]], - [[1, 1, 1, 0, 0], [0, 0, 0, 0, 0]], - [[1, 1, 0, 1, 0], [0, 0, 0, 0, 0]], - [[0, 0, 0, 1, 0], [0, 0, 0, 0, 0]] - ], - "ExistK": [ - [[1, 1, 1, 1, 0], [0, 0, 0, 0, 0]], - [[1, 1, 1, 1, 0], [0, 0, 0, 0, 0]], - [[1, 1, 1, 0, 0], [0, 0, 0, 0, 0]], - [[1, 1, 1, 1, 0], [0, 0, 0, 0, 0]], - [[0, 0, 0, 1, 0], [1, 1, 0, 0, 0]] - ], - "CorrIK": [ - [ - [[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], - [[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], - [[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], - [[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], - [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]] - ] - ], - "CorrIJ": [ - [ - [[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], - [[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], - [[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], - [[0, 0, 0, 0, 0], [1, 0, 1, 1, 0]], - [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]] - ] - ], - "CorrJK": [ - [ - [[1, 0, 1, 1, 0], [0, 0, 0, 0, 0]], - [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], - [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], - [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], - [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]] - ] - ], - "CorrJI": [ - [ - [[1, 0, 1, 1, 0], [0, 0, 0, 0, 0]], - [[0, 0, 1, 1, 0], [0, 0, 0, 0, 0]], - [[1, 0, 1, 0, 0], [0, 0, 0, 0, 0]], - [[1, 0, 0, 1, 0], [0, 0, 0, 0, 0]], - [[0, 0, 0, 1, 0], [0, 0, 0, 0, 0]] - ] - ], - "CorrKJ": [ - [ - [[1, 1, 1, 1, 0], [0, 0, 0, 0, 0]], - [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], - [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], - [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], - [[0, 0, 0, 0, 1], [1, 1, 0, 0, 0]] - ] - ], - "CorrKI": [ - [ - [[1, 1, 0, 1, 0], [0, 0, 0, 0, 0]], - [[0, 0, 1, 0, 0], [0, 0, 0, 0, 0]], - [[1, 1, 0, 0, 0], [0, 0, 0, 0, 0]], - [[1, 1, 1, 0, 0], [0, 0, 0, 0, 0]], - [[0, 0, 0, 1, 0], [1, 1, 0, 0, 0]] - ] - ] -} \ No newline at end of file diff --git a/glue/lattice_surgery/setup.py b/glue/lattice_surgery/setup.py new file mode 100644 index 000000000..447af34b2 --- /dev/null +++ b/glue/lattice_surgery/setup.py @@ -0,0 +1,27 @@ +from setuptools import find_packages, setup + +with open('README.md', encoding='UTF-8') as f: + long_description = f.read() + +__version__ = '0.1.0' + +setup( + name='olssco', + version=__version__, + author='Daniel Bochen Tan', + author_email='tbcdebug@outlook.com', + url='https://github.com/quantumlib/stim/', + license='Apache 2', + packages=find_packages(), + description='A Compiler for Lattice Surgery Subroutines', + long_description=long_description, + long_description_content_type='text/markdown', + python_requires='>=3.6.0', + data_files=['README.md'], + install_requires=[ + 'z3-solver==4.12.1.0', + 'stim', + 'networkx', + ], + tests_require=['pytest', 'python3-distutils'], +) diff --git a/glue/lattice_surgery/stimzx/__init__.py b/glue/lattice_surgery/stimzx/__init__.py new file mode 100644 index 000000000..93489c421 --- /dev/null +++ b/glue/lattice_surgery/stimzx/__init__.py @@ -0,0 +1,14 @@ +__version__ = '1.12.dev0' +from ._external_stabilizer import ( + ExternalStabilizer, +) + +from ._text_diagram_parsing import ( + text_diagram_to_networkx_graph, +) + +from ._zx_graph_solver import ( + zx_graph_to_external_stabilizers, + text_diagram_to_zx_graph, + ZxType, +) diff --git a/glue/lattice_surgery/stimzx/_external_stabilizer.py b/glue/lattice_surgery/stimzx/_external_stabilizer.py new file mode 100644 index 000000000..1363fed4d --- /dev/null +++ b/glue/lattice_surgery/stimzx/_external_stabilizer.py @@ -0,0 +1,90 @@ +from typing import List, Any + +import stim + + +class ExternalStabilizer: + """An input-to-output relationship enforced by a stabilizer circuit.""" + + def __init__(self, *, input: stim.PauliString, output: stim.PauliString): + self.input = input + self.output = output + + @staticmethod + def from_dual(dual: stim.PauliString, num_inputs: int) -> 'ExternalStabilizer': + sign = dual.sign + + # Transpose input. Ys get negated. + for k in range(num_inputs): + if dual[k] == 2: + sign *= -1 + + return ExternalStabilizer( + input=dual[:num_inputs], + output=dual[num_inputs:], + ) + + @staticmethod + def canonicals_from_duals(duals: List[stim.PauliString], num_inputs: int) -> List['ExternalStabilizer']: + if not duals: + return [] + duals = [e.copy() for e in duals] + num_qubits = len(duals[0]) + num_outputs = num_qubits - num_inputs + id_out = stim.PauliString(num_outputs) + + # Pivot on output qubits, to potentially isolate input-only stabilizers. + _eliminate_stabilizers(duals, range(num_inputs, num_qubits)) + + # Separate input-only stabilizers from the rest. + input_only_stabilizers = [] + output_using_stabilizers = [] + for dual in duals: + if dual[num_inputs:] == id_out: + input_only_stabilizers.append(dual) + else: + output_using_stabilizers.append(dual) + + # Separately canonicalize the output-using and input-only stabilizers. + _eliminate_stabilizers(output_using_stabilizers, range(num_qubits)) + _eliminate_stabilizers(input_only_stabilizers, range(num_inputs)) + + duals = input_only_stabilizers + output_using_stabilizers + return [ExternalStabilizer.from_dual(e, num_inputs) for e in duals] + + def __mul__(self, other: 'ExternalStabilizer') -> 'ExternalStabilizer': + return ExternalStabilizer(input=other.input * self.input, output=self.output * other.output) + + def __str__(self) -> str: + return str(self.input) + ' -> ' + str(self.output) + + def __eq__(self, other: Any) -> bool: + if not isinstance(other, ExternalStabilizer): + return NotImplemented + return self.output == other.output and self.input == other.input + + def __ne__(self, other: Any) -> bool: + return not self == other + + def __repr__(self): + return f'stimzx.ExternalStabilizer(input={self.input!r}, output={self.output!r})' + + +def _eliminate_stabilizers(stabilizers: List[stim.PauliString], elimination_indices: range): + """Performs partial Gaussian elimination on the list of stabilizers.""" + min_pivot = 0 + for q in elimination_indices: + for b in [1, 3]: + for pivot in range(min_pivot, len(stabilizers)): + p = stabilizers[pivot][q] + if p == 2 or p == b: + break + else: + continue + for k, stabilizer in enumerate(stabilizers): + p = stabilizer[q] + if k != pivot and (p == 2 or p == b): + stabilizer *= stabilizers[pivot] + if min_pivot != pivot: + stabilizers[min_pivot], stabilizers[pivot] = stabilizers[pivot], stabilizers[min_pivot] + min_pivot += 1 diff --git a/glue/lattice_surgery/stimzx/_external_stabilizer_test.py b/glue/lattice_surgery/stimzx/_external_stabilizer_test.py new file mode 100644 index 000000000..b0e940b4e --- /dev/null +++ b/glue/lattice_surgery/stimzx/_external_stabilizer_test.py @@ -0,0 +1,7 @@ +import stim +import stimzx + + +def test_repr(): + e = stimzx.ExternalStabilizer(input=stim.PauliString("XX"), output=stim.PauliString("Y")) + assert eval(repr(e), {'stimzx': stimzx, 'stim': stim}) == e diff --git a/glue/lattice_surgery/stimzx/_text_diagram_parsing.py b/glue/lattice_surgery/stimzx/_text_diagram_parsing.py new file mode 100644 index 000000000..36c1068af --- /dev/null +++ b/glue/lattice_surgery/stimzx/_text_diagram_parsing.py @@ -0,0 +1,178 @@ +import re +from typing import Dict, Tuple, TypeVar, List, Set, Callable + +import networkx as nx + +K = TypeVar("K") + + +def text_diagram_to_networkx_graph(text_diagram: str, *, value_func: Callable[[str], K] = str) -> nx.MultiGraph: + r"""Converts a text diagram into a networkx multi graph. + + Args: + text_diagram: An ascii text diagram of the graph, linking nodes together with edges. Edges can be horizontal + (-), vertical (|), diagonal (/\), crossing (+), or changing direction (*). Nodes can be alphanumeric with + parentheses. It is assumed that all text is shown with a fixed-width font. + value_func: An optional transformation to apply to the node text in order to get the node's value. Otherwise + the node's value is just its text. + + Example: + + >>> import stimzx + >>> import networkx as nx + >>> actual = stimzx.text_diagram_to_networkx_graph(r''' + ... + ... A + ... | + ... NODE1--+--NODE2----------* + ... | | / + ... B | / + ... *------NODE4 + ... + ... ''') + >>> expected = nx.MultiGraph() + >>> expected.add_node(0, value='A') + >>> expected.add_node(1, value='NODE1') + >>> expected.add_node(2, value='NODE2') + >>> expected.add_node(3, value='B') + >>> expected.add_node(4, value='NODE4') + >>> _ = expected.add_edge(0, 3) + >>> _ = expected.add_edge(1, 2) + >>> _ = expected.add_edge(2, 4) + >>> _ = expected.add_edge(2, 4) + >>> nx.testing.assert_graphs_equal(actual, expected) + + Returns: + A networkx multi graph containing the graph from the text diagram. Nodes in the graph are integers (the ordering + of nodes is in the natural string ordering from left to right then top to bottom in the diagram), and have a + "value" attribute containing either the node's string from the diagram or else a function of that string if + value_func was specified. + """ + char_map = _text_to_char_map(text_diagram) + node_ids, nodes = _find_nodes(char_map, value_func) + edges = _find_all_edges(char_map, node_ids) + result = nx.MultiGraph() + for k, v in enumerate(nodes): + result.add_node(k, value=v) + for a, b in edges: + result.add_edge(a, b) + return result + + +def _text_to_char_map(text: str) -> Dict[complex, str]: + char_map = {} + x = 0 + y = 0 + for c in text: + if c == '\n': + x = 0 + y += 1 + continue + if c != ' ': + char_map[x + 1j*y] = c + x += 1 + return char_map + + +DIR_TO_CHARS = { + -1 - 1j: '\\', + 0 - 1j: '|+', + 1 - 1j: '/', + -1: '-+', + 1: '-+', + -1 + 1j: '/', + 1j: '|+', + 1 + 1j: '\\', +} + +CHAR_TO_DIR = { + '\\': 1 + 1j, + '-': 1, + '|': 1j, + '/': -1 + 1j, +} + + +def _find_all_edges(char_map: Dict[complex, str], terminal_map: Dict[complex, K]) -> List[Tuple[K, K]]: + edges = [] + already_travelled = set() + for xy, c in char_map.items(): + x = int(xy.real) + y = int(xy.imag) + if xy in terminal_map or xy in already_travelled or c in '*+': + continue + already_travelled.add(xy) + dxy = CHAR_TO_DIR.get(c) + if dxy is None: + raise ValueError(f"Character {x+1} ('{c}') in line {y+1} isn't part in a node or an edge") + n1 = _find_end_of_edge(xy + dxy, dxy, char_map, terminal_map, already_travelled) + n2 = _find_end_of_edge(xy - dxy, -dxy, char_map, terminal_map, already_travelled) + edges.append((n2, n1)) + return edges + + +def _find_end_of_edge(xy: complex, dxy: complex, char_map: Dict[complex, str], terminal_map: Dict[complex, K], already_travelled: Set[complex]): + while True: + c = char_map[xy] + if xy in terminal_map: + return terminal_map[xy] + + if c != '+': + if xy in already_travelled: + raise ValueError("Edge used twice.") + already_travelled.add(xy) + + next_deltas: List[complex] = [] + if c == '*': + for dx2 in [-1, 0, 1]: + for dy2 in [-1, 0, 1]: + dxy2 = dx2 + dy2 * 1j + c2 = char_map.get(xy + dxy2) + if dxy2 != 0 and dxy2 != -dxy and c2 is not None and c2 in DIR_TO_CHARS[dxy2]: + next_deltas.append(dxy2) + if len(next_deltas) != 1: + raise ValueError(f"Edge junction ('*') at character {int(xy.real)+1}$ in line {int(xy.imag)+1} doesn't have exactly 2 legs.") + dxy, = next_deltas + else: + expected = DIR_TO_CHARS[dxy] + if c not in expected: + raise ValueError(f"Dangling edge at character {int(xy.real)+1} in line {int(xy.imag)+1} travelling dx=${int(dxy.real)},dy={int(dxy.imag)}.") + xy += dxy + + +def _find_nodes(char_map: Dict[complex, str], value_func: Callable[[str], K]) -> Tuple[Dict[complex, int], List[K]]: + node_ids = {} + nodes = [] + + node_chars = re.compile("^[a-zA-Z0-9()]$") + next_node_id = 0 + + for xy, lead_char in char_map.items(): + if xy in node_ids: + continue + if not node_chars.match(lead_char): + continue + + n = 0 + nested = 0 + full_name = '' + while True: + c = char_map.get(xy + n, ' ') + if c == ' ' and nested > 0: + raise ValueError("Label ended before ')' to go with '(' was found.") + if nested == 0 and not node_chars.match(c): + break + full_name += c + if c == '(': + nested += 1 + elif c == ')': + nested -= 1 + n += 1 + + nodes.append(value_func(full_name)) + node_id = next_node_id + next_node_id += 1 + for k in range(n): + node_ids[xy + k] = node_id + + return node_ids, nodes diff --git a/glue/lattice_surgery/stimzx/_text_diagram_parsing_test.py b/glue/lattice_surgery/stimzx/_text_diagram_parsing_test.py new file mode 100644 index 000000000..eef8e9003 --- /dev/null +++ b/glue/lattice_surgery/stimzx/_text_diagram_parsing_test.py @@ -0,0 +1,149 @@ +import networkx as nx +import pytest +from ._text_diagram_parsing import _find_nodes, _text_to_char_map, _find_end_of_edge, _find_all_edges, text_diagram_to_networkx_graph + + +def test_text_to_char_map(): + assert _text_to_char_map(""" +ABC DEF +G + HI + """) == { + 0 + 1j: 'A', + 1 + 1j: 'B', + 2 + 1j: 'C', + 4 + 1j: 'D', + 5 + 1j: 'E', + 6 + 1j: 'F', + 0 + 2j: 'G', + 1 + 3j: 'H', + 2 + 3j: 'I', + } + + +def test_find_nodes(): + assert _find_nodes(_text_to_char_map(''), lambda e: e) == ({}, []) + with pytest.raises(ValueError, match="base 10"): + _find_nodes(_text_to_char_map('NOTANINT'), int) + with pytest.raises(ValueError, match=r"ended before '\)'"): + _find_nodes(_text_to_char_map('X(run_off'), str) + assert _find_nodes(_text_to_char_map('X'), str) == ( + { + 0j: 0, + }, + ['X'], + ) + assert _find_nodes(_text_to_char_map('\n X'), str) == ( + { + 3 + 1j: 0, + }, + ['X'], + ) + assert _find_nodes(_text_to_char_map('X(pi)'), str) == ( + { + 0: 0, + 1: 0, + 2: 0, + 3: 0, + 4: 0, + }, + ['X(pi)'], + ) + assert _find_nodes(_text_to_char_map('X--Z'), str) == ( + { + 0: 0, + 3: 1, + }, + ['X', 'Z'], + ) + assert _find_nodes(_text_to_char_map(""" +X--* + / + Z +"""), str) == ( + { + 1j: 0, + 1 + 3j: 1, + }, + ['X', 'Z'], + ) + assert _find_nodes(_text_to_char_map(""" +X(pi)--Z +"""), str) == ( + { + 0 + 1j: 0, + 1 + 1j: 0, + 2 + 1j: 0, + 3 + 1j: 0, + 4 + 1j: 0, + 7 + 1j: 1, + }, + ["X(pi)", "Z"], + ) + + +def test_find_end_of_edge(): + c = _text_to_char_map(r""" +1--------* + \ 2 | + 5 \ *--++-* + *-----+-* |/ + | | / + 2 |/ + * + """) + terminal = {1: 'ONE', 18 + 6j: 'TWO'} + seen = set() + assert _find_end_of_edge(1 + 1j, 1, c, terminal, seen) == 'TWO' + assert len(seen) == 31 + + +def test_find_all_edges(): + c = _text_to_char_map(r""" +X---Z H----X(pi/2) + / + Z(pi/2) + """) + node_ids, _ = _find_nodes(c, str) + assert _find_all_edges(c, node_ids) == [ + (0, 1), + (2, 3), + (2, 4), + ] + + +def test_from_text_diagram(): + actual = text_diagram_to_networkx_graph(""" +in---Z---H---------out + | +in---X---Z(-pi/2)---out + """) + expected = nx.MultiGraph() + expected.add_node(0, value='in'), + expected.add_node(1, value='Z'), + expected.add_node(2, value='H'), + expected.add_node(3, value='out'), + expected.add_node(4, value='in'), + expected.add_node(5, value='X'), + expected.add_node(6, value='Z(-pi/2)'), + expected.add_node(7, value='out'), + expected.add_edge(0, 1) + expected.add_edge(1, 2) + expected.add_edge(2, 3) + expected.add_edge(1, 5) + expected.add_edge(4, 5) + expected.add_edge(5, 6) + expected.add_edge(6, 7) + nx.testing.assert_graphs_equal(actual, expected) + + actual = text_diagram_to_networkx_graph(""" + Z-* + | | + X-* + """) + expected = nx.MultiGraph() + expected.add_node(0, value='Z') + expected.add_node(1, value='X') + expected.add_edge(0, 1) + expected.add_edge(0, 1) + nx.testing.assert_graphs_equal(actual, expected) diff --git a/glue/lattice_surgery/stimzx/_zx_graph_solver.py b/glue/lattice_surgery/stimzx/_zx_graph_solver.py new file mode 100644 index 000000000..ff5bd0918 --- /dev/null +++ b/glue/lattice_surgery/stimzx/_zx_graph_solver.py @@ -0,0 +1,196 @@ +from typing import Dict, Tuple, List, Any, Union +import stim +import networkx as nx + +from ._text_diagram_parsing import text_diagram_to_networkx_graph +from ._external_stabilizer import ExternalStabilizer + + +class ZxType: + """Data describing a ZX node.""" + + def __init__(self, kind: str, quarter_turns: int = 0): + self.kind = kind + self.quarter_turns = quarter_turns + + def __eq__(self, other): + if not isinstance(other, ZxType): + return NotImplemented + return self.kind == other.kind and self.quarter_turns == other.quarter_turns + + def __ne__(self, other): + return not self == other + + def __hash__(self): + return hash((ZxType, self.kind, self.quarter_turns)) + + def __repr__(self): + return f'ZxType(kind={self.kind!r}, quarter_turns={self.quarter_turns!r})' + + +ZX_TYPES = { + "X": ZxType("X"), + "X(pi/2)": ZxType("X", 1), + "X(pi)": ZxType("X", 2), + "X(-pi/2)": ZxType("X", 3), + "Z": ZxType("Z"), + "Z(pi/2)": ZxType("Z", 1), + "Z(pi)": ZxType("Z", 2), + "Z(-pi/2)": ZxType("Z", 3), + "H": ZxType("H"), + "in": ZxType("in"), + "out": ZxType("out"), +} + + +def text_diagram_to_zx_graph(text_diagram: str) -> nx.MultiGraph: + """Converts an ASCII text diagram into a ZX graph (represented as a networkx MultiGraph). + + Supported node types: + "X": X spider with angle set to 0. + "Z": Z spider with angle set to 0. + "X(pi/2)": X spider with angle set to pi/2. + "X(pi)": X spider with angle set to pi. + "X(-pi/2)": X spider with angle set to -pi/2. + "Z(pi/2)": X spider with angle set to pi/2. + "Z(pi)": X spider with angle set to pi. + "Z(-pi/2)": X spider with angle set to -pi/2. + "H": Hadamard node. Must have degree 2. + "in": Input node. Must have degree 1. + "out": Output node. Must have degree 1. + + Args: + text_diagram: A text diagram containing ZX nodes (e.g. "X(pi)") and edges (e.g. "------") connecting them. + + Example: + >>> import stimzx + >>> import networkx + >>> actual: networkx.MultiGraph = stimzx.text_diagram_to_zx_graph(r''' + ... in----X------out + ... | + ... in---Z(pi)---out + ... ''') + >>> expected = networkx.MultiGraph() + >>> expected.add_node(0, value=stimzx.ZxType("in")) + >>> expected.add_node(1, value=stimzx.ZxType("X")) + >>> expected.add_node(2, value=stimzx.ZxType("out")) + >>> expected.add_node(3, value=stimzx.ZxType("in")) + >>> expected.add_node(4, value=stimzx.ZxType("Z", quarter_turns=2)) + >>> expected.add_node(5, value=stimzx.ZxType("out")) + >>> _ = expected.add_edge(0, 1) + >>> _ = expected.add_edge(1, 2) + >>> _ = expected.add_edge(1, 4) + >>> _ = expected.add_edge(3, 4) + >>> _ = expected.add_edge(4, 5) + >>> networkx.testing.assert_graphs_equal(actual, expected) + + Returns: + A networkx MultiGraph containing the nodes and edges from the diagram. Nodes are numbered 0, 1, 2, etc in + reading ordering from the diagram, and have a "value" attribute of type `stimzx.ZxType`. + """ + return text_diagram_to_networkx_graph(text_diagram, value_func=ZX_TYPES.__getitem__) + + +def _reduced_zx_graph(graph: Union[nx.Graph, nx.MultiGraph]) -> nx.Graph: + """Return an equivalent graph without self edges or repeated edges.""" + reduced_graph = nx.Graph() + odd_parity_edges = set() + for n1, n2 in graph.edges(): + if n1 == n2: + continue + odd_parity_edges ^= {frozenset([n1, n2])} + for n, value in graph.nodes('value'): + reduced_graph.add_node(n, value=value) + for n1, n2 in odd_parity_edges: + reduced_graph.add_edge(n1, n2) + return reduced_graph + + +def zx_graph_to_external_stabilizers(graph: Union[nx.Graph, nx.MultiGraph]) -> List[ExternalStabilizer]: + """Computes the external stabilizers of a ZX graph; generators of Paulis that leave it unchanged including sign. + + Args: + graph: A non-contradictory connected ZX graph with nodes annotated by 'type' and optionally by 'angle'. + Allowed types are 'x', 'z', 'h', and 'out'. + Allowed angles are multiples of `math.pi/2`. Only 'x' and 'z' node types can have angles. + 'out' nodes must have degree 1. + 'h' nodes must have degree 2. + + Returns: + A list of canonicalized external stabilizer generators for the graph. + """ + + graph = _reduced_zx_graph(graph) + sim = stim.TableauSimulator() + + # Interpret each edge as a cup producing an EPR pair. + # - The qubits of the EPR pair fly away from the center of the edge, towards their respective nodes. + # - The qubit keyed by (a, b) is the qubit heading towards b from the edge between a and b. + qubit_ids: Dict[Tuple[Any, Any], int] = {} + for n1, n2 in graph.edges: + qubit_ids[(n1, n2)] = len(qubit_ids) + qubit_ids[(n2, n1)] = len(qubit_ids) + sim.h(qubit_ids[(n1, n2)]) + sim.cnot(qubit_ids[(n1, n2)], qubit_ids[(n2, n1)]) + + # Interpret each internal node as a family of post-selected parity measurements. + for n, node_type in graph.nodes('value'): + if node_type.kind in 'XZ': + # Surround X type node with Hadamards so it can be handled as if it were Z type. + if node_type.kind == 'X': + for neighbor in graph.neighbors(n): + sim.h(qubit_ids[(neighbor, n)]) + elif node_type.kind == 'H': + # Hadamard one input so the H node can be handled as if it were Z type. + neighbor, _ = graph.neighbors(n) + sim.h(qubit_ids[(neighbor, n)]) + elif node_type.kind in ['out', 'in']: + continue # Don't measure qubits leaving the system. + else: + raise ValueError(f"Unknown node type {node_type!r}") + + # Handle Z type node. + # - Postselects the ZZ observable over each pair of incoming qubits. + # - Postselects the (S**quarter_turns X S**-quarter_turns)XX..X observable over all incoming qubits. + neighbors = [n2 for n2 in graph.neighbors(n) if n2 != n] + center = qubit_ids[(neighbors[0], n)] # Pick one incoming qubit to be the common control for the others. + # Handle node angle using a phasing operation. + [id, sim.s, sim.z, sim.s_dag][node_type.quarter_turns](center) + # Use multi-target CNOT and Hadamard to transform postselected observables into single-qubit Z observables. + for n2 in neighbors[1:]: + sim.cnot(center, qubit_ids[(n2, n)]) + sim.h(center) + # Postselect the observables. + for n2 in neighbors: + _pseudo_postselect(sim, qubit_ids[(n2, n)]) + + # Find output qubits. + in_nodes = sorted(n for n, value in graph.nodes('value') if value.kind == 'in') + out_nodes = sorted(n for n, value in graph.nodes('value') if value.kind == 'out') + ext_nodes = in_nodes + out_nodes + out_qubits = [] + for out in ext_nodes: + (neighbor,) = graph.neighbors(out) + out_qubits.append(qubit_ids[(neighbor, out)]) + + # Remove qubits corresponding to non-external edges. + for i, q in enumerate(out_qubits): + sim.swap(q, len(qubit_ids) + i) + for i, q in enumerate(out_qubits): + sim.swap(i, len(qubit_ids) + i) + sim.set_num_qubits(len(out_qubits)) + + # Stabilizers of the simulator state are the external stabilizers of the graph. + dual_stabilizers = sim.canonical_stabilizers() + return ExternalStabilizer.canonicals_from_duals(dual_stabilizers, len(in_nodes)) + + +def _pseudo_postselect(sim: stim.TableauSimulator, target: int): + """Pretend to postselect by using classical feedback to consistently get into the measurement-was-false state.""" + measurement_result, kickback = sim.measure_kickback(target) + if kickback is not None: + for qubit, pauli in enumerate(kickback): + feedback_op = [None, sim.cnot, sim.cy, sim.cz][pauli] + if feedback_op is not None: + feedback_op(stim.target_rec(-1), qubit) + assert kickback is not None or not measurement_result, "Impossible postselection. Graph contained a contradiction." diff --git a/glue/lattice_surgery/stimzx/_zx_graph_solver_test.py b/glue/lattice_surgery/stimzx/_zx_graph_solver_test.py new file mode 100644 index 000000000..9db02fdf9 --- /dev/null +++ b/glue/lattice_surgery/stimzx/_zx_graph_solver_test.py @@ -0,0 +1,137 @@ +from typing import List + +import stim + +from ._zx_graph_solver import zx_graph_to_external_stabilizers, text_diagram_to_zx_graph, ExternalStabilizer + + +def test_disconnected(): + assert zx_graph_to_external_stabilizers(text_diagram_to_zx_graph(""" + in---X X---out + """)) == [ + ExternalStabilizer(input=stim.PauliString("Z"), output=stim.PauliString("_")), + ExternalStabilizer(input=stim.PauliString("_"), output=stim.PauliString("Z")), + ] + assert zx_graph_to_external_stabilizers(text_diagram_to_zx_graph(""" + in---Z---out + | + X + """)) == [ + ExternalStabilizer(input=stim.PauliString("Z"), output=stim.PauliString("_")), + ExternalStabilizer(input=stim.PauliString("_"), output=stim.PauliString("Z")), + ] + assert zx_graph_to_external_stabilizers(text_diagram_to_zx_graph(""" + in---Z---X---out + | | + *---* + """)) == [ + ExternalStabilizer(input=stim.PauliString("X"), output=stim.PauliString("_")), + ExternalStabilizer(input=stim.PauliString("_"), output=stim.PauliString("Z")), + ] + + +def test_cnot(): + assert zx_graph_to_external_stabilizers(text_diagram_to_zx_graph(""" + in---X---out + | + in---Z---out + """)) == external_stabilizers_of_circuit(stim.Circuit("CNOT 1 0")) + + assert zx_graph_to_external_stabilizers(text_diagram_to_zx_graph(""" + in---Z---out + | + in---X---out + """)) == external_stabilizers_of_circuit(stim.Circuit("CNOT 0 1")) + + +def test_cz(): + assert zx_graph_to_external_stabilizers(text_diagram_to_zx_graph(""" + in---Z---out + | + H + | + in---Z---out + """)) == external_stabilizers_of_circuit(stim.Circuit("CZ 0 1")) + + +def test_s(): + assert zx_graph_to_external_stabilizers(text_diagram_to_zx_graph(""" + in---Z(pi/2)---out + """)) == external_stabilizers_of_circuit(stim.Circuit("S 0")) + + +def test_s_dag(): + assert zx_graph_to_external_stabilizers(text_diagram_to_zx_graph(""" + in---Z(-pi/2)---out + """)) == external_stabilizers_of_circuit(stim.Circuit("S_DAG 0")) + + +def test_sqrt_x(): + assert zx_graph_to_external_stabilizers(text_diagram_to_zx_graph(""" + in---X(pi/2)---out + """)) == external_stabilizers_of_circuit(stim.Circuit("SQRT_X 0")) + + +def test_sqrt_x_sqrt_x(): + assert zx_graph_to_external_stabilizers(text_diagram_to_zx_graph(""" + in---X(pi/2)---X(pi/2)---out + """)) == external_stabilizers_of_circuit(stim.Circuit("X 0")) + + +def test_sqrt_z_sqrt_z(): + assert zx_graph_to_external_stabilizers(text_diagram_to_zx_graph(""" + in---Z(pi/2)---Z(pi/2)---out + """)) == external_stabilizers_of_circuit(stim.Circuit("Z 0")) + + +def test_sqrt_x_dag(): + assert zx_graph_to_external_stabilizers(text_diagram_to_zx_graph(""" + in---X(-pi/2)---out + """)) == external_stabilizers_of_circuit(stim.Circuit("SQRT_X_DAG 0")) + + +def test_x(): + assert zx_graph_to_external_stabilizers(text_diagram_to_zx_graph(""" + in---X(pi)---out + """)) == external_stabilizers_of_circuit(stim.Circuit("X 0")) + + +def test_z(): + assert zx_graph_to_external_stabilizers(text_diagram_to_zx_graph(""" + in---Z(pi)---out + """)) == external_stabilizers_of_circuit(stim.Circuit("Z 0")) + + +def test_id(): + assert zx_graph_to_external_stabilizers(text_diagram_to_zx_graph(""" + in---X---Z---out + """)) == external_stabilizers_of_circuit(stim.Circuit("I 0")) + + +def test_s_state_distill(): + assert zx_graph_to_external_stabilizers(text_diagram_to_zx_graph(r""" + * *---------------Z--------------------Z-------Z(pi/2) + / \ | | | + *-----* *------------Z---+---------------+---Z----------------+-------Z(pi/2) + | | | | | | + X---X---Z(pi/2) X---X---Z(pi/2) X---X---Z(pi/2) X---X---Z(pi/2) + | | | | | | + *---+------------------Z-------------------+--------------------+---Z---Z(pi/2) + | | | + in-------Z--------------------------------------Z-------------------Z(pi)--------out + """)) == external_stabilizers_of_circuit(stim.Circuit("S 0")) + + +def external_stabilizers_of_circuit(circuit: stim.Circuit) -> List[ExternalStabilizer]: + n = circuit.num_qubits + s = stim.TableauSimulator() + s.do(circuit) + t = s.current_inverse_tableau()**-1 + stabilizers = [] + for k in range(n): + p = [0] * n + p[k] = 1 + stabilizers.append(stim.PauliString(p) + t.x_output(k)) + p[k] = 3 + stabilizers.append(stim.PauliString(p) + t.z_output(k)) + return [ExternalStabilizer.from_dual(e, circuit.num_qubits) for e in stabilizers] From cdda7501a92b9b258035a1b352bd0edef0847d2c Mon Sep 17 00:00:00 2001 From: Daniel Bochen Tan <33230390+qu-tan-um@users.noreply.github.com> Date: Fri, 17 May 2024 22:35:54 -0700 Subject: [PATCH 3/3] updates for LaSSynth (#770) - Cleaned up code and added comments. - Adapt to finalized naming in the paper. README and demo notebook also updated. - Fixed issue of missing faces when generated GLTF is opened in other software. Now every face is actually two back-to-back sides both providing color. User can also opt in to add the IJK axes in the gltf. - Unified a lot of code in the textfig, zigxag, and graph generator to Stim ZX. These three now are all based on `ZXGridGraph`. --------- Co-authored-by: Daniel Tan --- glue/lattice_surgery/.gitignore | 9 - glue/lattice_surgery/README.md | 40 +- glue/lattice_surgery/docs/demo.ipynb | 729 ++--- glue/lattice_surgery/lassynth/__init__.py | 2 + .../lassynth/lattice_surgery_synthesis.py | 590 ++++ .../rewrite_passes/__init__.py | 0 .../lassynth/rewrite_passes/attach_fixups.py | 86 + .../lassynth/rewrite_passes/color_z.py | 210 ++ .../rewrite_passes/remove_unconnected.py | 152 + .../sat_synthesis}/__init__.py | 0 .../sat_synthesis/lattice_surgery_sat.py | 1842 ++++++++++++ .../lassynth/tools/__init__.py | 0 .../lassynth/tools/verify_stabilizers.py | 38 + .../lassynth/translators/__init__.py | 1 + .../lassynth/translators/gltf_generator.py | 2622 +++++++++++++++++ .../translators/networkx_generator.py | 53 + .../lassynth/translators/textfig_generator.py | 217 ++ .../lassynth/translators/zx_grid_graph.py | 292 ++ glue/lattice_surgery/olssco/__init__.py | 2 - .../olssco/lattice_surgery_compiler.py | 460 --- .../olssco/rewrite_passes/attach_fixups.py | 64 - .../olssco/rewrite_passes/color_z.py | 176 -- .../rewrite_passes/remove_unconnected.py | 134 - .../olssco/sat_lattice_surgery_solver.py | 1805 ------------ .../olssco/tools/verify_stabilizers.py | 40 - .../olssco/translators/__init__.py | 1 - .../olssco/translators/gltf_generator.py | 1582 ---------- .../olssco/translators/networkx_generator.py | 250 -- .../olssco/translators/textfig_generator.py | 184 -- .../olssco/translators/zigxag_generator.py | 301 -- .../olssco/translators/zx_grid_graph.py | 157 - .../paper/graph_state_olssco.py | 111 - glue/lattice_surgery/paper/graphs8.json | 106 - glue/lattice_surgery/paper/graphs_large.json | 889 ------ .../paper/rand_graph_baseline_opt.py | 103 - .../paper/rand_graph_olsco_hier.py | 193 -- glue/lattice_surgery/setup.py | 13 +- 37 files changed, 6409 insertions(+), 7045 deletions(-) delete mode 100644 glue/lattice_surgery/.gitignore create mode 100644 glue/lattice_surgery/lassynth/__init__.py create mode 100644 glue/lattice_surgery/lassynth/lattice_surgery_synthesis.py rename glue/lattice_surgery/{olssco => lassynth}/rewrite_passes/__init__.py (100%) create mode 100644 glue/lattice_surgery/lassynth/rewrite_passes/attach_fixups.py create mode 100644 glue/lattice_surgery/lassynth/rewrite_passes/color_z.py create mode 100644 glue/lattice_surgery/lassynth/rewrite_passes/remove_unconnected.py rename glue/lattice_surgery/{olssco/tools => lassynth/sat_synthesis}/__init__.py (100%) create mode 100644 glue/lattice_surgery/lassynth/sat_synthesis/lattice_surgery_sat.py create mode 100644 glue/lattice_surgery/lassynth/tools/__init__.py create mode 100644 glue/lattice_surgery/lassynth/tools/verify_stabilizers.py create mode 100644 glue/lattice_surgery/lassynth/translators/__init__.py create mode 100644 glue/lattice_surgery/lassynth/translators/gltf_generator.py create mode 100644 glue/lattice_surgery/lassynth/translators/networkx_generator.py create mode 100644 glue/lattice_surgery/lassynth/translators/textfig_generator.py create mode 100644 glue/lattice_surgery/lassynth/translators/zx_grid_graph.py delete mode 100644 glue/lattice_surgery/olssco/__init__.py delete mode 100644 glue/lattice_surgery/olssco/lattice_surgery_compiler.py delete mode 100644 glue/lattice_surgery/olssco/rewrite_passes/attach_fixups.py delete mode 100644 glue/lattice_surgery/olssco/rewrite_passes/color_z.py delete mode 100644 glue/lattice_surgery/olssco/rewrite_passes/remove_unconnected.py delete mode 100644 glue/lattice_surgery/olssco/sat_lattice_surgery_solver.py delete mode 100644 glue/lattice_surgery/olssco/tools/verify_stabilizers.py delete mode 100644 glue/lattice_surgery/olssco/translators/__init__.py delete mode 100644 glue/lattice_surgery/olssco/translators/gltf_generator.py delete mode 100644 glue/lattice_surgery/olssco/translators/networkx_generator.py delete mode 100644 glue/lattice_surgery/olssco/translators/textfig_generator.py delete mode 100644 glue/lattice_surgery/olssco/translators/zigxag_generator.py delete mode 100644 glue/lattice_surgery/olssco/translators/zx_grid_graph.py delete mode 100644 glue/lattice_surgery/paper/graph_state_olssco.py delete mode 100644 glue/lattice_surgery/paper/graphs8.json delete mode 100644 glue/lattice_surgery/paper/graphs_large.json delete mode 100644 glue/lattice_surgery/paper/rand_graph_baseline_opt.py delete mode 100644 glue/lattice_surgery/paper/rand_graph_olsco_hier.py diff --git a/glue/lattice_surgery/.gitignore b/glue/lattice_surgery/.gitignore deleted file mode 100644 index fb6b59ce3..000000000 --- a/glue/lattice_surgery/.gitignore +++ /dev/null @@ -1,9 +0,0 @@ -__pycache__/ -.vscode/ -/tmp/ -.idea/ -*.zip -new_run/ -*.egg-info -/build/ -.ipynb_checkpoints/ diff --git a/glue/lattice_surgery/README.md b/glue/lattice_surgery/README.md index 4b3fa6dcc..613674808 100644 --- a/glue/lattice_surgery/README.md +++ b/glue/lattice_surgery/README.md @@ -1,11 +1,39 @@ -# Optimal Lattice Surgery Subroutine Compiler (OLSSCo) +# Lattice Surgery Subroutine Synthesizer (LaSsynth) +A lattice surgery subroutine (LaS) is a confined volume with a set of ports. +Within this volume, lattice surgery merges and splits are performed. +The function of a LaS is characterized by a set of stabilizers on these ports. -## installation -In this directory `pip install .` This will also install a few packages that we need: 3 packaes from pypi `z3-solver`, `networkx`, and `stim`; 1 package from included files `stimzx` [(source)](https://github.com/quantumlib/Stim/tree/0fdddef863cfe777f3f2086a092ba99785725c07/glue/zx). +The lattice surgery subroutine synthesizer (LaSsynth) uses SAT/SMT solvers to synthesize LaS given the volume, the ports, and the stabilizers. +LaSsynth outputs a textual representation of LaS (LaSRe) which is a JSON file with filename extension `.lasre`. +LaSsynth can also generate 3D modelling files in the [GLTF](https://www.khronos.org/gltf/) format from LaSRe files. + +The main ideas of this project is provided in the paper [A SAT Scalpel for Lattice Surgery](http://arxiv.org/abs/2404.18369) by Tan, Niu, and Gidney. +For files specific to the paper, please refer to [its Zenodo archive](https://zenodo.org/doi/10.5281/zenodo.11051465). + +## Installation +It is recommended to create a virtual Python environment. Once inside the environment, in this directory, `pip install .` +Apart from LaSsynth, this will install a few packages that we need: + - `z3-solver` version `4.12.1.0`, from pip + - `networkx` default version, from pip + - `stim` default version, from pip + - `stimzx` from files included in sirectory `./stimzx/`. We copied these files from [here](https://github.com/quantumlib/Stim/tree/0fdddef863cfe777f3f2086a092ba99785725c07/glue/zx). + - `ipykernel` default version, from pip, to view the demo Jupyter notebook. We have a dependency [kissat](https://github.com/arminbiere/kissat) which is a SAT solver, not a Python package. It is recommended to install it and find out the directory of the executable `kissat` because we will need it later. -Our compiler can be used without Kissat, in which case it just uses `z3-solver`, but on certain cases Kissat can offer big runtime improvements. +LaSsynth can be used without Kissat, in which case it just uses `z3-solver`, but on certain cases Kissat can offer big runtime improvements. + +## How to use +See the [demo notebook in the docs directory](docs/demo.ipynb) -## how to use -See the [demo notebook in the docs directory](docs/demo.ipynb) \ No newline at end of file +## Cite this work +```bibtex +@inproceedings{tan-niu-gidney_lattice_surgery, + author = {Tan, Daniel Bochen and Niu, Murphy Yuezhen and Gidney, Craig}, + title = {A {SAT} Scalpel for Lattice Surgery: Representation and Synthesis of Subroutines for Surface-Code Fault-Tolerant Quantum Computing}, + shorttitle = {A {SAT} Scalpel for Lattice Surgery}, + booktitle = {2024 ACM/IEEE 51st Annual International Symposium on Computer Architecture ({ISCA})}, + year = {2024}, + url = {http://arxiv.org/abs/2404.18369}, +} +``` \ No newline at end of file diff --git a/glue/lattice_surgery/docs/demo.ipynb b/glue/lattice_surgery/docs/demo.ipynb index 952612d5e..36dfe2185 100644 --- a/glue/lattice_surgery/docs/demo.ipynb +++ b/glue/lattice_surgery/docs/demo.ipynb @@ -5,7 +5,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Introduction to the Lattice Surgery Subroutine Compiler" + "# Introduction to the LaSSynth, Lattice Surgery Subroutine Synthesizer" ] }, { @@ -20,9 +20,9 @@ "metadata": {}, "source": [ "\n", - "This Jupyter notebook aims at giving a minimal demo on how to use this compiler.\n", + "This Jupyter notebook aims at giving a minimal demo on how to use this software.\n", "The reader needs to know how lattice surgery works to fully understand this notebook.\n", - "The most direct reference is [our paper]() (link TBA) which, in itself, also provides more pointers to background knowledge references.\n", + "The most direct reference is [our paper](http://arxiv.org/abs/2404.18369) which, in itself, also provides more pointers to background knowledge references.\n", "There are two we would like to mention here.\n", "- [arXiv:1704.08670](https://arxiv.org/abs/1704.08670) links merging and spliting operations in lattice surgery to ZX calculus.\n", "We leverage this connection a lot in our software.\n", @@ -47,13 +47,13 @@ "Some of these patches correspond to logical qubits whereas others can be temporary ancilla during computation.\n", "\n", "Since the logical qubits are in a 2D grid, and there is the time dimension, the compilation problem is laying out operations in a 3D grid to realize certain computation.\n", - "We consider only a bounded spacetime and what *can* be realized within the bounds is called a *lattice surgery subroutine* (LSS), because it should be considered as a subroutine in the whole quantum algorithm.\n", + "We consider only a bounded spacetime and what *can* be realized within the bounds is called a *lattice surgery subroutine* (LaS), because it should be considered as a subroutine in the whole quantum algorithm.\n", "\n", - "Because of the connection between lattice surgery and ZX calculus, an LSS can be seen as a ZX diagram with nodes at points in a 3D grid and edges only between nearest neighbors, as seen on the right in the figure below.\n", + "Because of the connection between lattice surgery and ZX calculus, a LaS can be seen as a ZX diagram with nodes at points in a 3D grid and edges only between nearest neighbors, as seen in the figure below.\n", "If you have worked with ZX calculus, you would know that this ZX diagram is a CNOT.\n", "However, it seems that there are two \"unnecessary\" identity nodes in the middle.\n", "This is because there are other constraints when it comes to realizing the CNOT in a surface code memory.\n", - "Our representation of an LSS, the 'pipe diagram' below, does account for these extra constraints." + "Our representation of a LaS, the \"pipe diagram\" below, does account for these extra constraints." ] }, { @@ -88,9 +88,9 @@ "If we want the pipe diagram to look like exactly what happens on chip, we need to draw them in scale, e.g, shown on the right below.\n", "There are four patches of surface codes, and only three are used in the computation.\n", "These three are identified by their coordinates in the I-J plane: (1,0), (1,1), and (0,1) from left to right in the picture.\n", - "Between the patches, there are some 'gaps' which are lines on physical qubits.\n", + "Between the patches, there are some \"gaps\" which are lines on physical qubits.\n", "We can perform merging and splitting of patches with these gaps.\n", - "Since the gap is narrow compared to the patches, but what happens there are really what decides the computation.\n", + "Since the gap is very narrow compared to the patches, but what happens there are really what decides the computation.\n", "Thus, to see these merging and splitting more clearly, we often stretch the gaps in the pipe diagram, resulting in something like the picture on the left below.\n", "\n", "The unit in all three dimension is the code distance.\n", @@ -98,7 +98,7 @@ "These cubes are sitting at integer points in the I-J-K grid.\n", "Nontrivial logical operations are done by connecting these cubes with pipes.\n", "For example, two cubes connected in the I-J plane correspond to performing merging and splitting of two patches; a cube that has a vertical connection below but not above is a logical measurement; etc.\n", - "At this point, we see that the problem of compiling LSS is laying out these cubes and pipes in a limited spacetime." + "At this point, we see that the problem of compiling LaS is laying out these cubes and pipes in a limited spacetime." ] }, { @@ -117,19 +117,17 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## LSS Specification" + "## LaS Specification" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "\n", - "\n", "There are some constraints in the construction of these diagrams, e.g., matching colors at intersection of two pipes, but we are not going to introduce them here.\n", - "After all, the purpose of a compiler is to let a computer consider those constraints instead of humans.\n", + "After all, the purpose of a synthesizer is to let a computer consider those constraints instead of humans.\n", "The reader can refer to our paper, or even to the code in this repo for these constraints later on.\n", - "What we are going to detail now is how to specify a problem to the compiler, so that the reader can start using the compiler." + "What we are going to detail now is how to specify a problem to the compiler, so that the reader can start using the software." ] }, { @@ -148,14 +146,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The LSS specification is shown in part b) of the figure above.\n", + "The LaS specification is shown in part b) of the figure above.\n", "`max_i`, `max_j` and `max_k` are the bounds of spacetime.\n", "In our example, they are 2, 2, and 3, which means all the cubes and pipes are within 2x2x3 volume." ] }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 10, "metadata": {}, "outputs": [], "source": [ @@ -169,15 +167,15 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "There are certain *ports* that connects the LSS to the outside (which makes sense since a subroutine in classical computing always has some arguements and some returns).\n", - "In this example, there are two ports on the bottom floor corresponding to the two qubits before the CNOT; then, there is some manipulationi of these two qubits implmented with the pipes in the gray box; on the top floor, the two ports are the qubits after going through the CNOT.\n", + "There are certain *ports* that connects the LaS to the outside (which makes sense since a subroutine in classical computing always has some arguements and some returns).\n", + "In this example, there are two ports on the bottom floor corresponding to the two qubits before the CNOT; then, there is some manipulation of these two qubits implmented with the pipes in the gray box; on the top floor, the two ports are the qubits after going through the CNOT.\n", "\n", "We need to provide three things to specify each port.\n", "Let us look at the port for the output of control qubit in the CNOT indicated in the callout in part a) of the figure above.\n", "In the code block below, it is the third port in `input_dict[\"ports\"]`.\n", "- Its `location` is `[1,0,3]` because that is where the information is going out of the LSS.\n", "- In general, the pipe connecting a port can also be in I, J or K direction.\n", - "Additionally, we need another character (`-` or `+`) to indicate the direction from the port to the other parts of the LSS.\n", + "Additionally, we need another character (`-` or `+`) to indicate the direction from the port to the other parts of the LaS.\n", "In this example, the pipe is in the K direction, and we need to go downward from `[1, 0, 3]` to everything else, so the `direction` of the port is `-K`.\n", "- Finally, surface code patches have a space orientation of the X and Z boundaries indicated by red and blue above.\n", "We provide which one of I, J, and K is orthogonal to the face of Z boundary (blue).\n", @@ -186,7 +184,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 11, "metadata": {}, "outputs": [], "source": [ @@ -203,8 +201,8 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Finally, we need to provide the stabilizer constraints on the ports to ensure that the LSS indeed realizes the logical operations we want to perform.\n", - "Although intuitively there are input and output ports for the CNOT, in LSS, there is no inherent distinction between inputs and outputs.\n", + "Finally, we need to provide the stabilizer constraints on the ports to ensure that the LaS indeed realizes the logical operations we want to perform.\n", + "Although intuitively there are input and output ports for the CNOT, in a LaS, there is no inherent distinction between inputs and outputs.\n", "What matters is that the given stabilizers have to match the ordering of the ports.\n", "Our ordering is (control qubit input, target qubit input, control qubit output, target qubit output), so the correct stabilizers are ZIZI, IZZZ, XIXX, and IXIX.\n", "If we change the ordering of the `\"ports\"` list above, we also need to change the stabilizers." @@ -212,7 +210,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 12, "metadata": {}, "outputs": [], "source": [ @@ -224,7 +222,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Solving LSS" + "## Solving LaS" ] }, { @@ -232,41 +230,32 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "By now we have finished preparing the specification of the LSS.\n", - "We can use our software package `olssco`, specifically the class `LatticeSurgeryCompiler` to solve the problem.\n", - "It can be intialized with the specification dictionary.\n", - "When we invoke `solve` method, the compiler gives us a solution." + "By now we have finished preparing the specification of the LaS.\n", + "We can use our software package `lassynth`, specifically the class `LatticeSurgerySynthesizer` to solve the problem.\n", + "When we invoke `solve` method, the synthesizer gives us a solution with respect to a `specification`." ] }, { "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "from olssco import LatticeSurgeryCompiler\n", - "\n", - "lss = LatticeSurgeryCompiler(specification=input_dict)\n", - "result = lss.solve()" - ] - }, - { - "cell_type": "code", - "execution_count": 5, + "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 5, + "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ + "from lassynth import LatticeSurgerySynthesizer\n", + "\n", + "las_synth = LatticeSurgerySynthesizer()\n", + "result = las_synth.solve(specification=input_dict)\n", "result" ] }, @@ -274,316 +263,162 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## To-do" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We're ready to really solve the problem.\n", - "Isn't that existing!\n", - "There are a few optional arguments to get more information about the solving process.\n", - "When solving using Kissat, we will generate a `.dimacs` file for the SAT problem, and call Kissat on that file.\n", - "Then, we will analyze the output of Kissat to derive the solution.\n", - "The optional arguments are:\n", - "- `print_detail`: if set to `True`, you will see the Kissat log on screen during the solving process.\n", - "- `dimacs_file_name`: a file to store the `.dimacs` we generated for the problem.\n", - "- `sat_log_file_name`: a file to store the Kissat log.\n", - "- `result_file_name`: a file to store the solution in terms of value assignments to our defined LSS variables." + "As you have noticed, the return value is of a class `LatticeSurgerySolution`.\n", + "We implement a few methods for this class to help us further manipulate the solution.\n", + "To see the \"raw\" solution, i.e., LaSRe (lattice surgery subroutine representation) in the paper, you can access the `lasre` of this result.\n", + "Due to technical reasons, the `ports` here is another encoding compared to the `ports` in the specification.\n", + "Intersted readers can refer to comments in the code to understand this encoding, but it is not too important in this notebook." ] }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 14, "metadata": {}, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "c ---- [ banner ] ------------------------------------------------------------\n", - "c\n", - "c Kissat SAT Solver\n", - "c \n", - "c Copyright (c) 2021-2023 Armin Biere University of Freiburg\n", - "c Copyright (c) 2019-2021 Armin Biere Johannes Kepler University Linz\n", - "c \n", - "c Version 3.1.0 630d64d4d63c2816fc79a1a0340286b39677e97d\n", - "c gcc (Debian 12.2.0-14) 12.2.0 -W -Wall -O3 -DNDEBUG\n", - "c Mon Jun 26 11:52:55 PM UTC 2023 Linux qutanum.c.googlers.com 6.1.25-1rodete1-amd64 x86_64\n", - "c\n", - "c ---- [ parsing ] -----------------------------------------------------------\n", - "c\n", - "c opened and reading DIMACS file:\n", - "c\n", - "c ./cnot.dimacs\n", - "c\n", - "c parsed 'p cnf 462 2164' header\n", - "c closing input after reading 39292 bytes (38 KB)\n", - "c finished parsing after 0.00 seconds\n", - "c\n", - "c ---- [ solving ] -----------------------------------------------------------\n", - "c\n", - "c seconds switched conflicts irredundant variables\n", - "c MB reductions redundant trail remaining\n", - "c level restarts binary glue\n", - "c\n", - "c * 0.00 2 0 0 0 0 0 0 634 1470 0% 0 402 87%\n", - "c { 0.00 2 0 0 0 0 0 0 634 1470 0% 0 402 87%\n", - "c } 0.00 2 31 0 0 0 31 22 639 1469 45% 3 402 87%\n", - "c 1 0.00 2 31 0 0 0 31 22 639 1469 45% 3 402 87%\n", - "c\n", - "c ---- [ result ] ------------------------------------------------------------\n", - "c\n", - "s SATISFIABLE\n", - "v 1 -2 -3 -4 5 -6 -7 -8 9 10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22\n", - "v -23 -24 25 26 -27 -28 -29 30 -31 -32 33 -34 -35 -36 37 38 39 40 41 42 43 44\n", - "v 45 46 47 48 -49 50 -51 -52 -53 54 -55 -56 -57 -58 -59 60 -61 62 -63 64 65\n", - "v -66 -67 -68 69 -70 71 -72 -73 -74 75 -76 -77 -78 79 -80 81 -82 -83 -84 85 86\n", - "v -87 -88 -89 90 91 -92 -93 94 95 96 -97 98 -99 100 101 -102 -103 -104 105 106\n", - "v -107 -108 109 110 111 112 -113 114 115 116 117 118 119 120 121 122 -123 -124\n", - "v -125 -126 127 128 -129 -130 131 132 133 134 -135 -136 137 138 139 140 141\n", - "v 142 143 -144 145 -146 -147 148 149 150 -151 152 -153 154 -155 156 -157 -158\n", - "v 159 160 161 -162 163 164 -165 -166 -167 168 169 -170 171 172 -173 174 -175\n", - "v 176 177 178 179 180 -181 182 183 184 -185 186 -187 188 189 190 -191 192 193\n", - "v 194 -195 -196 197 198 199 -200 -201 202 -203 204 205 206 207 208 -209 -210\n", - "v -211 212 213 214 215 -216 -217 218 219 220 221 222 223 224 -225 226 -227 228\n", - "v -229 230 231 232 233 -234 235 236 237 238 -239 -240 241 242 -243 244 245\n", - "v -246 247 -248 -249 250 251 -252 -253 254 -255 -256 257 -258 259 260 261 262\n", - "v 263 -264 265 266 267 -268 -269 270 271 272 -273 -274 275 -276 277 278 279\n", - "v 280 281 282 283 -284 285 -286 287 288 289 290 -291 292 -293 -294 295 -296\n", - "v 297 298 299 300 301 302 303 -304 -305 306 307 308 -309 310 -311 312 313 -314\n", - "v 315 316 -317 318 -319 320 321 322 -323 324 325 -326 327 328 329 -330 331 332\n", - "v 333 334 335 336 -337 -338 339 340 341 -342 -343 344 345 346 347 348 -349 350\n", - "v 351 352 353 354 -355 -356 -357 358 359 360 361 362 363 -364 365 -366 -367\n", - "v 368 369 370 -371 372 -373 374 375 376 -377 -378 379 380 381 -382 383 384\n", - "v -385 -386 -387 388 389 390 391 392 393 394 -395 396 397 -398 -399 400 401\n", - "v -402 -403 404 -405 406 407 408 409 -410 -411 412 413 414 415 -416 -417 418\n", - "v -419 420 -421 422 423 424 425 426 427 428 429 430 -431 432 433 434 435 436\n", - "v 437 438 439 -440 441 442 443 444 445 446 447 448 -449 450 -451 452 -453 454\n", - "v 455 456 457 -458 459 460 461 462 0\n", - "c\n", - "c ---- [ profiling ] ---------------------------------------------------------\n", - "c\n", - "c 0.00 43.12 % parse\n", - "c 0.00 42.30 % search\n", - "c 0.00 34.02 % focused\n", - "c 0.00 0.00 % simplify\n", - "c =============================================\n", - "c 0.00 100.00 % total\n", - "c\n", - "c ---- [ statistics ] --------------------------------------------------------\n", - "c\n", - "c conflicts: 31 17744.71 per second\n", - "c decisions: 224 7.23 per conflict\n", - "c jumped_reasons: 674 26 % propagations\n", - "c propagations: 2550 1459645 per second\n", - "c queue_decisions: 224 100 % decision\n", - "c random_decisions: 0 0 % decision\n", - "c random_sequences: 0 0 interval\n", - "c score_decisions: 0 0 % decision\n", - "c switched: 0 0 interval\n", - "c vivify_checks: 0 0 per vivify\n", - "c vivify_units: 0 0 % variables\n", - "c\n", - "c ---- [ resources ] ---------------------------------------------------------\n", - "c\n", - "c maximum-resident-set-size: 117702656 bytes 112 MB\n", - "c process-time: 0.00 seconds\n", - "c\n", - "c ---- [ shutting down ] -----------------------------------------------------\n", - "c\n", - "c exit 10\n", - "kissat SAT\n", - "Construct a Z3 SMT model and solve...\n", - "elapsed time: 0.020379s\n", - "Z3 SAT\n" - ] + "data": { + "text/plain": [ + "{'n_i': 2,\n", + " 'n_j': 2,\n", + " 'n_k': 3,\n", + " 'n_p': 4,\n", + " 'n_s': 4,\n", + " 'ports': [{'i': 1, 'j': 0, 'k': 0, 'd': 'K', 'e': '-', 'c': 1},\n", + " {'i': 0, 'j': 1, 'k': 0, 'd': 'K', 'e': '-', 'c': 1},\n", + " {'i': 1, 'j': 0, 'k': 2, 'd': 'K', 'e': '+', 'c': 1},\n", + " {'i': 0, 'j': 1, 'k': 2, 'd': 'K', 'e': '+', 'c': 1}],\n", + " 'stabs': [[{'KI': 0, 'KJ': 1},\n", + " {'KI': 0, 'KJ': 0},\n", + " {'KI': 0, 'KJ': 1},\n", + " {'KI': 0, 'KJ': 0}],\n", + " [{'KI': 0, 'KJ': 0},\n", + " {'KI': 0, 'KJ': 1},\n", + " {'KI': 0, 'KJ': 1},\n", + " {'KI': 0, 'KJ': 1}],\n", + " [{'KI': 1, 'KJ': 0},\n", + " {'KI': 0, 'KJ': 0},\n", + " {'KI': 1, 'KJ': 0},\n", + " {'KI': 1, 'KJ': 0}],\n", + " [{'KI': 0, 'KJ': 0},\n", + " {'KI': 1, 'KJ': 0},\n", + " {'KI': 0, 'KJ': 0},\n", + " {'KI': 1, 'KJ': 0}]],\n", + " 'port_cubes': [(1, 0, 0), (0, 1, 0), (1, 0, 3), (0, 1, 3)],\n", + " 'optional': {},\n", + " 'ExistI': [[[0, 1, 0], [0, 1, 0]], [[0, 0, 0], [0, 0, 0]]],\n", + " 'ExistJ': [[[0, 0, 1], [0, 0, 0]], [[0, 0, 0], [0, 0, 0]]],\n", + " 'ExistK': [[[0, 1, 0], [1, 1, 1]], [[1, 1, 1], [1, 1, 0]]],\n", + " 'ColorI': [[[0, 1, 1], [0, 0, 0]], [[0, 0, 0], [0, 0, 0]]],\n", + " 'ColorJ': [[[0, 0, 0], [0, 0, 0]], [[0, 0, 1], [0, 0, 0]]],\n", + " 'NodeY': [[[0, 0, 0], [0, 0, 0]], [[0, 0, 0], [1, 0, 1]]],\n", + " 'CorrIJ': [[[[0, 0, 0], [0, 0, 0]], [[0, 0, 0], [0, 0, 0]]],\n", + " [[[0, 1, 0], [0, 0, 0]], [[0, 0, 0], [0, 0, 0]]],\n", + " [[[0, 0, 0], [0, 0, 0]], [[0, 0, 0], [0, 0, 0]]],\n", + " [[[0, 0, 0], [0, 0, 0]], [[0, 0, 0], [0, 0, 0]]]],\n", + " 'CorrIK': [[[[0, 0, 0], [0, 0, 1]], [[0, 0, 0], [0, 0, 0]]],\n", + " [[[0, 0, 0], [0, 0, 0]], [[0, 0, 0], [0, 0, 0]]],\n", + " [[[0, 1, 0], [0, 0, 0]], [[0, 0, 0], [0, 0, 0]]],\n", + " [[[0, 0, 0], [0, 1, 0]], [[0, 0, 0], [0, 0, 0]]]],\n", + " 'CorrJK': [[[[0, 0, 0], [0, 0, 0]], [[0, 0, 0], [0, 0, 0]]],\n", + " [[[0, 0, 1], [0, 0, 0]], [[0, 0, 0], [0, 0, 0]]],\n", + " [[[0, 0, 0], [0, 0, 0]], [[0, 0, 0], [0, 0, 0]]],\n", + " [[[0, 0, 0], [0, 0, 0]], [[0, 0, 0], [0, 0, 0]]]],\n", + " 'CorrJI': [[[[0, 0, 0], [0, 0, 0]], [[0, 0, 0], [0, 0, 0]]],\n", + " [[[0, 0, 0], [0, 0, 0]], [[0, 0, 0], [0, 0, 0]]],\n", + " [[[0, 0, 1], [0, 0, 0]], [[0, 0, 0], [0, 0, 0]]],\n", + " [[[0, 0, 0], [0, 0, 0]], [[0, 0, 0], [0, 0, 0]]]],\n", + " 'CorrKI': [[[[1, 0, 1], [0, 0, 0]], [[0, 0, 0], [0, 0, 0]]],\n", + " [[[1, 0, 1], [0, 0, 0]], [[0, 0, 0], [0, 0, 0]]],\n", + " [[[1, 1, 1], [0, 0, 1]], [[1, 1, 1], [0, 0, 0]]],\n", + " [[[0, 0, 0], [1, 1, 1]], [[0, 0, 0], [1, 1, 0]]]],\n", + " 'CorrKJ': [[[[0, 0, 1], [0, 0, 0]], [[1, 1, 1], [0, 0, 0]]],\n", + " [[[1, 1, 1], [1, 1, 1]], [[0, 1, 1], [0, 0, 0]]],\n", + " [[[1, 0, 1], [0, 0, 0]], [[0, 0, 0], [0, 0, 0]]],\n", + " [[[0, 0, 0], [0, 0, 0]], [[0, 0, 0], [1, 1, 0]]]]}" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ - "result = lss.solve(\n", - " print_detail=True,\n", - " dimacs_file_name=\"./cnot.dimacs\",\n", - " sat_log_file_name=\"./cnot.sat\",\n", - " result_file_name=\"./cnot.json\",\n", - ")" + "result.lasre" ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ - "You should see three new files in the same directory to this Jupyter notebook.\n", - "It would be nice to open up each one to get a sense of what they are.\n", - "Now, the result of the SAT solving is in a variable named `result`.\n", - "It is actually an object from a class `LatticeSurgerySubroutine` we also define in the package.\n", - "There are a few translation methods to generate more huamn-readable formats of our result.\n", - "\n", - "We can generate a 3D modelling file of the solution in `.gltf` format.\n", - "You can open it up online (search gltf viewer) or in other common 3D modelling software like Blender." + "## Post-process and Output LaS" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We provide a few rewrite passes to remove valid but unnecessary structures in the solution, and also color the K-pipes.\n", + "These can be applied with the follow call. " ] }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 15, "metadata": {}, "outputs": [], "source": [ - "result.generate_gltf(output_file_name=\"./cnot.gltf\")" + "result = result.after_default_optimizations()" ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ - "Maybe you have already noticed that our LSS is no other than a ZX-diagram with spiders on grid points.\n", - "There are three formats closely related to this fact.\n", - "The first one is a simple text figure for the LSS that spilits it up to slices in time.\n", - "The slices later in time is on top of the print out.\n", - "In each slice, time goes from bottom left to top right.\n", - "The slashes are pipes in the time (K) direction.\n", - "It's a good idea to compare the text figure with the 3d model rendered with the `.gltf` file now.\n", - "A T intersection with red faces drawing the T is an X-spider; if it's the blue faces that draw the T, it's a Z-spider.\n", - "If there are only two pipes at an intersectioni, then it doesn't matter if we lable it X or Z, because they are both identity." + "We can export the result to a few formats.\n", + "The most direct one is to save the LaSRe, which is now just a dictionary" ] }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 16, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - " / \n", - " . H \n", - " / \n", - " \n", - " / \n", - " H . \n", - "/ \n", - " \n", - " \n", - " \n", - "\n", - "======================================\n", - " / \n", - " X---X \n", - "/ / \n", - " \n", - " / \n", - " X . \n", - "/ \n", - " \n", - " \n", - " \n", - "\n", - "======================================\n", - " / / \n", - " X H \n", - "/ / \n", - " \n", - " / \n", - " X . \n", - "/ \n", - " \n", - " \n", - " \n", - "\n", - "======================================\n", - " / / \n", - " X X \n", - " | / \n", - " | \n", - " |/ \n", - " Z . \n", - "/ \n", - " \n", - " \n", - " \n", - "\n", - "======================================\n", - " / \n", - " . X \n", - " / \n", - " \n", - " / \n", - " H . \n", - "/ \n", - " \n", - " \n", - " \n", - "\n", - "======================================\n", - " \n", - " . . \n", - " \n", - " \n", - " \n", - " . . \n", - " \n", - " \n", - " \n", - " \n", - "\n", - "======================================\n", - "\n" - ] - } - ], + "outputs": [], "source": [ - "print(result.generate_textfig())" + "result.save_lasre(\"cnot.lasre.json\")" ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ - "A very similar format is a link to be opened with an online tool ZigXag.\n", - "We stitch the time slices together here.\n", - "With some rotation and reflection of the gltf, you should be able to spot the similarity of it and the ZigXag figure." + "We can also create a 3D modelling file in the [GLTF](https://www.khronos.org/gltf/) format.\n", + "This can be opened in many software, a lot of them are also web-based.\n", + "The `attach_axes` flag attaches I (red), J (green), and K (blue) axis to the GLTF." ] }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 17, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "https://algassert.com/zigxag#0,-4,O;0,-8,O;-1,-1,out;-1,-5,@;-1,-9,O;-1,-13,out;3,0,out;3,-4,O;3,-8,O;3,-12,out:0,-4,-1,-5,-;0,-4,0,-8,-;0,-8,3,-8,-;-1,-1,-1,-5,h;-1,-5,-1,-9,-;-1,-9,-1,-13,h;3,0,3,-4,-;3,-4,3,-8,h;3,-8,3,-12,h\n" - ] - } - ], + "outputs": [], "source": [ - "print(result.generate_zigxag())" + "result.to_3d_model_gltf(\"cnot.gltf\", attach_axes=True)" ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ - "The third format is an annotated NetworkX graph where the nodes are ZX spiders and edges are, well, just edges between them.\n", - "(You can use `generate_networkx` to get this `networkx.Graph`. We skip that here.)\n", - "The annotation follows the convention in [Stim ZX](https://github.com/quantumlib/Stim/tree/main/glue/zx), so we can easily derive the stabilizers of graph with stimzx.\n", - "Then, we can use stim to check whether this set of resulting stabilizers are the same with the stabiliers we specified previously.\n", - "(Both sets will be displayed if setting optional argument `print_stabilizers=True`.)\n", - "If so, we verified the correctness of our compiled result." + "Like mentioned previously, the generated LaS can be easily mapped to a ZX-diagram.\n", + "We can use this connection to verify our result.\n", + "Internally, we construct the ZX-diagram and let [Stim ZX](https://github.com/quantumlib/Stim/tree/main/glue/zx) to derive the stabilizers.\n", + "Then, we check whether these stabilizers are commutable with the ones in the specification.\n", + "If all are commutable, then our LaS is correct." ] }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 18, "metadata": {}, "outputs": [ { @@ -595,13 +430,13 @@ "+_ZZZ\n", "+X_XX\n", "+_X_X\n", - "==================================================================\n", + "==============================================================\n", "resulting:\n", "+X_XX\n", "+Z_Z_\n", "+_X_X\n", "+_ZZZ\n", - "==================================================================\n", + "==============================================================\n", "specified and resulting stabilizers are equivalent.\n" ] }, @@ -611,216 +446,178 @@ "True" ] }, - "execution_count": 13, + "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "result.verify_stabilizers_stimzx(print_stabilizers=True)" + "result.verify_stabilizers_stimzx(specification=input_dict, print_stabilizers=True)" ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ - "Sometimes, we'd like optimize a certain aspect of the LSS to the optimal value.\n", - "We provide an example to optimize the height of the LSS, which is, in turn, proportional to the depth of the circuit to actually run this LSS.\n", - "You can give a specific starting depth, and the `optimize_depth` method will try to solve the LSS with increased and decreased depth until it finds a solution with the optimal depth.\n", - "That is, decreasing the depth by 1 will make the problem unsatisfiable.\n", - "Note that in this method we assume that every port on the top floor will still be on the top floor when we increase or decrease the height." - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "optimal depth of the LSS is 3\n" - ] - } - ], - "source": [ - "optimal_solution = lss.optimize_depth(2)\n", - "print(f\"optimal depth of the LSS is {optimal_solution.get_depth()}\")" + "## Using Other SAT solver" ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ - "You can also save more information on the optimization process.\n", - "Since the compiler may solve multiple problems with different height in the process, there are multiple sets of `.dimacs`, Kissat log, and solution files.\n", - "So the optional argument here are, e.g., `dimacs_file_name_prefix` instead of just the file name.\n", - "We'll append `_d=XX` in the file names to indicate the depth the file corresponds to.\n", - "Since we increased depth from 2 to 3 previously, we shall try to optimize from above the optimal value, starting from 4 this time." + "So far, we are using the [Z3 SMT solver](https://github.com/Z3Prover/z3) to do everything.\n", + "In our experience, it may be faster to generate an SAT problem with Z3 and solve it using other solvers, like Kissat.\n", + "For the user, it is very easy to change: just initiate the `LatticeSurgerySynthesizer` with the directory where Kissat is installed in your system." ] }, { "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "3" - ] - }, - "execution_count": 15, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "lss.optimize_depth(\n", - " 4,\n", - " dimacs_file_name_prefix='./cnot_dimacs',\n", - " sat_log_file_name_prefix='./cnot_sat',\n", - " result_file_name_prefix='./cnot_result',\n", - ").get_depth()" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "You should see a few new files poping up in the directory.\n", - "Notice that only the satisfiable problems will have the result file, while all problems have DIMACS and Kissat log.\n", - "In this example, the compiler finds that depth=4 and 3 are satisfiable, while depth=2 is not.\n", - "Thus, it concludes that the optimal depth is 3." - ] - }, - { - "attachments": {}, - "cell_type": "markdown", + "execution_count": 19, "metadata": {}, + "outputs": [], "source": [ - "Sometimes, we'd like to try permuting some ports.\n", - "We also provides a method `try_all_permutations` to explore all permutations of a given set of ports.\n", - "To demonstrate this involves a more complex specificed in a file `./maj.json`.\n", - "We let the compiler explore permuting the ports 2, 4, and 6.\n", - "There are two new optional arguments to notice:\n", - "- `parallelism`: the number of parallel process the compiler can use\n", - "- `shuffle`: default to `True`, meaning the order of issueing the compilation jobs corresponding to different permutations is random.\n", - "\n", - "Note that here we're using Z3 to solve SAT because we do not set `solver=\"kissat\"` and it defaults to Z3." + "las_synth = LatticeSurgerySynthesizer(solver=\"kissat\", kissat_dir=\"\")\n", + "# you need to add the kissat dir based on where kissat is on your computer" ] }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "(4, 2, 6): SAT\n", - "(2, 4, 6): SAT\n", - "(6, 2, 4): SAT\n", - "(4, 6, 2): SAT\n", - "(6, 4, 2): UNSAT\n", - "(2, 6, 4): UNSAT\n" + "Adding constraints time: 0.207474946975708\n", + "CNF generation time: 0.004982948303222656\n", + "c ---- [ banner ] ------------------------------------------------------------\n", + "c\n", + "c Kissat SAT Solver\n", + "c \n", + "c Copyright (c) 2021-2023 Armin Biere University of Freiburg\n", + "c Copyright (c) 2019-2021 Armin Biere Johannes Kepler University Linz\n", + "c \n", + "c Version 3.1.1 71caafb4d182ced9f76cef45b00f37cc598f2a37\n", + "c Apple clang version 15.0.0 (clang-1500.3.9.4) -W -Wall -O3 -DNDEBUG\n", + "c Sun May 12 13:03:10 PDT 2024 Darwin MacBook-Pro-2 23.4.0 arm64\n", + "c\n", + "c ---- [ parsing ] -----------------------------------------------------------\n", + "c\n", + "c opened and reading DIMACS file:\n", + "c\n", + "c cnot.dimacs\n", + "c\n", + "c parsed 'p cnf 462 2231' header\n", + "c closing input after reading 40739 bytes (40 KB)\n", + "c finished parsing after 0.00 seconds\n", + "c\n", + "c ---- [ options ] -----------------------------------------------------------\n", + "c\n", + "c --seed=916189 (different from default '0')\n", + "c\n", + "c ---- [ solving ] -----------------------------------------------------------\n", + "c\n", + "c seconds switched conflicts irredundant variables\n", + "c MB reductions redundant trail remaining\n", + "c level restarts binary glue\n", + "c\n", + "c * 0.00 2 0 0 0 0 0 0 614 1557 0% 0 402 87%\n", + "c { 0.00 2 0 0 0 0 0 0 614 1557 0% 0 402 87%\n", + "c i 0.00 2 22 0 0 0 38 23 623 1556 44% 2 398 86%\n", + "c i 0.00 2 22 0 0 0 39 23 623 1556 44% 2 397 86%\n", + "c } 0.00 2 22 0 0 0 39 23 623 1556 44% 2 397 86%\n", + "c 1 0.00 2 22 0 0 0 39 23 623 1556 44% 2 397 86%\n", + "c\n", + "c ---- [ result ] ------------------------------------------------------------\n", + "c\n", + "s SATISFIABLE\n", + "v 1 -2 -3 -4 5 -6 -7 -8 9 10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22\n", + "v 23 -24 -25 -26 -27 28 -29 -30 -31 -32 33 -34 35 -36 37 38 39 40 41 42 43 44\n", + "v 45 46 47 48 -49 50 -51 -52 -53 54 -55 -56 -57 -58 -59 60 -61 62 -63 64 65\n", + "v -66 -67 -68 69 -70 71 -72 -73 -74 75 -76 -77 -78 79 -80 -81 -82 -83 -84 85\n", + "v 86 -87 -88 -89 90 91 92 93 94 95 -96 -97 -98 99 100 101 -102 -103 -104 -105\n", + "v -106 -107 -108 109 110 111 112 113 -114 115 116 117 118 119 120 121 122 -123\n", + "v -124 -125 -126 127 128 129 130 131 132 133 134 135 -136 137 -138 139 -140\n", + "v 141 142 143 -144 145 -146 147 148 -149 -150 -151 152 153 154 -155 -156 -157\n", + "v 158 159 160 -161 -162 163 -164 165 166 -167 168 169 -170 171 172 173 174\n", + "v -175 176 177 178 179 180 -181 182 183 184 185 -186 187 188 189 190 191 192\n", + "v 193 -194 -195 196 197 198 -199 -200 201 202 -203 204 205 206 207 208 209\n", + "v -210 -211 212 213 214 215 216 217 218 219 -220 221 -222 -223 -224 225 226\n", + "v 227 228 -229 230 -231 232 -233 234 235 236 -237 -238 239 240 241 242 243\n", + "v -244 245 246 247 -248 249 -250 251 -252 -253 254 255 256 257 258 -259 260\n", + "v 261 262 263 -264 -265 266 267 268 -269 270 -271 272 273 -274 275 276 277 278\n", + "v 279 280 281 282 283 284 -285 286 -287 288 289 290 -291 292 293 -294 -295 296\n", + "v 297 -298 299 300 301 302 303 -304 305 -306 307 -308 309 -310 311 312 313\n", + "v -314 315 -316 317 318 319 -320 321 322 323 -324 -325 326 327 328 -329 330\n", + "v 331 332 333 334 335 336 -337 -338 339 340 341 -342 -343 344 345 346 347 348\n", + "v 349 350 351 352 353 354 355 -356 357 -358 359 -360 361 362 363 -364 365 -366\n", + "v 367 368 369 -370 371 -372 373 -374 -375 376 -377 378 -379 380 -381 382 -383\n", + "v -384 385 386 -387 388 389 390 391 392 393 394 395 -396 -397 398 -399 400\n", + "v -401 402 403 -404 405 406 407 408 -409 -410 411 412 413 414 415 -416 -417\n", + "v 418 -419 420 421 422 423 424 425 426 427 428 429 430 -431 432 433 434 435\n", + "v 436 437 438 439 -440 441 442 443 444 445 446 447 448 -449 450 451 452 453\n", + "v 454 455 456 457 -458 459 -460 461 462 0\n", + "c\n", + "c ---- [ profiling ] ---------------------------------------------------------\n", + "c\n", + "c 0.00 39.95 % parse\n", + "c 0.00 36.66 % search\n", + "c 0.00 34.35 % focused\n", + "c 0.00 0.00 % simplify\n", + "c =============================================\n", + "c 0.00 100.00 % total\n", + "c\n", + "c ---- [ statistics ] --------------------------------------------------------\n", + "c\n", + "c conflicts: 39 12268.01 per second\n", + "c decisions: 186 4.77 per conflict\n", + "c jumped_reasons: 1002 29 % propagations\n", + "c propagations: 3417 1074866 per second\n", + "c queue_decisions: 186 100 % decision\n", + "c random_decisions: 0 0 % decision\n", + "c random_sequences: 0 0 interval\n", + "c score_decisions: 0 0 % decision\n", + "c switched: 0 0 interval\n", + "c vivify_checks: 0 0 per vivify\n", + "c vivify_units: 0 0 % variables\n", + "c\n", + "c ---- [ resources ] ---------------------------------------------------------\n", + "c\n", + "c maximum-resident-set-size: 1828716544 bytes 1744 MB\n", + "c process-time: 0.00 seconds\n", + "c\n", + "c ---- [ shutting down ] -----------------------------------------------------\n", + "c\n", + "c exit 10\n", + "kissat runtime: 0.008579015731811523\n", + "kissat SAT!\n", + "Construct a Z3 SMT model and solve...\n", + "elapsed time: 0.021113s\n", + "Z3 SAT\n", + "Total solving time: 0.04399609565734863\n" ] - }, - { - "data": { - "text/plain": [ - "{'SAT': [(4, 6, 2), (2, 4, 6), (6, 2, 4), (4, 2, 6)],\n", - " 'UNSAT': [(2, 6, 4), (6, 4, 2)]}" - ] - }, - "execution_count": 16, - "metadata": {}, - "output_type": "execute_result" } ], "source": [ - "import json\n", - "with open(\"./maj.json\", \"r\") as f:\n", - " data = json.load(f)\n", - "lss = LatticeSurgeryCompiler(specification=data)\n", - "lss.try_all_permutations([2, 4, 6], parallelism=6)" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "You should see that some permutation yields solutions while others are unsatisfiable.\n", - "Note that this method is to be used with caution.\n", - "When we permute the ports without changing the stabilizers (which is what we're doing here), our package does not check whether it's functionally equivalent to the original setting.\n", - "In fact, permuting the ports like above makes the LSS comething else than what specified in `./maj.json`.\n", - "(We just want to demonstrate this class method somehow.)\n", - "It's up to the user's judgement whether it makes sense to permute ports." - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can also set values of variables to 'force' the solution in some ways.\n", - "For example, we notice that there is a pipe in the I direction from (0,0,2) to (1,0,2).\n", - "We can forbid it in two ways.\n", - "The first way is to provide a dictionary of arrays of values.\n", - "If we do not want to set that value, use -1 at the spot; otherwise use 0 or 1 to set the value.\n", - "Since we want to set an `ExistI` variable, the dimension of the array is 2x2x3 and we need to sat [0][0][2] element to 0.\n", - "With this method, we can set many variable values together.\n", - "\n", - "Also note that we can set the optional argument `specification` of `lss.solve()` to whatever problem we want to solve.\n", - "And since we're not initializing the `LatticeSurgeryCompiler` again, we're using Z3 for SAT still." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "# reload the CNOT example\n", - "specification = pickle.loads(b'\\x80\\x04\\x95\\xea\\x00\\x00\\x00\\x00\\x00\\x00\\x00}\\x94(\\x8c\\x05max_i\\x94K\\x02\\x8c\\x05max_j\\x94K\\x02\\x8c\\x05max_k\\x94K\\x03\\x8c\\x05ports\\x94]\\x94(}\\x94(\\x8c\\x08location\\x94]\\x94(K\\x01K\\x00K\\x00e\\x8c\\tdirection\\x94\\x8c\\x02+K\\x94\\x8c\\x11z_basis_direction\\x94\\x8c\\x01J\\x94u}\\x94(h\\x07]\\x94(K\\x00K\\x01K\\x00eh\\th\\nh\\x0bh\\x0cu}\\x94(h\\x07]\\x94(K\\x01K\\x00K\\x03eh\\t\\x8c\\x02-K\\x94h\\x0bh\\x0cu}\\x94(h\\x07]\\x94(K\\x00K\\x01K\\x03eh\\th\\x11h\\x0bh\\x0cue\\x8c\\x0bstabilizers\\x94]\\x94(\\x8c\\x04Z.Z.\\x94\\x8c\\x04.ZZZ\\x94\\x8c\\x04X.XX\\x94\\x8c\\x04.X.X\\x94eu.')\n", - "\n", - "arr_vals = [\n", - " [[-1, -1, 0], [-1, -1, -1]],\n", - " [[-1, -1, -1], [-1, -1, -1]],\n", - "]\n", - "result = lss.solve(specification=specification, given_arrs={\"ExistI\": arr_vals})\n", - "result.generate_gltf(output_file_name=\"./cnot_forbid_arr.gltf\")" + "result = las_synth.solve(\n", + " specification=input_dict,\n", + " print_detail=True,\n", + " dimacs_file_name=\"cnot\",\n", + " sat_log_file_name=\"cnot\"\n", + ")" ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ - "Comparing the most recently generated gltf with `cnot.gltf`, we can see the difference of forbidding that pipe in the I direction: the 'bridge' between the two 'pillars' is flipped in a way.\n", - "We can also set individual values, instead of array of values.\n", - "We do so by specify a list of dictioinaries, each one contains 1) the name of the array, 2) indices in the array, and 3) value to sat (0 or 1).\n", - "If both `given_arrs` and `given_vals` are given, the latter will overwrite the former.\n", - "For example, let us forbid the pipe in the J direction from (0,0,2) to (0,1,2).\n", - "Inspect the output gltf, you should see a difference with `./cnot_forbid_arr.gltf`." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [], - "source": [ - "result = lss.solve(specification=specification, given_vals=[\n", - " {\"array\": \"ExistJ\", \"indices\": [0,0,2], \"value\": 0},\n", - "])\n", - "result.generate_gltf(output_file_name=\"./cnot_forbid_val.gltf\")" + "We used a few optional arguments above.\n", + "`print_detail` will display the output of Kissat on the screen. \n", + "`dimacs_file_name` specifies where to store the SAT problem instance in the DIMACS format.\n", + "This instance is generated by Z3 and then solved by Kissat.\n", + "`sat_log_file_name` saves the output of Kissat, which is basically what you have seen as the output (from `c ---- [ banner ]` to `c exit 10`)." ] } ], @@ -840,7 +637,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.11.5" + "version": "3.8.19" } }, "nbformat": 4, diff --git a/glue/lattice_surgery/lassynth/__init__.py b/glue/lattice_surgery/lassynth/__init__.py new file mode 100644 index 000000000..9640f285c --- /dev/null +++ b/glue/lattice_surgery/lassynth/__init__.py @@ -0,0 +1,2 @@ +from .lattice_surgery_synthesis import LatticeSurgerySynthesizer +from .lattice_surgery_synthesis import LatticeSurgerySolution diff --git a/glue/lattice_surgery/lassynth/lattice_surgery_synthesis.py b/glue/lattice_surgery/lassynth/lattice_surgery_synthesis.py new file mode 100644 index 000000000..fe83bb23f --- /dev/null +++ b/glue/lattice_surgery/lassynth/lattice_surgery_synthesis.py @@ -0,0 +1,590 @@ +"""Two wrapper classes, rewrite passes, and translators.""" + +import functools +import itertools +import json +import time +import multiprocessing +import random +import networkx +from typing import Any, Literal, Mapping, Optional, Sequence +from lassynth.rewrite_passes.attach_fixups import attach_fixups +from lassynth.rewrite_passes.color_z import color_z +from lassynth.rewrite_passes.remove_unconnected import remove_unconnected +from lassynth.sat_synthesis.lattice_surgery_sat import LatticeSurgerySAT +from lassynth.tools.verify_stabilizers import verify_stabilizers +from lassynth.translators.gltf_generator import gltf_generator +from lassynth.translators.textfig_generator import textfig_generator +from lassynth.translators.zx_grid_graph import ZXGridGraph +from lassynth.translators.networkx_generator import networkx_generator + + +def check_lasre(lasre: Mapping[str, Any]) -> None: + """check aspects of LaSRe other than SMT constraints, i.e., data layout.""" + if "n_i" not in lasre: + raise ValueError( + f"upper bound of I dimension, `n_i`, is missing in lasre.") + if lasre["n_i"] <= 0: + raise ValueError("n_i <= 0.") + if "n_j" not in lasre: + raise ValueError( + f"upper bound of J dimension, `n_j`, is missing in lasre.") + if lasre["n_j"] <= 0: + raise ValueError("n_j <= 0.") + if "n_k" not in lasre: + raise ValueError( + f"upper bound of K dimension, `n_k`, is missing in lasre.") + if lasre["n_k"] <= 0: + raise ValueError("n_k <= 0.") + if "n_p" not in lasre: + raise ValueError(f"number of ports, `n_p`, is missing in lasre.") + if lasre["n_p"] <= 0: + raise ValueError("n_p <= 0.") + if "n_s" not in lasre: + raise ValueError(f"number of stabilizers, `n_s`, is missing in lasre.") + if lasre["n_s"] < 0: + raise ValueError("n_s < 0.") + if lasre["n_s"] == 0: + print("no stabilizer!") + + if "ports" not in lasre: + raise ValueError(f"`ports` is missing in lasre.") + if len(lasre["ports"]) != lasre["n_p"]: + raise ValueError("number of ports in `ports` is different from `n_p`.") + for port in lasre["ports"]: + if "i" not in port: + raise ValueError(f"location `i` missing from port {port}.") + if port["i"] not in range(lasre["n_i"]): + raise ValueError(f"i out of range in port {port}.") + if "j" not in port: + raise ValueError(f"location `j` missing from port {port}.") + if port["j"] not in range(lasre["n_j"]): + raise ValueError(f"j out of range in port {port}.") + if "k" not in port: + raise ValueError(f"location `k` missing from port {port}.") + if port["k"] not in range(lasre["n_k"]): + raise ValueError(f"k out of range in port {port}.") + if "d" not in port: + raise ValueError(f"direction `d` missing from port {port}.") + if port["d"] not in ["I", "J", "K"]: + raise ValueError(f"direction not I, J, or K in port {port}.") + if "e" not in port: + raise ValueError(f"open end `e` missing from port {port}.") + if port["e"] not in ["-", "+"]: + raise ValueError(f"open end not - or + in port {port}.") + if "c" not in port: + raise ValueError(f"color `c` missing from port {port}.") + if port["c"] not in [0, 1]: + raise ValueError(f"color not 0 or 1 in port {port}.") + + if "stabs" not in lasre: + raise ValueError(f"`stabs` is missing in lasre.") + if len(lasre["stabs"]) != lasre["n_s"]: + raise ValueError("number of stabs in `stabs` is different from `n_s`.") + for stab in lasre["stabs"]: + if len(stab) != lasre["n_p"]: + raise ValueError("number of boundary corrsurf is not `n_p`.") + for i, corrsurf in enumerate(stab): + for (k, v) in corrsurf.items(): + if lasre["ports"][i]["d"] == "I" and k not in ["IJ", "IK"]: + raise ValueError(f"stabs[{i}] key invalid {stab}.") + if lasre["ports"][i]["d"] == "J" and k not in ["JI", "JK"]: + raise ValueError(f"stabs[{i}] key invalid {stab}.") + if lasre["ports"][i]["d"] == "K" and k not in ["KI", "KJ"]: + raise ValueError(f"stabs[{i}] key invalid {stab}.") + if v not in [0, 1]: + raise ValueError(f"stabs[{i}] value not 0 or 1 {stab}.") + + port_cubes = [] + for p in lasre["ports"]: + # if e=-, (i,j,k); otherwise, +1 in the proper direction + if p["e"] == "-": + port_cubes.append((p["i"], p["j"], p["k"])) + elif p["d"] == "I": + port_cubes.append((p["i"] + 1, p["j"], p["k"])) + elif p["d"] == "J": + port_cubes.append((p["i"], p["j"] + 1, p["k"])) + elif p["d"] == "K": + port_cubes.append((p["i"], p["j"], p["k"] + 1)) + lasre["port_cubes"] = port_cubes + + if "optional" not in lasre: + lasre["optional"] = {} + + for key in [ + "NodeY", + "ExistI", + "ExistJ", + "ExistK", + "ColorI", + "ColorJ", + ]: + if key not in lasre: + raise ValueError(f"`{key}` missing from lasre.") + if len(lasre[key]) != lasre["n_i"]: + raise ValueError(f"dimension of {key} is wrong.") + for tmp in lasre[key]: + if len(tmp) != lasre["n_j"]: + raise ValueError(f"dimension of {key} is wrong.") + for tmptmp in tmp: + if len(tmptmp) != lasre["n_k"]: + raise ValueError(f"dimension of {key} is wrong.") + + if lasre["n_s"] > 0: + for key in [ + "CorrIJ", + "CorrIK", + "CorrJI", + "CorrJK", + "CorrKI", + "CorrKJ", + ]: + if key not in lasre: + raise ValueError(f"`{key}` missing from lasre.") + if len(lasre[key]) != lasre["n_s"]: + raise ValueError(f"dimension of {key} is wrong.") + for tmp in lasre[key]: + if len(tmp) != lasre["n_i"]: + raise ValueError(f"dimension of {key} is wrong.") + for tmptmp in tmp: + if len(tmptmp) != lasre["n_j"]: + raise ValueError(f"dimension of {key} is wrong.") + for tmptmptmp in tmptmp: + if len(tmptmptmp) != lasre["n_k"]: + raise ValueError(f"dimension of {key} is wrong.") + + +class LatticeSurgerySolution: + """A class for the result of synthesizer lattice surgery subroutine. + + It internally saves an LaSRe (Lattice Surgery Subroutine Representation) + and we can apply rewrite passes to it, or use translators to derive + other formats of the LaS solution + """ + + def __init__( + self, + lasre: Mapping[str, Any], + ) -> None: + """initialization for LatticeSurgerySubroutine + + Args: + lasre (Mapping[str, Any]): LaSRe + """ + check_lasre(lasre) + self.lasre = lasre + + def get_depth(self) -> int: + """get the depth/height of the LaS in LaSRe. + + Returns: + int: depth/height of the LaS in LaSRe + """ + return self.lasre["n_k"] + + def after_removing_disconnected_pieces(self): + """remove_unconnected.""" + return LatticeSurgerySolution(lasre=remove_unconnected(self.lasre)) + + def after_color_k_pipes(self): + """coloring K pipes.""" + return LatticeSurgerySolution(lasre=color_z(self.lasre)) + + def after_default_optimizations(self): + """default optimizations: remove unconnected, and then color K pipes.""" + solution = LatticeSurgerySolution(lasre=remove_unconnected(self.lasre)) + solution = LatticeSurgerySolution(lasre=color_z(solution.lasre)) + return solution + + def after_t_factory_default_optimizations(self): + """default optimization for T-factories.""" + solution = LatticeSurgerySolution(lasre=remove_unconnected(self.lasre)) + solution = LatticeSurgerySolution(lasre=color_z(solution.lasre)) + solution = LatticeSurgerySolution(lasre=attach_fixups(solution.lasre)) + return solution + + def save_lasre(self, file_name: str) -> None: + """save the current LaSRe to a file. + + Args: + file_name (str): file name including extension to save the LaSRe + """ + with open(file_name, "w") as f: + json.dump(self.lasre, f) + + def to_3d_model_gltf(self, + output_file_name: str, + stabilizer: int = -1, + tube_len: float = 2.0, + no_color_z: bool = False, + attach_axes: bool = False, + rm_dir: Optional[str] = None) -> None: + """generate gltf file (for 3D modelling). + + Args: + output_file_name (str): file name including extension to save gltf + stabilizer (int, optional): Defaults to -1 meaning do not draw + correlation surfaces. If the value is in [0, n_s), + the correlation surfaces corresponding to that stabilizer + are drawn and faces in one of the directions are revealed + to unveil the correlation surfaces. + tube_len (float, optional): Length of the pipe comapred to + the cube. Defaults to 2.0. + no_color_z (bool, optional): Do not color the K pipes. + Defaults to False. + attach_axes (bool, optional): attach IJK axes. Defaults to False. + If attached, the color coding is I->red, J->green, K->blue. + rm_dir (str, optional): the (+|-)(I|J|K) faces to remove. + Intended to reveal correlation surfaces. Default to None. + """ + gltf = gltf_generator( + self.lasre, + stabilizer=stabilizer, + tube_len=tube_len, + no_color_z=no_color_z, + attach_axes=attach_axes, + rm_dir=rm_dir if rm_dir else (":+J" if stabilizer >= 0 else None), + ) + with open(output_file_name, "w") as f: + json.dump(gltf, f) + + def to_zigxag_url( + self, + io_spec: Optional[Sequence[str]] = None, + ) -> str: + """generate a link that leads to a ZigXag figure. + + Args: + io_spec (Optional[Sequence[str]], optional): Specify whether + each port is an input or an output. Length must be the same + with the number of ports. Defaults to None, which means + all ports are outputs. + + Returns: + str: the ZigXag link + """ + zxgridgraph = ZXGridGraph(self.lasre) + return zxgridgraph.to_zigxag_url(io_spec=io_spec) + + def to_text_diagram(self) -> str: + """generate the text figure of LaS time slices. + + Returns: + str: text figure of the LaS + """ + return textfig_generator(self.lasre) + + def to_networkx_graph(self) -> networkx.Graph: + """generate a annotated networkx.Graph correponding to the LaS. + + Returns: + networkx.Graph: + """ + return networkx_generator(self.lasre) + + def verify_stabilizers_stimzx(self, + specification: Mapping[str, Any], + print_stabilizers: bool = False) -> bool: + """verify the stabilizer of the LaS. + + Use StimZX to deduce the stabilizers from the annotated networkx graph. + Then use Stim to ensure that this set of stabilizers and the set of + stabilizers specified in the input are equivalent. + + Args: + specification (Mapping[str, Any]): the LaS specification to verify + the current solution against. + print_stabilizers (bool, optional): If True, print the two sets of + stabilizers. Defaults to False. + + Returns: + bool: True if the two sets are equivalent; otherwise False. + """ + paulistrings = [ + paulistring.replace(".", "_") + for paulistring in specification["stabilizers"] + ] + return verify_stabilizers( + paulistrings, + self.to_networkx_graph(), + print_stabilizers=print_stabilizers, + ) + + +class LatticeSurgerySynthesizer: + """A class to synthesize LaS.""" + + def __init__( + self, + solver: Literal["kissat", "z3"] = "z3", + kissat_dir: Optional[str] = None, + ) -> None: + """initialize. + + Args: + solver (Literal["kissat", "z3"], optional): the solver to use. + Defaults to "z3". "kissat" is recommended. + kissat_dir (Optional[str], optional): directory of the kissat + executable. Defaults to None. + """ + self.solver = solver + self.kissat_dir = kissat_dir + + def solve( + self, + specification: Mapping[str, Any], + given_arrs: Optional[Mapping[str, Any]] = None, + given_vals: Optional[Sequence[Mapping[str, Any]]] = None, + print_detail: bool = False, + dimacs_file_name: Optional[str] = None, + sat_log_file_name: Optional[str] = None, + ) -> Optional[LatticeSurgerySolution]: + """solve an LaS synthesis problem. + + Args: + specification (Mapping[str, Any]): the LaS specification to solve. + given_arrs (Optional[Mapping[str, Any]], optional): given array of + known values to plug in. Defaults to None. + given_vals (Optional[Sequence[Mapping[str, Any]]], optional): given + known values to plug in. Defaults to None. Format should be + a sequence of dicts. Each one contains three fields: "array", + the name of the array, e.g., "ExistI"; "indices", a sequence of + the indices, e.g., [0, 0, 0]; and "value", 0 or 1. + print_detail (bool, optional): whether to print details in + SAT solving. Defaults to False. + dimacs_file_name (Optional[str], optional): file to save the + DIMACS. Defaults to None. + sat_log_file_name (Optional[str], optional): file to save the + SAT solver log. Defaults to None. + + Returns: + Optional[LatticeSurgerySubroutine]: if the problem is + unsatisfiable, this is None; otherwise, a + LatticeSurgerySolution initialized by the compiled result. + """ + start_time = time.time() + sat_synthesis = LatticeSurgerySAT( + input_dict=specification, + given_arrs=given_arrs, + given_vals=given_vals, + ) + if print_detail: + print(f"Adding constraints time: {time.time() - start_time}") + + start_time = time.time() + if self.solver == "z3": + if_sat = sat_synthesis.check_z3(print_progress=print_detail) + else: + if_sat = sat_synthesis.check_kissat( + dimacs_file_name=dimacs_file_name, + sat_log_file_name=sat_log_file_name, + print_progress=print_detail, + kissat_dir=self.kissat_dir, + ) + if print_detail: + print(f"Total solving time: {time.time() - start_time}") + + if if_sat: + solver_result = sat_synthesis.get_result() + return LatticeSurgerySolution(lasre=solver_result) + else: + return None + + def optimize_depth( + self, + specification: Mapping[str, Any], + start_depth: Optional[int] = None, + print_detail: bool = False, + dimacs_file_name_prefix: Optional[str] = None, + sat_log_file_name_prefix: Optional[str] = None, + ) -> LatticeSurgerySolution: + """find the optimal solution in terms of depth/height of the LaS. + + Args: + specification (Mapping[str, Any]): the LaS specification to solve. + start_depth (int, optional): starting depth of the exploration. If not + provided, use the depth given in the specification + print_detail (bool, optional): whether to print details in SAT solving. + Defaults to False. + dimacs_file_name_prefix (Optional[str], optional): file prefix to save + the DIMACS. The full file name will contain the specific depth + after this prefix. Defaults to None. + sat_log_file_name_prefix (Optional[str], optional): file prefix to save + the SAT log. The full file name will contain the specific depth + after this prefix. Defaults to None. + result_file_name_prefix (Optional[str], optional): file prefix to save + the variable assignments. The full file name will contain the + specific depth after this prefix. Defaults to None. + post_optimization (str, optional): optimization to perform when + initializing the LatticeSurgerySubroutine object for the result. + Defaults to "default". + + Raises: + ValueError: starting depth is too low. + + Returns: + LatticeSurgerySolution: compiled result with the optimal depth. + """ + self.specification = dict(specification) + if start_depth is None: + depth = self.specification["max_k"] + else: + depth = int(start_depth) + if depth < 2: + raise ValueError("depth too low.") + + checked_depth = {} + while True: + # the ports on the top floor will still be on the top floor when we + # increase the height. This is an assumption. Adapt to your case. + for port in self.specification["ports"]: + if port["location"][2] == self.specification["max_k"]: + port["location"][2] = depth + self.specification["max_k"] = depth + + result = self.solve( + specification=self.specification, + print_detail=print_detail, + dimacs_file_name=dimacs_file_name_prefix + + f"_d={depth}" if dimacs_file_name_prefix else None, + sat_log_file_name=sat_log_file_name_prefix + + f"_d={depth}" if sat_log_file_name_prefix else None, + ) + if result is None: + checked_depth[str(depth)] = "UNSAT" + if str(depth + 1) in checked_depth: + # since this depth leads to UNSAT, we need to increase + # the depth, but if depth+1 is already checked, we can stop + break + else: + depth += 1 + else: + checked_depth[str(depth)] = "SAT" + self.sat_result = LatticeSurgerySolution(lasre=result.lasre) + if str(depth - 1) in checked_depth: + # since this depth leads to SAT, we need to try decreasing + # the depth, but if depth-1 is already checked, we can stop + break + else: + depth -= 1 + + return self.sat_result + + def try_one_permutation( + self, + perm: Sequence[int], + specification: Mapping[str, Any], + print_detail: bool = False, + dimacs_file_name_prefix: Optional[str] = None, + sat_log_file_name_prefix: Optional[str] = None, + ) -> Optional[LatticeSurgerySolution]: + """check if the problem is satisfiable given a port permutation. + + Args: + specification (Mapping[str, Any]): the LaS specification to solve. + perm (Sequence[int]): the given permutation, which is an integer + tuple of length n (n being the number of ports permuted). + print_detail (bool, optional): whether to print details in + SAT solving. Defaults to False. + dimacs_file_name_prefix (Optional[str], optional): file prefix + to save the DIMACS. The full file name will contain the + specific permutation after this prefix. Defaults to None. + sat_log_file_name_prefix (Optional[str], optional): file prefix + to save the SAT log. The full file name will contain the + specific permutation after this prefix. Defaults to None. + + Returns: + Optional[LatticeSurgerySubroutine]: if the problem is + unsatisfiable, this is None; otherwise, a + LatticeSurgerySolution initialized by the compiled result. + """ + + # say `perm` is [0,3,2], then `original` is in order, i.e., [0,2,3] + # the full permutation is 0,1,2,3 -> 0,1,3,2 + original = sorted(perm) + this_spec = dict(specification) + new_ports = [] + for p, port in enumerate(specification["ports"]): + if p not in perm: + # the p-th port is not involved in `perm`, e.g., 1 is unchanged + new_ports.append(port) + + else: + # after the permutation, the index of the p-th port in + # specification is the k-th port in `perm` where k is the place + # of p in `original`. In this example, when p=0 and 1, nothing + # changed. When p=2, we find `place` to be 1, and perm[place]=3 + # so we attach port_3. When p=3, we end up attach port_2 + place = original.index(p) + new_ports.append(specification["ports"][perm[place]]) + this_spec["ports"] = new_ports + + result = self.solve( + specification=this_spec, + print_detail=print_detail, + dimacs_file_name=dimacs_file_name_prefix + "_" + + perm.__repr__().replace(" ", "") + if dimacs_file_name_prefix else None, + sat_log_file_name=sat_log_file_name_prefix + "_" + + perm.__repr__().replace(" ", "") + if sat_log_file_name_prefix else None, + ) + print(f"{perm}: {'SAT' if result else 'UNSAT'}") + return result + + def solve_all_port_permutations( + self, + permute_ports: Sequence[int], + parallelism: int = 1, + shuffle: bool = True, + **kwargs, + ) -> Mapping[str, Sequence[Sequence[int]]]: + """try all the permutations of given ports, which ones are satisfiable. + + Note that we do not check that the LaS after permuting the ports (we do + not permute the stabilizers accordingly) is functionally equivalent. + The user should use this method based on their judgement. Also, the + number of permutations scales exponentially with the number of ports + to permute, so this method can easily take an immense amount of time. + + Args: + permute_ports (Sequence[int]): the indices of ports to permute + parallelism (int, optional): number of parallel process. Each one + try one permutation. A New proess starts when an old one + finishes. Defaults to 1. + shuffle (bool, optional): whether using a random order to start the + processes. Defaults to True. + **kwargs: other arguments to `try_one_permutation`. + + Returns: + Mapping[str, Sequence[Sequence[int]]]: a dict with two keys. + "SAT": [.] a list containing all the satisfiable permutations; + "UNSAT": [.] all the unsatisfiable permutations. + """ + perms = list(itertools.permutations(permute_ports)) + if shuffle: + random.shuffle(perms) + + pool = multiprocessing.Pool(parallelism) + # issue the job one by one (chuck=1) + results = pool.map( + functools.partial( + self.try_one_permutation, + **kwargs, + ), + perms, + chunksize=1, + ) + + sat_perms = [] + unsat_perms = [] + for p, result in enumerate(results): + if result is None: + unsat_perms.append(perms[p]) + else: + sat_perms.append(perms[p]) + + return { + "SAT": sat_perms, + "UNSAT": unsat_perms, + } diff --git a/glue/lattice_surgery/olssco/rewrite_passes/__init__.py b/glue/lattice_surgery/lassynth/rewrite_passes/__init__.py similarity index 100% rename from glue/lattice_surgery/olssco/rewrite_passes/__init__.py rename to glue/lattice_surgery/lassynth/rewrite_passes/__init__.py diff --git a/glue/lattice_surgery/lassynth/rewrite_passes/attach_fixups.py b/glue/lattice_surgery/lassynth/rewrite_passes/attach_fixups.py new file mode 100644 index 000000000..cad628f34 --- /dev/null +++ b/glue/lattice_surgery/lassynth/rewrite_passes/attach_fixups.py @@ -0,0 +1,86 @@ +"""assuming all T injections requiring fixup are on the top floor. +The output is also on the top floor""" + +from typing import Mapping, Any + + +def attach_fixups(lasre: Mapping[str, Any]) -> Mapping[str, Any]: + n_s = lasre["n_s"] + n_i = lasre["n_i"] + n_j = lasre["n_j"] + n_k = lasre["n_k"] + + fixup_locs = [] + for p in lasre["optional"]["top_fixups"]: + fixup_locs.append((lasre["ports"][p]["i"], lasre["ports"][p]["j"])) + + lasre["n_k"] += 2 + # we add two layers on the top. The lower layer will contain fixups dressed + # as Y cubes that is connecting downwards. The upper layer will contain no + # new cubes. This corresponds to waiting the machine to apply the fixups + # because there is a finite interaction time from the machine knows whether + # the injection is T or T^dagger to apply the fixups. + for i in range(n_i): + for j in range(n_j): + if (i, j) in fixup_locs: + lasre["NodeY"][i][j].append(1) # fixup dressed as Y cubes + lasre["ExistK"][i][j][n_k - 1] = 1 # connect fixup downwards + else: + lasre["NodeY"][i][j].append(0) # no fixup + lasre["ExistK"][i][j][n_k - 1] = 0 + lasre["NodeY"][i][j].append(0) # the upper layer is empty + + # do not add any new pipes in the added layer + for arr in ["ExistI", "ExistJ", "ExistK"]: + lasre[arr][i][j].append(0) + lasre[arr][i][j].append(0) + for arr in ["ColorI", "ColorJ", "ColorKM", "ColorKP"]: + lasre[arr][i][j].append(-1) + lasre[arr][i][j].append(-1) + for s in range(n_s): + for arr in [ + "CorrIJ", "CorrIK", "CorrJK", "CorrJI", "CorrKI", + "CorrKJ" + ]: + lasre[arr][s][i][j].append(0) + lasre[arr][s][i][j].append(0) + + # the output ports need to be extended in the two added layers + for port in lasre["ports"]: + if "f" in port and port["f"] == "output": + ii, jj = port["i"], port["j"] + lasre["ExistK"][ii][jj][n_k - 1] = 1 + lasre["ExistK"][ii][jj][n_k] = 1 + lasre["ExistK"][ii][jj][n_k + 1] = 1 + lasre["ColorKM"][ii][jj][n_k] = lasre["ColorKP"][ii][jj][n_k - 1] + lasre["ColorKM"][ii][jj][n_k + 1] = lasre["ColorKM"][ii][jj][n_k] + lasre["ColorKP"][ii][jj][n_k] = lasre["ColorKM"][ii][jj][n_k] + lasre["ColorKP"][ii][jj][n_k + 1] = lasre["ColorKP"][ii][jj][n_k] + for s in range(n_s): + lasre["CorrKI"][s][ii][jj][n_k] = lasre["CorrKI"][s][ii][jj][ + n_k - 1] + lasre["CorrKI"][s][ii][jj][n_k + + 1] = lasre["CorrKI"][s][ii][jj][n_k] + lasre["CorrKJ"][s][ii][jj][n_k] = lasre["CorrKJ"][s][ii][jj][ + n_k - 1] + lasre["CorrKJ"][s][ii][jj][n_k + + 1] = lasre["CorrKJ"][s][ii][jj][n_k] + port["k"] += 2 + new_cubes = [] + for c in lasre["port_cubes"]: + if c[0] == port["i"] and c[1] == port["j"]: + new_cubes.append((c[0], c[1], port["k"] + 1)) + else: + new_cubes.append(c) + lasre["port_cubes"] = new_cubes + + t_injections = [] + for port in lasre["ports"]: + if port["f"] == "T": + if port["e"] == "+": + t_injections.append([port["i"], port["j"], port["k"] + 1]) + else: + t_injections.append([port["i"], port["j"], port["k"]]) + lasre["optional"]["t_injections"] = t_injections + + return lasre diff --git a/glue/lattice_surgery/lassynth/rewrite_passes/color_z.py b/glue/lattice_surgery/lassynth/rewrite_passes/color_z.py new file mode 100644 index 000000000..7c0c956db --- /dev/null +++ b/glue/lattice_surgery/lassynth/rewrite_passes/color_z.py @@ -0,0 +1,210 @@ +"""We do not have ColorZ from the SAT/SMT. Now we color the Z-pipes.""" + +from typing import Sequence, Mapping, Any, Union, Tuple + + +def if_uncolorK(n_i: int, n_j: int, n_k: int, + ExistK: Sequence[Sequence[Sequence[int]]], + ColorKP: Sequence[Sequence[Sequence[int]]], + ColorKM: Sequence[Sequence[Sequence[int]]]) -> bool: + """return whether there are uncolored K-pipes""" + for i in range(n_i): + for j in range(n_j): + for k in range(n_k): + if ExistK[i][j][k] and (ColorKP[i][j][k] == -1 + or ColorKM[i][j][k] == -1): + return True + return False + + +def in_bound(n_i: int, n_j: int, n_k: int, i: int, j: int, k: int) -> bool: + if i in range(n_i) and j in range(n_j) and k in range(n_k): + return True + return False + + +def propogate_IJcolor(n_i: int, n_j: int, n_k: int, + ExistI: Sequence[Sequence[Sequence[int]]], + ExistJ: Sequence[Sequence[Sequence[int]]], + ExistK: Sequence[Sequence[Sequence[int]]], + ColorI: Sequence[Sequence[Sequence[int]]], + ColorJ: Sequence[Sequence[Sequence[int]]], + ColorKP: Sequence[Sequence[Sequence[int]]], + ColorKM: Sequence[Sequence[Sequence[int]]]) -> None: + """propagate the color of I- and J-pipes to their neighbor K-pipes.""" + + for i in range(n_i): + for j in range(n_j): + for k in range(n_k): + if ExistK[i][j][k]: + # 4 possible neighbor I/J pipe for the minus end of K-pipe + if in_bound(n_i, n_j, n_k, i - 1, j, + k) and ExistI[i - 1][j][k]: + ColorKM[i][j][k] = 1 - ColorI[i - 1][j][k] + if ExistI[i][j][k]: + ColorKM[i][j][k] = 1 - ColorI[i][j][k] + if in_bound(n_i, n_j, n_k, i, j - 1, + k) and ExistJ[i][j - 1][k]: + ColorKM[i][j][k] = 1 - ColorJ[i][j - 1][k] + if ExistJ[i][j][k]: + ColorKM[i][j][k] = 1 - ColorJ[i][j][k] + + # 4 possible neighbor I/J pipe for the plus end of K-pipe + if (in_bound(n_i, n_j, n_k, i - 1, j, k + 1) + and ExistI[i - 1][j][k + 1]): + ColorKP[i][j][k] = 1 - ColorI[i - 1][j][k + 1] + if in_bound(n_i, n_j, n_k, i, j, + k + 1) and ExistI[i][j][k + 1]: + ColorKP[i][j][k] = 1 - ColorI[i][j][k + 1] + if (in_bound(n_i, n_j, n_k, i, j - 1, k + 1) + and ExistJ[i][j - 1][k + 1]): + ColorKP[i][j][k] = 1 - ColorJ[i][j - 1][k + 1] + if in_bound(n_i, n_j, n_k, i, j, + k + 1) and ExistJ[i][j][k + 1]: + ColorKP[i][j][k] = 1 - ColorJ[i][j][k + 1] + + +def propogate_Kcolor(n_i: int, n_j: int, n_k: int, + ExistK: Sequence[Sequence[Sequence[int]]], + ColorKP: Sequence[Sequence[Sequence[int]]], + ColorKM: Sequence[Sequence[Sequence[int]]], + NodeY: Sequence[Sequence[Sequence[int]]]) -> bool: + """propagate color from colored K-pipes to uncolored K-pipes. + If no new color can be assigned, return False; otherwise, return True.""" + + did_something = False + for i in range(n_i): + for j in range(n_j): + for k in range(n_k): + if ExistK[i][j][k]: + # consider propagate color from below + if in_bound( + n_i, n_j, n_k, i, j, k - + 1) and ExistK[i][j][k - 1] and NodeY[i][j][k - + 1] == 0: + if ColorKP[i][j][k - + 1] > -1 and ColorKM[i][j][k] == -1: + ColorKM[i][j][k] = ColorKP[i][j][k - 1] + did_something = True + # consider propagate color from above + if in_bound( + n_i, n_j, n_k, i, j, k + + 1) and ExistK[i][j][k + 1] and NodeY[i][j][k + + 1] == 0: + if ColorKM[i][j][k + + 1] > -1 and ColorKP[i][j][k] == -1: + ColorKP[i][j][k] = ColorKM[i][j][k + 1] + did_something = True + + # if K-pipe connects a Y Cube, two ends can be colored same + if (NodeY[i][j][k] and ColorKM[i][j][k] == -1 + and ColorKP[i][j][k] > -1): + ColorKM[i][j][k] = ColorKP[i][j][k] + did_something = True + if (in_bound(n_i, n_j, n_k, i, j, k + 1) + and NodeY[i][j][k + 1] and ColorKM[i][j][k] > -1 + and ColorKP[i][j][k] == -1): + ColorKP[i][j][k] = ColorKM[i][j][k] + did_something = True + return did_something + + +def assign_Kcolor(n_i: int, n_j: int, n_k: int, + ExistK: Sequence[Sequence[Sequence[int]]], + ColorKP: Sequence[Sequence[Sequence[int]]], + ColorKM: Sequence[Sequence[Sequence[int]]], + NodeY: Sequence[Sequence[Sequence[int]]]) -> None: + """when no color can be deducted by propagating from other K-pipes, we + assign some color variables at will. Then, we can continue to propagate.""" + + # assign a color by letting the two ends of a K-pipe to be the same + for i in range(n_i): + for j in range(n_j): + for k in range(n_k): + if ExistK[i][j][k]: + if ColorKM[i][j][k] > -1 and ColorKP[i][j][k] == -1: + ColorKP[i][j][k] = ColorKM[i][j][k] + break + # For K-pipes that have no color at both ends and connects a Y-cube + for i in range(n_i): + for j in range(n_j): + for k in range(n_k): + if ExistK[i][j][k]: + if NodeY[i][j][k] and ColorKM[i][j][k] == -1: + ColorKM[i][j][k] = 0 + break + if (in_bound(n_i, n_j, n_k, i, j, k + 1) + and NodeY[i][j][k + 1] and ColorKP[i][j][k] == -1): + ColorKP[i][j][k] = 0 + break + + +def color_ports(ports: Sequence[Mapping[str, Union[str, int]]], + ColorKP: Sequence[Sequence[Sequence[int]]], + ColorKM: Sequence[Sequence[Sequence[int]]]) -> None: + for port in ports: + if port['d'] == 'K': + if port['e'] == '+': + ColorKP[port['i']][port['j']][port['k']] = port['c'] + else: + ColorKM[port['i']][port['j']][port['k']] = port['c'] + + +def color_kp_km( + n_i: int, + n_j: int, + n_k: int, + ExistI: Sequence[Sequence[Sequence[int]]], + ExistJ: Sequence[Sequence[Sequence[int]]], + ExistK: Sequence[Sequence[Sequence[int]]], + ColorI: Sequence[Sequence[Sequence[int]]], + ColorJ: Sequence[Sequence[Sequence[int]]], + ports: Sequence[Mapping[str, Union[str, int]]], + NodeY: Sequence[Sequence[Sequence[int]]], +) -> Tuple[Sequence[Sequence[Sequence[int]]], + Sequence[Sequence[Sequence[int]]]]: + ColorKP = [[[-1 for _ in range(n_k)] for _ in range(n_j)] + for _ in range(n_i)] + ColorKM = [[[-1 for _ in range(n_k)] for _ in range(n_j)] + for _ in range(n_i)] + + # at ports, the color follows from the port configuration + color_ports(ports, ColorKP, ColorKM) + + # propogate the color of I-pipes and J-pipes to their neighboring K-pipes + propogate_IJcolor(n_i, n_j, n_k, ExistI, ExistJ, ExistK, ColorI, ColorJ, + ColorKP, ColorKM) + + # the rest of the K-pipes are only neighboring other K-pipes. Until all of + # them are colored, we propagate colors of the existing K-pipes. If at one + # point, nothing can be implied via propagation, we assign a color at will + # and continue. Because of the domain wall operation, we can do this. + while if_uncolorK(n_i, n_j, n_k, ExistK, ColorKP, ColorKM): + if not propogate_Kcolor(n_i, n_j, n_k, ExistK, ColorKP, ColorKM, + NodeY): + assign_Kcolor(n_i, n_j, n_k, ExistK, ColorKP, ColorKM, NodeY) + return ColorKP, ColorKM + + +def color_z(lasre: Mapping[str, Any]) -> Mapping[str, Any]: + n_i, n_j, n_k = ( + lasre['n_i'], + lasre['n_j'], + lasre['n_k'], + ) + ExistI, ColorI, ExistJ, ColorJ, ExistK = ( + lasre['ExistI'], + lasre['ColorI'], + lasre['ExistJ'], + lasre['ColorJ'], + lasre['ExistK'], + ) + NodeY = lasre['NodeY'] + ports = lasre['ports'] + + # for a K-pipe (i,j,k)-(i,j,k+1), ColorKP (plus) is its color at (i,j,k+1) + # and ColorKM (minus) is its color at (i,j,k) + lasre['ColorKP'], lasre['ColorKM'] = color_kp_km(n_i, n_j, n_k, ExistI, + ExistJ, ExistK, ColorI, + ColorJ, ports, NodeY) + return lasre diff --git a/glue/lattice_surgery/lassynth/rewrite_passes/remove_unconnected.py b/glue/lattice_surgery/lassynth/rewrite_passes/remove_unconnected.py new file mode 100644 index 000000000..e983b0092 --- /dev/null +++ b/glue/lattice_surgery/lassynth/rewrite_passes/remove_unconnected.py @@ -0,0 +1,152 @@ +"""In the generated LaS, there can be some 'floating donuts' not connecting to +any ports. These objects won't affect the function of the LaS. We remove them. +""" + +from typing import Mapping, Any, Sequence, Union, Tuple + + +def check_cubes( + n_i: int, n_j: int, n_k: int, ExistI: Sequence[Sequence[Sequence[int]]], + ExistJ: Sequence[Sequence[Sequence[int]]], + ExistK: Sequence[Sequence[Sequence[int]]], + ports: Sequence[Mapping[str, Union[str, int]]], + NodeY: Sequence[Sequence[Sequence[int]]] +) -> Sequence[Sequence[Sequence[int]]]: + # we linearize the cubes, cube at (i,j,k) -> index i*n_j*n_k + j*n_k + k + # construct adjancency list of the cubes from the pipes + adj = [[] for _ in range(n_i * n_j * n_k)] + for i in range(n_i): + for j in range(n_j): + for k in range(n_k): + if ExistI[i][j][k] and i + 1 < n_i: + adj[i * n_j * n_k + j * n_k + + k].append((i + 1) * n_j * n_k + j * n_k + k) + adj[(i + 1) * n_j * n_k + j * n_k + + k].append(i * n_j * n_k + j * n_k + k) + if ExistJ[i][j][k] and j + 1 < n_j: + adj[i * n_j * n_k + j * n_k + k].append(i * n_j * n_k + + (j + 1) * n_k + k) + adj[i * n_j * n_k + (j + 1) * n_k + + k].append(i * n_j * n_k + j * n_k + k) + if ExistK[i][j][k] and k + 1 < n_k: + adj[i * n_j * n_k + j * n_k + k].append(i * n_j * n_k + + j * n_k + k + 1) + adj[i * n_j * n_k + j * n_k + k + 1].append(i * n_j * n_k + + j * n_k + k) + + # if a cube can reach any of the vips, i.e., open cube for a port + vips = [p["i"] * n_j * n_k + p["j"] * n_k + p["k"] for p in ports] + + # first assume all cubes are nonconnected + connected_cubes = [[[0 for _ in range(n_k)] for _ in range(n_j)] + for _ in range(n_i)] + + # a Y cube is only effective if it is connected to a cube (i,j,k) that is + # connected to ports. In this case, (i,j,k) will be in `connected_cubes` + # and all pipes from (i,j,k) will be selected in `check_pipes`, so we can + # assume all the Y cubes to be nonconnected for now. + y_cubes = [ + i * n_j * n_k + j * n_k + k for i in range(n_i) for j in range(n_j) + for k in range(n_k) if NodeY[i][j][k] + ] + + for i in range(n_i): + for j in range(n_j): + for k in range(n_k): + # breadth first search for each cube + queue = [ + i * n_j * n_k + j * n_k + k, + ] + if i * n_j * n_k + j * n_k + k in y_cubes: + continue + visited = [0 for _ in range(n_i * n_j * n_k)] + while len(queue) > 0: + if queue[0] in vips: + connected_cubes[i][j][k] = 1 + break + visited[queue[0]] = 1 + for v in adj[queue[0]]: + if not visited[v] and v not in y_cubes: + queue.append(v) + queue.pop(0) + + return connected_cubes + + +def check_pipes( + n_i: int, n_j: int, n_k: int, ExistI: Sequence[Sequence[Sequence[int]]], + ExistJ: Sequence[Sequence[Sequence[int]]], + ExistK: Sequence[Sequence[Sequence[int]]], + connected_cubes: Sequence[Sequence[Sequence[int]]] +) -> Tuple[Sequence[Sequence[Sequence[int]]], + Sequence[Sequence[Sequence[int]]], + Sequence[Sequence[Sequence[int]]]]: + EffectI = [[[0 for _ in range(n_k)] for _ in range(n_j)] + for _ in range(n_i)] + EffectJ = [[[0 for _ in range(n_k)] for _ in range(n_j)] + for _ in range(n_i)] + EffectK = [[[0 for _ in range(n_k)] for _ in range(n_j)] + for _ in range(n_i)] + for i in range(n_i): + for j in range(n_j): + for k in range(n_k): + if ExistI[i][j][k] and (connected_cubes[i][j][k] or + (i + 1 < n_i + and connected_cubes[i + 1][j][k])): + EffectI[i][j][k] = 1 + if ExistJ[i][j][k] and (connected_cubes[i][j][k] or + (j + 1 < n_j + and connected_cubes[i][j + 1][k])): + EffectJ[i][j][k] = 1 + if ExistK[i][j][k] and (connected_cubes[i][j][k] or + (k + 1 < n_k + and connected_cubes[i][j][k + 1])): + EffectK[i][j][k] = 1 + return EffectI, EffectJ, EffectK + + +def array3DAnd( + arr0: Sequence[Sequence[Sequence[int]]], + arr1: Sequence[Sequence[Sequence[int]]] +) -> Sequence[Sequence[Sequence[int]]]: + """taking the AND of two arrays of bits""" + a = len(arr0) + b = len(arr0[0]) + c = len(arr0[0][0]) + arrAnd = [[[0 for _ in range(c)] for _ in range(b)] for _ in range(a)] + for i in range(a): + for j in range(b): + for k in range(c): + if arr0[i][j][k] == 1 and arr1[i][j][k] == 1: + arrAnd[i][j][k] = 1 + return arrAnd + + +def remove_unconnected(lasre: Mapping[str, Any]) -> Mapping[str, Any]: + n_i, n_j, n_k = ( + lasre["n_i"], + lasre["n_j"], + lasre["n_k"], + ) + ExistI, ExistJ, ExistK, NodeY = ( + lasre["ExistI"], + lasre["ExistJ"], + lasre["ExistK"], + lasre["NodeY"], + ) + ports = lasre["ports"] + + connected_cubes = check_cubes(n_i, n_j, n_k, ExistI, ExistJ, ExistK, ports, + NodeY) + connectedI, connectedJ, connectedK = check_pipes(n_i, n_j, n_k, ExistI, + ExistJ, ExistK, + connected_cubes) + maskedI, maskedJ, maskedK = ( + array3DAnd(ExistI, connectedI), + array3DAnd(ExistJ, connectedJ), + array3DAnd(ExistK, connectedK), + ) + lasre["ExistI"], lasre["ExistJ"], lasre[ + "ExistK"] = maskedI, maskedJ, maskedK + + return lasre diff --git a/glue/lattice_surgery/olssco/tools/__init__.py b/glue/lattice_surgery/lassynth/sat_synthesis/__init__.py similarity index 100% rename from glue/lattice_surgery/olssco/tools/__init__.py rename to glue/lattice_surgery/lassynth/sat_synthesis/__init__.py diff --git a/glue/lattice_surgery/lassynth/sat_synthesis/lattice_surgery_sat.py b/glue/lattice_surgery/lassynth/sat_synthesis/lattice_surgery_sat.py new file mode 100644 index 000000000..da6bd6706 --- /dev/null +++ b/glue/lattice_surgery/lassynth/sat_synthesis/lattice_surgery_sat.py @@ -0,0 +1,1842 @@ +"""LatticeSurgerySAT to encode the synthesis problem to SAT/SMT""" + +import os +import subprocess +import sys +import tempfile +import time +from typing import Any, Mapping, Sequence, Union, Tuple, Optional +import z3 + + +def var_given( + data: Mapping[str, Any], + arr: str, + i: int, + j: int, + k: int, + l: Optional[int] = None, +) -> bool: + """Check whether data[arr][i][j][k]([l]) is given. + + If the given indices are not found, return False; otherwise return True. + + Args: + data (Mapping[str, Any]): contain arrays + arr (str): ExistI, etc. + i (int): first index + j (int): second index + k (int): third index + l (int, optional): optional fourth index. Defaults to None. + + Returns: + bool: whether the variable value is given + + Raises: + ValueError: found value, but not 0 nor 1 nor -1. + """ + + if arr not in data: + return False + if l is None: + if data[arr][i][j][k] == -1: + return False + elif data[arr][i][j][k] != 0 and data[arr][i][j][k] != 1: + raise ValueError(f"{arr}[{i}, {j}, {k}] is not 0 nor 1 nor -1.") + return True + # l is not None, then + if data[arr][i][j][k][l] == -1: + return False + elif data[arr][i][j][k][l] != 0 and data[arr][i][j][k][l] != 1: + raise ValueError(f"{arr}[{i}, {j}, {k}, {l}] is not 0 nor 1 nor -1.") + return True + + +def port_incident_pipes( + port: Mapping[str, Union[str, int]], n_i: int, n_j: int, + n_k: int) -> Tuple[Sequence[str], Sequence[Tuple[int, int, int]]]: + """Compute the pipes incident to a port. + + A port is an pipe with a open end. The incident pipes of a port are the + five other pipes connecting to that end. However, some of these pipes + can be out of bound, we just want to compute those that are in bound. + + Args: + port (Mapping[str, Union[str, int]]): the port to consider + n_i (int): spatial bound on I direction + n_j (int): spatial bound on J direction + n_k (int): spatial bound on K direction + + Returns: + Tuple[Sequence[str], Sequence[Tuple[int, int, int]]]: + Two lists of the same length [0,6): (dirs, coords) + dirs: the direction of the incident pipes, can be "I", "J", or "K" + coords: the coordinates of the incident pipes, each one is (i,j,k) + """ + coords = [] + dirs = [] + + # first, just consider adjancency without caring about out-of-bound + if port["d"] == "I": + adj_dirs = ["I", "J", "J", "K", "K"] + if port["e"] == "-": # empty cube is (i,j,k) + adj_coords = [ + (port["i"] - 1, port["j"], port["k"]), # (i-1,j,k)---(i,j,k) + (port["i"], port["j"] - 1, port["k"]), # (i,j-1,k)---(i,j,k) + (port["i"], port["j"], port["k"]), # (i,j,k)---(i,j+1,k) + (port["i"], port["j"], port["k"] - 1), # (i,j,k-1)---(i,j,k) + (port["i"], port["j"], port["k"]), # (i,j,k)---(i,j,k+1) + ] + elif port["e"] == "+": # empty cube is (i+1,j,k) + adj_coords = [ + (port["i"] + 1, port["j"], port["k"]), # (i+1,j,k)---(i+2,j,k) + (port["i"] + 1, port["j"] - 1, + port["k"]), # (i+1,j-1,k)---(i+1,j,k) + (port["i"] + 1, port["j"], + port["k"]), # (i+1,j,k)---(i+1,j+1,k) + (port["i"] + 1, port["j"], + port["k"] - 1), # (i+1,j,k-1)---(i+1,j,k) + (port["i"] + 1, port["j"], + port["k"]), # (i+1,j,k)---(i+1,j,k+1) + ] + + if port["d"] == "J": + adj_dirs = ["J", "K", "K", "I", "I"] + if port["e"] == "-": + adj_coords = [ + (port["i"], port["j"] - 1, port["k"]), + (port["i"], port["j"], port["k"] - 1), + (port["i"], port["j"], port["k"]), + (port["i"] - 1, port["j"], port["k"]), + (port["i"], port["j"], port["k"]), + ] + elif port["e"] == "+": + adj_coords = [ + (port["i"], port["j"] + 1, port["k"]), + (port["i"], port["j"] + 1, port["k"] - 1), + (port["i"], port["j"] + 1, port["k"]), + (port["i"] - 1, port["j"] + 1, port["k"]), + (port["i"], port["j"] + 1, port["k"]), + ] + + if port["d"] == "K": + adj_dirs = ["K", "I", "I", "J", "J"] + if port["e"] == "-": + adj_coords = [ + (port["i"], port["j"], port["k"] - 1), + (port["i"] - 1, port["j"], port["k"]), + (port["i"], port["j"], port["k"]), + (port["i"], port["j"] - 1, port["k"]), + (port["i"], port["j"], port["k"]), + ] + elif port["e"] == "+": + adj_coords = [ + (port["i"], port["j"], port["k"] + 1), + (port["i"] - 1, port["j"], port["k"] + 1), + (port["i"], port["j"], port["k"] + 1), + (port["i"], port["j"] - 1, port["k"] + 1), + (port["i"], port["j"], port["k"] + 1), + ] + + # only keep the pipes in bound + for i, coord in enumerate(adj_coords): + if ((coord[0] in range(n_i)) and (coord[1] in range(n_j)) + and (coord[2] in range(n_k))): + coords.append(adj_coords[i]) + dirs.append(adj_dirs[i]) + + return dirs, coords + + +def cnf_even_parity_upto4(eles: Sequence[Any]) -> Any: + """Compute the CNF format of parity of up to four Z3 binary variables. + + Args: + eles (Sequence[Any]): the binary variables. + + Returns: + (Any) the Z3 constraint meaning the parity of the inputs is even. + + Raises: + ValueError: number of elements is not 1, 2, 3, or 4. + """ + + if len(eles) == 1: + # 1 var even parity -> this var is false + return z3.Not(eles[0]) + + elif len(eles) == 2: + # 2 vars even pairty -> both True or both False + return z3.Or(z3.And(z3.Not(eles[0]), z3.Not(eles[1])), + z3.And(eles[0], eles[1])) + + elif len(eles) == 3: + # 3 vars even parity -> all False, or 2 True and 1 False + return z3.Or( + z3.And(z3.Not(eles[0]), z3.Not(eles[1]), z3.Not(eles[2])), + z3.And(eles[0], eles[1], z3.Not(eles[2])), + z3.And(eles[0], z3.Not(eles[1]), eles[2]), + z3.And(z3.Not(eles[0]), eles[1], eles[2]), + ) + + elif len(eles) == 4: + # 4 vars even parity -> 0, 2, or 4 vars are True + return z3.Or( + z3.And(z3.Not(eles[0]), z3.Not(eles[1]), z3.Not(eles[2]), + z3.Not(eles[3])), + z3.And(z3.Not(eles[0]), z3.Not(eles[1]), eles[2], eles[3]), + z3.And(z3.Not(eles[0]), eles[1], z3.Not(eles[2]), eles[3]), + z3.And(z3.Not(eles[0]), eles[1], eles[2], z3.Not(eles[3])), + z3.And(eles[0], z3.Not(eles[1]), z3.Not(eles[2]), eles[3]), + z3.And(eles[0], z3.Not(eles[1]), eles[2], z3.Not(eles[3])), + z3.And(eles[0], eles[1], z3.Not(eles[2]), z3.Not(eles[3])), + z3.And(eles[0], eles[1], eles[2], eles[3]), + ) + + else: + raise ValueError("This function only supports 1, 2, 3, or 4 vars.") + + +class LatticeSurgerySAT: + """class of synthesizing LaSRe using Z3 SMT solver and Kissat SAT solver. + + It encodes a lattice surgery synthesis problem to SAT/SMT and checks + whether there is a solution. We are given certain spacetime volume, certain + ports, and certain stabilizers. LatticeSurgerySAT encodes the constraints + on LaSRe variables such that the resulting variable assignments consist of + a valid lattice surgery subroutine with the correct functionality + (satisfies all the given stabilizers). LatticeSurgerySAT finds the solution + with a SAT/SMT solver. + """ + + def __init__( + self, + input_dict: Mapping[str, Any], + color_ij: bool = True, + given_arrs: Optional[Mapping[str, Any]] = None, + given_vals: Optional[Sequence[Mapping[str, Any]]] = None, + ) -> None: + """initialization of LatticeSurgerySAT. + + Args: + input_dict (Mapping[str, Any]): specification of LaS. + color_ij (bool, optional): if the color matching constraints of + I and J pipes are imposed. Defaults to True. So far, we always + impose these constraints. + given_arrs (Mapping[str, Any], optional): + Arrays of values to plug in. Defaults to None. + given_vals (Sequence[Mapping[str, Any]], optional): + Values to plug in. Defaults to None. These values will + replace existing values if already set by given_arrs. + """ + self.input_dict = input_dict + self.color_ij = color_ij + self.goal = z3.Goal() + self.process_input(input_dict) + self.build_smt_model(given_arrs=given_arrs, given_vals=given_vals) + + def process_input(self, input_dict: Mapping[str, Any]) -> None: + """read input specification, mainly translating the info at the ports. + + Args: + input_dict (Mapping[str, Any]): LaS specification. + + Raises: + ValueError: missing key in input specification. + ValueError: some spatial bound <= 0. + ValueError: more stabilizers than ports. + ValueError: stabilizer length is not the same as + the number of ports. + ValueError: stabilizer contains things other than I, X, Y, or Z. + ValueError: missing key in port. + ValueError: port location is not a 3-tuple. + ValueError: port direction is not 2-string. + ValueError: port sign (which end is dangling) is not - or +. + ValueError: port axis is not I, J, or K. + ValueError: port location+direction is out of bound. + ValueError: port Z basis direction is not I, J, or K, and + the same with the pipe. + ValueError: forbidden cube location is not a 3-tuple. + ValueError: forbiddent cube location is out of bounds. + """ + data = input_dict + + for key in ["max_i", "max_j", "max_k", "ports", "stabilizers"]: + if key not in data: + raise ValueError(f"missing key {key} in input specification.") + + # load spatial bound, check > 0 + self.n_i = data["max_i"] + self.n_j = data["max_j"] + self.n_k = data["max_k"] + if min([self.n_i, self.n_j, self.n_k]) <= 0: + raise ValueError("max_i or _j or _k <= 0.") + + self.n_p = len(data["ports"]) + self.n_s = len(data["stabilizers"]) + # there should be at most as many stabilizers as ports + if self.n_s > self.n_p: + raise ValueError( + f"{self.n_s} stabilizers, too many for {self.n_p} ports.") + + # stabilizers should be paulistrings of length #ports + self.paulistrings = [s.replace(".", "I") for s in data["stabilizers"]] + for s in self.paulistrings: + if len(s) != self.n_p: + raise ValueError( + f"len({s}) = {len(s)}, but there are {self.n_p} ports.") + for i in range(len(s)): + if s[i] not in ["I", "X", "Y", "Z"]: + raise ValueError( + f"{s} has invalid Pauli. I, X, Y, and Z are allowed.") + + # transform port data + self.ports = [] + for port in data["ports"]: + for key in ["location", "direction", "z_basis_direction"]: + if key not in port: + raise ValueError(f"missing key {key} in port {port}") + + if len(port["location"]) != 3: + raise ValueError(f"port location should be 3-tuple {port}.") + + if len(port["direction"]) != 2: + raise ValueError( + f"port direction should have 2 characters {port}.") + if port["direction"][0] not in ["+", "-"]: + raise ValueError(f"port direction with invalid sign {port}.") + if port["direction"][1] not in ["I", "J", "K"]: + raise ValueError(f"port direction with invalid axis {port}.") + + if port["direction"][0] == "-" and port["direction"][ + 1] == "I" and (port["location"][0] not in range( + 1, self.n_i + 1)): + raise ValueError( + f"{port['location']} with direction {port['direction']}" + f" should be in range [1, f{self.n_i+1}).") + if port["direction"][0] == "+" and port["direction"][ + 1] == "I" and (port["location"][0] not in range( + 0, self.n_i)): + raise ValueError( + f"{port['location']} with direction {port['direction']}" + f" should be in range [0, f{self.n_i}).") + if port["direction"][0] == "-" and port["direction"][ + 1] == "J" and (port["location"][1] not in range( + 1, self.n_j + 1)): + raise ValueError( + f"{port['location']} with direction {port['direction']}" + f" should be in range [1, {self.n_j+1}).") + if port["direction"][0] == "+" and port["direction"][ + 1] == "J" and (port["location"][1] not in range( + 0, self.n_j)): + raise ValueError( + f"{port['location']} with direction {port['direction']}" + f" should be in range [0, f{self.n_j}).") + if port["direction"][0] == "-" and port["direction"][ + 1] == "K" and (port["location"][2] not in range( + 1, self.n_k + 1)): + raise ValueError( + f"{port['location']} with direction {port['direction']}" + f" should be in range [1, f{self.n_k+1}).") + if port["direction"][0] == "+" and port["direction"][ + 1] == "K" and (port["location"][2] not in range( + 0, self.n_k)): + raise ValueError( + f"{port['location']} with direction {port['direction']}" + f" should be in range [0, f{self.n_k}).") + + # internally, a port is an pipe. This is different from what we + # expose to the user: in LaS specification, a port is a cube and + # associated with a direction, e.g., cube [i,j,k] and direction + # "-K". This means the port should be the pipe connecting (i,j,k) + # downwards to the volume of LaS. Thus, that pipe is (i,j,k-1) -- + # (i,j,k) which by convention is the K-pipe (i,j,k-1). + # a port here has fields "i", "j", "k", "d", "e", "f", "c" + my_port = {} + + # "i", "j", and "k" are the i,j,k of the pipe + my_port["i"], my_port["j"], my_port["k"] = port["location"] + if port["direction"][0] == "-": + my_port[port["direction"][1].lower()] -= 1 + + # "d" is one of I, J, and K, corresponding to the port being an + # I-pipe, J-pipe, or a K-pipe + my_port["d"] = port["direction"][1] + + # "e" is the end of the pipe that is open. For example, if the port + # is a K-pipe (i,j,k), then "e"="+" means the cube (i,j,k+1) is + # open; otherwise, "e"="-" means cube (i,j,k) is open. + my_port["e"] = "-" if port["direction"][0] == "+" else "+" + + # "c" is the color variable of the pipe corresponding to the port + z_dir = port["z_basis_direction"] + if z_dir not in ["I", "J", "K"] or z_dir == my_port["d"]: + raise ValueError( + f"port with invalid Z basis direction {port}.") + if my_port["d"] == "I": + my_port["c"] = 0 if z_dir == "J" else 1 + if my_port["d"] == "J": + my_port["c"] = 0 if z_dir == "K" else 1 + if my_port["d"] == "K": + my_port["c"] = 0 if z_dir == "I" else 1 + + # "f" is the function of the pipe, e.g., it can say this port is a + # T injection. This field is not used in the SAT synthesis, but + # we keep this info to use in later stages like gltf generation + if "function" in port: + my_port["f"] = port["function"] + + self.ports.append(my_port) + + # from paulistrings to correlation surfaces + self.stabs = self.derive_corr_boundary(self.paulistrings) + + self.optional = {} + self.forbidden_cubes = [] + if "optional" in data: + self.optional = data["optional"] + + if "forbidden_cubes" in data["optional"]: + for cube in data["optional"]["forbidden_cubes"]: + if len(cube) != 3: + raise ValueError( + f"forbid cube should be 3-tuple {cube}.") + if (cube[0] not in range(self.n_i) + or cube[1] not in range(self.n_j) + or cube[2] not in range(self.n_k)): + raise ValueError( + f"forbidden {cube} out of range " + f"(i,j,k) < ({self.n_i, self.n_j, self.n_k})") + self.forbidden_cubes.append(cube) + + self.get_port_cubes() + + def get_port_cubes(self) -> None: + """calculate which cubes are the open cube for the ports. + Note that these are *** 3-tuples ***, not lists with 3 elements.""" + self.port_cubes = [] + for p in self.ports: + # if e=-, (i,j,k); otherwise, +1 in the proper direction + if p["e"] == "-": + self.port_cubes.append((p["i"], p["j"], p["k"])) + elif p["d"] == "I": + self.port_cubes.append((p["i"] + 1, p["j"], p["k"])) + elif p["d"] == "J": + self.port_cubes.append((p["i"], p["j"] + 1, p["k"])) + elif p["d"] == "K": + self.port_cubes.append((p["i"], p["j"], p["k"] + 1)) + + def derive_corr_boundary( + self, paulistrings: Sequence[str] + ) -> Sequence[Sequence[Mapping[str, int]]]: + """derive the boundary correlation surface variable values. + + From the color orientation of the ports and the stabilizers, we can + derive which correlation surface variables evaluates to True and which + to False at the ports for each stabilizer. + + Args: + paulistrings (Sequence[str]): stabilizers as a list of Paulistrings + + Returns: + Sequence[Sequence[Mapping[str, int]]]: Outer layer list is the + list of stabilizers. Inner layer list is the situation at each port + for one specifeic stabilizer. Each port is specified with a + dictionary of 2 bits for the 2 correaltion surfaces. + """ + stabs = [] + for paulistring in paulistrings: + corr = [] + for p in range(self.n_p): + if paulistring[p] == "I": + # I -> no corr surf should be present + if self.ports[p]["d"] == "I": + corr.append({"IJ": 0, "IK": 0}) + if self.ports[p]["d"] == "J": + corr.append({"JI": 0, "JK": 0}) + if self.ports[p]["d"] == "K": + corr.append({"KI": 0, "KJ": 0}) + + if paulistring[p] == "Y": + # Y -> both corr surf should be present + if self.ports[p]["d"] == "I": + corr.append({"IJ": 1, "IK": 1}) + if self.ports[p]["d"] == "J": + corr.append({"JI": 1, "JK": 1}) + if self.ports[p]["d"] == "K": + corr.append({"KI": 1, "KJ": 1}) + + if paulistring[p] == "X": + # X -> only corr surf touching red faces + if self.ports[p]["d"] == "I": + if self.ports[p]["c"]: + corr.append({"IJ": 1, "IK": 0}) + else: + corr.append({"IJ": 0, "IK": 1}) + if self.ports[p]["d"] == "J": + if self.ports[p]["c"]: + corr.append({"JI": 0, "JK": 1}) + else: + corr.append({"JI": 1, "JK": 0}) + if self.ports[p]["d"] == "K": + if self.ports[p]["c"]: + corr.append({"KI": 1, "KJ": 0}) + else: + corr.append({"KI": 0, "KJ": 1}) + + if paulistring[p] == "Z": + # Z -> only corr surf touching blue faces + if self.ports[p]["d"] == "I": + if not self.ports[p]["c"]: + corr.append({"IJ": 1, "IK": 0}) + else: + corr.append({"IJ": 0, "IK": 1}) + if self.ports[p]["d"] == "J": + if not self.ports[p]["c"]: + corr.append({"JI": 0, "JK": 1}) + else: + corr.append({"JI": 1, "JK": 0}) + if self.ports[p]["d"] == "K": + if not self.ports[p]["c"]: + corr.append({"KI": 1, "KJ": 0}) + else: + corr.append({"KI": 0, "KJ": 1}) + stabs.append(corr) + return stabs + + def build_smt_model( + self, + given_arrs: Optional[Mapping[str, Any]] = None, + given_vals: Optional[Sequence[Mapping[str, Any]]] = None, + ) -> None: + """build the SMT model with variables and constraints. + + Args: + given_arrs (Mapping[str, Any], optional): + Arrays of values to plug in. Defaults to None. + given_vals (Sequence[Mapping[str, Any]], optional): + Values to plug in. Defaults to None. These values will + replace existing values if already set by given_arrs. + """ + self.define_vars() + if given_arrs is not None: + self.plugin_arrs(given_arrs) + if given_vals is not None: + self.plugin_vals(given_vals) + + # baseline order of constraint sets, '...' menas name in the paper + + # validity constraints that directly set variables values + self.constraint_forbid_cube() + self.constraint_port() # 'no fanouts' + self.constraint_connect_outside() # 'no unexpected ports' + + # more complex validity constraints involving boolean logic + self.constraint_timelike_y() # 'time-like Y cubes' + self.constraint_no_deg1() # 'no degree-1 non-Y cubes' + if self.color_ij: + # 'matching colors at passthroughs' and '... at turns' + self.constraint_ij_color() + self.constraint_3d_corner() # 'no 3D corners' + + # simpler functionality constraints + self.constraint_corr_ports() # 'stabilizer as boundary conditions' + self.constraint_corr_y() # 'both or non at Y cubes' + + # more complex functionality constraints + # 'all or no orthogonal surfaces at non-Y cubes: + self.constraint_corr_perp() + # 'even parity of parallel surfaces at non-Y cubes': + self.constraint_corr_para() + + def define_vars(self) -> None: + """define the variables in Z3 into self.vars.""" + self.vars = { + "ExistI": + [[[z3.Bool(f"ExistI({i},{j},{k})") for k in range(self.n_k)] + for j in range(self.n_j)] for i in range(self.n_i)], + "ExistJ": + [[[z3.Bool(f"ExistJ({i},{j},{k})") for k in range(self.n_k)] + for j in range(self.n_j)] for i in range(self.n_i)], + "ExistK": + [[[z3.Bool(f"ExistK({i},{j},{k})") for k in range(self.n_k)] + for j in range(self.n_j)] for i in range(self.n_i)], + "NodeY": + [[[z3.Bool(f"NodeY({i},{j},{k})") for k in range(self.n_k)] + for j in range(self.n_j)] for i in range(self.n_i)], + "CorrIJ": + [[[[z3.Bool(f"CorrIJ({s},{i},{j},{k})") for k in range(self.n_k)] + for j in range(self.n_j)] for i in range(self.n_i)] + for s in range(self.n_s)], + "CorrIK": + [[[[z3.Bool(f"CorrIK({s},{i},{j},{k})") for k in range(self.n_k)] + for j in range(self.n_j)] for i in range(self.n_i)] + for s in range(self.n_s)], + "CorrJK": + [[[[z3.Bool(f"CorrJK({s},{i},{j},{k})") for k in range(self.n_k)] + for j in range(self.n_j)] for i in range(self.n_i)] + for s in range(self.n_s)], + "CorrJI": + [[[[z3.Bool(f"CorrJI({s},{i},{j},{k})") for k in range(self.n_k)] + for j in range(self.n_j)] for i in range(self.n_i)] + for s in range(self.n_s)], + "CorrKI": + [[[[z3.Bool(f"CorrKI({s},{i},{j},{k})") for k in range(self.n_k)] + for j in range(self.n_j)] for i in range(self.n_i)] + for s in range(self.n_s)], + "CorrKJ": + [[[[z3.Bool(f"CorrKJ({s},{i},{j},{k})") for k in range(self.n_k)] + for j in range(self.n_j)] for i in range(self.n_i)] + for s in range(self.n_s)], + } + + if self.color_ij: + self.vars["ColorI"] = [[[ + z3.Bool(f"ColorI({i},{j},{k})") for k in range(self.n_k) + ] for j in range(self.n_j)] for i in range(self.n_i)] + self.vars["ColorJ"] = [[[ + z3.Bool(f"ColorJ({i},{j},{k})") for k in range(self.n_k) + ] for j in range(self.n_j)] for i in range(self.n_i)] + + def plugin_arrs(self, data: Mapping[str, Any]) -> None: + """plug in the given arrays of values. + + Args: + data (Mapping[str, Any]): contains gieven values. + + Raises: + ValueError: data contains an invalid array name. + ValueError: array given has wrong dimensions. + """ + + for key in data: + if key in [ + "NodeY", + "ExistI", + "ExistJ", + "ExistK", + "ColorI", + "ColorJ", + ]: + if len(data[key]) != self.n_i: + raise ValueError(f"dimension of {key} is wrong.") + for tmp in data[key]: + if len(tmp) != self.n_j: + raise ValueError(f"dimension of {key} is wrong.") + for tmptmp in tmp: + if len(tmptmp) != self.n_k: + raise ValueError(f"dimension of {key} is wrong.") + elif key in [ + "CorrIJ", + "CorrIK", + "CorrJI", + "CorrJK", + "CorrKI", + "CorrKJ", + ]: + if len(data[key]) != self.n_s: + raise ValueError(f"dimension of {key} is wrong.") + for tmp in data[key]: + if len(tmp) != self.n_i: + raise ValueError(f"dimension of {key} is wrong.") + for tmptmp in tmp: + if len(tmptmp) != self.n_j: + raise ValueError(f"dimension of {key} is wrong.") + for tmptmptmp in tmptmp: + if len(tmptmptmp) != self.n_k: + raise ValueError( + f"dimension of {key} is wrong.") + else: + raise ValueError(f"{key} is not a valid array name") + + arrs = [ + "NodeY", + "ExistI", + "ExistJ", + "ExistK", + ] + if self.color_ij: + arrs += ["ColorI", "ColorJ"] + + for s in range(self.n_s): + for i in range(self.n_i): + for j in range(self.n_j): + for k in range(self.n_k): + if s == 0: # Exist, Node, and Color vars + for arr in arrs: + if var_given(data, arr, i, j, k): + self.goal.add( + self.vars[arr][i][j][k] + if data[arr][i][j][k] == + 1 else z3.Not(self.vars[arr][i][j][k])) + # Corr vars + for arr in [ + "CorrIJ", + "CorrIK", + "CorrJI", + "CorrJK", + "CorrKI", + "CorrKJ", + ]: + if var_given(data, arr, s, i, j, k): + self.goal.add( + self.vars[arr][s][i][j][k] + if data[arr][s][i][j][k] == + 1 else z3.Not(self.vars[arr][s][i][j][k])) + + def plugin_vals(self, data_set: Sequence[Mapping[str, Any]]): + """plug in the given values + + Args: + data (Sequence[Mapping[str, Any]]): given values as a sequence + of dicts. Each one contains three fields: "array", the name of + the array, e.g., "ExistI"; "indices", a sequence of the indices; + and "value". + + Raises: + ValueError: given_vals missing a field. + ValueError: array name is not valid. + ValueError: indices dimension for certain array is wrong. + ValueError: index value out of bound. + ValueError: given value is neither 0 nor 1. + """ + for data in data_set: + for key in ["array", "indices", "value"]: + if key not in data: + raise ValueError(f"{key} is not in given val") + if data["array"] not in [ + "NodeY", + "ExistI", + "ExistJ", + "ExistK", + "ColorI", + "ColorJ", + "CorrIJ", + "CorrIK", + "CorrJI", + "CorrJK", + "CorrKI", + "CorrKJ", + ]: + raise ValueError(f"{data['array']} is not a valid array.") + if data["array"] in [ + "NodeY", + "ExistI", + "ExistJ", + "ExistK", + "ColorI", + "ColorJ", + ]: + if len(data["indices"] != 3): + raise ValueError(f"Need 3 indices for {data['array']}.") + if data["indices"][0] not in range(self.n_i): + raise ValueError(f"i index out of range") + if data["indices"][1] not in range(self.n_j): + raise ValueError(f"j index out of range") + if data["indices"][2] not in range(self.n_k): + raise ValueError(f"k index out of range") + + if data["array"] in [ + "CorrIJ", + "CorrIK", + "CorrJI", + "CorrJK", + "CorrKI", + "CorrKJ", + ]: + if len(data["indices"] != 4): + raise ValueError(f"Need 4 indices for {data['array']}.") + if data["indices"][0] not in range(self.n_s): + raise ValueError(f"s index out of range") + if data["indices"][1] not in range(self.n_i): + raise ValueError(f"i index out of range") + if data["indices"][2] not in range(self.n_j): + raise ValueError(f"j index out of range") + if data["indices"][3] not in range(self.n_k): + raise ValueError(f"k index out of range") + + if data["value"] not in [0, 1]: + raise ValueError("Given value can only be 0 or 1.") + + (arr, idx) = data["array"], data["indices"] + if arr.startswith("Corr"): + s, i, j, k = idx + if data["value"] == 1: + self.goal.add(self.vars[arr][s][i][j][k]) + else: + self.goal.add(z3.Not(self.vars[arr][s][i][j][k])) + else: + i, j, k = idx + if data["value"] == 1: + self.goal.add(self.vars[arr][i][j][k]) + else: + self.goal.add(z3.Not(self.vars[arr][i][j][k])) + + def constraint_forbid_cube(self) -> None: + """forbid a list of cubes.""" + for cube in self.forbidden_cubes: + (i, j, k) = cube[0], cube[1], cube[2] + self.goal.add(z3.Not(self.vars["NodeY"][i][j][k])) + if i > 0: + self.goal.add(z3.Not(self.vars["ExistI"][i - 1][j][k])) + self.goal.add(z3.Not(self.vars["ExistI"][i][j][k])) + if j > 0: + self.goal.add(z3.Not(self.vars["ExistJ"][i][j - 1][k])) + self.goal.add(z3.Not(self.vars["ExistJ"][i][j][k])) + if k > 0: + self.goal.add(z3.Not(self.vars["ExistK"][i][j][k - 1])) + self.goal.add(z3.Not(self.vars["ExistK"][i][j][k])) + + def constraint_port(self) -> None: + """some pipes must exist and some must not depending on the ports.""" + for port in self.ports: + # the pipe specified by the port exists + self.goal.add(self.vars[f"Exist{port['d']}"][port["i"]][port["j"]][ + port["k"]]) + # if I- or J-pipe exist, set the color value too to the given one + if self.color_ij: + if port["d"] != "K": + if port["c"] == 1: + self.goal.add(self.vars[f"Color{port['d']}"][port["i"]] + [port["j"]][port["k"]]) + else: + self.goal.add( + z3.Not(self.vars[f"Color{port['d']}"][port["i"]][ + port["j"]][port["k"]])) + + # collect the pipes touching the port to forbid them + dirs, coords = port_incident_pipes(port, self.n_i, self.n_j, + self.n_k) + for i, coord in enumerate(coords): + self.goal.add( + z3.Not(self.vars[f"Exist{dirs[i]}"][coord[0]][coord[1]][ + coord[2]])) + + def constraint_connect_outside(self) -> None: + """no pipe should cross the spatial bound except for ports.""" + for i in range(self.n_i): + for j in range(self.n_j): + # consider K-pipes crossing K-bound and not a port + if (i, j, self.n_k) not in self.port_cubes: + self.goal.add( + z3.Not(self.vars["ExistK"][i][j][self.n_k - 1])) + for i in range(self.n_i): + for k in range(self.n_k): + if (i, self.n_j, k) not in self.port_cubes: + self.goal.add( + z3.Not(self.vars["ExistJ"][i][self.n_j - 1][k])) + for j in range(self.n_j): + for k in range(self.n_k): + if (self.n_i, j, k) not in self.port_cubes: + self.goal.add( + z3.Not(self.vars["ExistI"][self.n_i - 1][j][k])) + + def constraint_timelike_y(self) -> None: + """forbid all I- and J- pipes to Y cubes.""" + for i in range(self.n_i): + for j in range(self.n_j): + for k in range(self.n_k): + if (i, j, k) not in self.port_cubes: + self.goal.add( + z3.Implies( + self.vars["NodeY"][i][j][k], + z3.Not(self.vars["ExistI"][i][j][k]), + )) + self.goal.add( + z3.Implies( + self.vars["NodeY"][i][j][k], + z3.Not(self.vars["ExistJ"][i][j][k]), + )) + if i - 1 >= 0: + self.goal.add( + z3.Implies( + self.vars["NodeY"][i][j][k], + z3.Not(self.vars["ExistI"][i - 1][j][k]), + )) + if j - 1 >= 0: + self.goal.add( + z3.Implies( + self.vars["NodeY"][i][j][k], + z3.Not(self.vars["ExistJ"][i][j - 1][k]), + )) + + def constraint_ij_color(self) -> None: + """color matching for I- and J-pipes.""" + for i in range(self.n_i): + for j in range(self.n_j): + for k in range(self.n_k): + if i >= 1 and j >= 1: + # (i-1,j,k)-(i,j,k) and (i,j-1,k)-(i,j,k) + self.goal.add( + z3.Implies( + z3.And( + self.vars["ExistI"][i - 1][j][k], + self.vars["ExistJ"][i][j - 1][k], + ), + z3.Or( + z3.And( + self.vars["ColorI"][i - 1][j][k], + z3.Not(self.vars["ColorJ"][i][j - + 1][k]), + ), + z3.And( + z3.Not(self.vars["ColorI"][i - + 1][j][k]), + self.vars["ColorJ"][i][j - 1][k], + ), + ), + )) + + if i >= 1: + # (i-1,j,k)-(i,j,k) and (i,j,k)-(i,j+1,k) + self.goal.add( + z3.Implies( + z3.And( + self.vars["ExistI"][i - 1][j][k], + self.vars["ExistJ"][i][j][k], + ), + z3.Or( + z3.And( + self.vars["ColorI"][i - 1][j][k], + z3.Not(self.vars["ColorJ"][i][j][k]), + ), + z3.And( + z3.Not(self.vars["ColorI"][i - + 1][j][k]), + self.vars["ColorJ"][i][j][k], + ), + ), + )) + # (i-1,j,k)-(i,j,k) and (i,j,k)-(i+1,j,k) + self.goal.add( + z3.Implies( + z3.And( + self.vars["ExistI"][i - 1][j][k], + self.vars["ExistI"][i][j][k], + ), + z3.Or( + z3.And( + self.vars["ColorI"][i - 1][j][k], + self.vars["ColorI"][i][j][k], + ), + z3.And( + z3.Not(self.vars["ColorI"][i - + 1][j][k]), + z3.Not(self.vars["ColorI"][i][j][k]), + ), + ), + )) + + if j >= 1: + # (i,j,k)-(i+1,j,k) and (i,j-1,k)-(i,j,k) + self.goal.add( + z3.Implies( + z3.And( + self.vars["ExistI"][i][j][k], + self.vars["ExistJ"][i][j - 1][k], + ), + z3.Or( + z3.And( + self.vars["ColorI"][i][j][k], + z3.Not(self.vars["ColorJ"][i][j - + 1][k]), + ), + z3.And( + z3.Not(self.vars["ColorI"][i][j][k]), + self.vars["ColorJ"][i][j - 1][k], + ), + ), + )) + # (i,j-1,k)-(i,j,k) and (i,j,k)-(i,j+1,k) + self.goal.add( + z3.Implies( + z3.And( + self.vars["ExistJ"][i][j - 1][k], + self.vars["ExistJ"][i][j][k], + ), + z3.Or( + z3.And( + self.vars["ColorJ"][i][j - 1][k], + self.vars["ColorJ"][i][j][k], + ), + z3.And( + z3.Not(self.vars["ColorJ"][i][j - + 1][k]), + z3.Not(self.vars["ColorJ"][i][j][k]), + ), + ), + )) + + # (i,j,k)-(i+1,j,k) and (i,j,k)-(i,j+1,k) + self.goal.add( + z3.Implies( + z3.And(self.vars["ExistI"][i][j][k], + self.vars["ExistJ"][i][j][k]), + z3.Or( + z3.And( + self.vars["ColorI"][i][j][k], + z3.Not(self.vars["ColorJ"][i][j][k]), + ), + z3.And( + z3.Not(self.vars["ColorI"][i][j][k]), + self.vars["ColorJ"][i][j][k], + ), + ), + )) + + def constraint_3d_corner(self) -> None: + """at least in one direction, both pipes nonexist.""" + for i in range(self.n_i): + for j in range(self.n_j): + for k in range(self.n_k): + i_pipes = [ + self.vars["ExistI"][i][j][k], + ] + if i - 1 >= 0: + i_pipes.append(self.vars["ExistI"][i - 1][j][k]) + j_pipes = [ + self.vars["ExistJ"][i][j][k], + ] + if j - 1 >= 0: + j_pipes.append(self.vars["ExistJ"][i][j - 1][k]) + k_pipes = [ + self.vars["ExistK"][i][j][k], + ] + if k - 1 >= 0: + k_pipes.append(self.vars["ExistK"][i][j][k - 1]) + + # at least one of the three terms is true. The first term + # is that both I-pipes connecting to (i,j,k) do not exist. + self.goal.add( + z3.Or( + z3.Not(z3.Or(i_pipes)), + z3.Not(z3.Or(j_pipes)), + z3.Not(z3.Or(k_pipes)), + )) + + def constraint_no_deg1(self) -> None: + """forbid degree-1 X or Z cubes by considering incident pipes.""" + for i in range(self.n_i): + for j in range(self.n_j): + for k in range(self.n_k): + for d in ["I", "J", "K"]: + for e in ["-", "+"]: + cube = {"I": i, "J": j, "K": k} + cube[d] += 1 if e == "+" else 0 + + # construct fake ports to get incident pipes + p0 = { + "i": i, + "j": j, + "k": k, + "d": d, + "e": e, + "c": 0 + } + found_p0 = False + for port in self.ports: + if (i == port["i"] and j == port["j"] + and k == port["k"] and d == port["d"]): + found_p0 = True + + # only non-port pipes need to consider + if (not found_p0 and cube["I"] < self.n_i + and cube["J"] < self.n_j + and cube["K"] < self.n_k): + # only cubes inside bound need to consider + dirs, coords = port_incident_pipes( + p0, self.n_i, self.n_j, self.n_k) + pipes = [ + self.vars[f"Exist{dirs[l]}"][coord[0]][ + coord[1]][coord[2]] + for l, coord in enumerate(coords) + ] + # if the cube is not Y and the pipe exist, then + # at least one of its incident pipes exists. + self.goal.add( + z3.Implies( + z3.And( + z3.Not( + self.vars["NodeY"][cube["I"]][ + cube["J"]][cube["K"]]), + self.vars[f"Exist{d}"][i][j][k], + ), + z3.Or(pipes), + )) + + def constraint_corr_ports(self) -> None: + """plug in the correlation surface values at the ports.""" + for s, stab in enumerate(self.stabs): + for p, corrs in enumerate(stab): + for k, v in corrs.items(): + if v == 1: + self.goal.add( + self.vars[f"Corr{k}"][s][self.ports[p]["i"]][ + self.ports[p]["j"]][self.ports[p]["k"]]) + else: + self.goal.add( + z3.Not(self.vars[f"Corr{k}"][s][self.ports[p]["i"]] + [self.ports[p]["j"]][self.ports[p]["k"]])) + + def constraint_corr_y(self) -> None: + """correlation surfaces at Y-cubes should both exist or nonexist.""" + for s in range(self.n_s): + for i in range(self.n_i): + for j in range(self.n_j): + for k in range(self.n_k): + self.goal.add( + z3.Or( + z3.Not(self.vars["NodeY"][i][j][k]), + z3.Or( + z3.And( + self.vars["CorrKI"][s][i][j][k], + self.vars["CorrKJ"][s][i][j][k], + ), + z3.And( + z3.Not( + self.vars["CorrKI"][s][i][j][k]), + z3.Not( + self.vars["CorrKJ"][s][i][j][k]), + ), + ), + )) + if k - 1 >= 0: + self.goal.add( + z3.Or( + z3.Not(self.vars["NodeY"][i][j][k]), + z3.Or( + z3.And( + self.vars["CorrKI"][s][i][j][k - + 1], + self.vars["CorrKJ"][s][i][j][k - + 1], + ), + z3.And( + z3.Not(self.vars["CorrKI"][s][i][j] + [k - 1]), + z3.Not(self.vars["CorrKJ"][s][i][j] + [k - 1]), + ), + ), + )) + + def constraint_corr_perp(self) -> None: + """for corr surf perpendicular to normal vector, all or none exists.""" + for s in range(self.n_s): + for i in range(self.n_i): + for j in range(self.n_j): + for k in range(self.n_k): + if (i, j, k) not in self.port_cubes: + # only consider X or Z spider + # if normal is K meaning meaning both + # (i,j,k)-(i,j,k+1) and (i,j,k)-(i,j,k-1) are + # out of range, or in range but nonexistent + normal = z3.And( + z3.Not(self.vars["NodeY"][i][j][k]), + z3.Not(self.vars["ExistK"][i][j][k]), + ) + if k - 1 >= 0: + normal = z3.And( + normal, + z3.Not(self.vars["ExistK"][i][j][k - 1])) + + # for other pipes, we need to build an intermediate + # expression for (i,j,k)-(i+1,j,k) and + # (i,j,k)-(i,j+1,k), built expression meaning + # the pipe is nonexistent or exist and has + # the correlation surface perpendicular to + # the normal vector in them. + no_pipe_or_with_corr = [ + z3.Or( + z3.Not(self.vars["ExistI"][i][j][k]), + self.vars["CorrIJ"][s][i][j][k], + ), + z3.Or( + z3.Not(self.vars["ExistJ"][i][j][k]), + self.vars["CorrJI"][s][i][j][k], + ), + ] + + # for (i,j,k)-(i+1,j,k) and (i,j,k)-(i,j+1,k), + # build expression meaning the pipe is nonexistent + # or exist and does not have the correlation + # surface perpendicular to the normal vector. + no_pipe_or_no_corr = [ + z3.Or( + z3.Not(self.vars["ExistI"][i][j][k]), + z3.Not(self.vars["CorrIJ"][s][i][j][k]), + ), + z3.Or( + z3.Not(self.vars["ExistJ"][i][j][k]), + z3.Not(self.vars["CorrJI"][s][i][j][k]), + ), + ] + + if i - 1 >= 0: + # add (i-1,j,k)-(i,j,k) to the expression + no_pipe_or_with_corr.append( + z3.Or( + z3.Not(self.vars["ExistI"][i - + 1][j][k]), + self.vars["CorrIJ"][s][i - 1][j][k], + )) + no_pipe_or_no_corr.append( + z3.Or( + z3.Not(self.vars["ExistI"][i - + 1][j][k]), + z3.Not( + self.vars["CorrIJ"][s][i - + 1][j][k]), + )) + + if j - 1 >= 0: + # add (i,j-1,k)-(i,j,k) to the expression + no_pipe_or_with_corr.append( + z3.Or( + z3.Not(self.vars["ExistJ"][i][j - + 1][k]), + self.vars["CorrJI"][s][i][j - 1][k], + )) + no_pipe_or_no_corr.append( + z3.Or( + z3.Not(self.vars["ExistJ"][i][j - + 1][k]), + z3.Not( + self.vars["CorrJI"][s][i][j - + 1][k]), + )) + + # if normal vector is K, then in all its + # incident pipes that exist all correlation surface + # in I-J plane exist or nonexist + self.goal.add( + z3.Implies( + normal, + z3.Or( + z3.And(no_pipe_or_with_corr), + z3.And(no_pipe_or_no_corr), + ), + )) + + # if normal is I + normal = z3.And( + z3.Not(self.vars["NodeY"][i][j][k]), + z3.Not(self.vars["ExistI"][i][j][k]), + ) + if i - 1 >= 0: + normal = z3.And( + normal, + z3.Not(self.vars["ExistI"][i - 1][j][k])) + no_pipe_or_with_corr = [ + z3.Or( + z3.Not(self.vars["ExistJ"][i][j][k]), + self.vars["CorrJK"][s][i][j][k], + ), + z3.Or( + z3.Not(self.vars["ExistK"][i][j][k]), + self.vars["CorrKJ"][s][i][j][k], + ), + ] + no_pipe_or_no_corr = [ + z3.Or( + z3.Not(self.vars["ExistJ"][i][j][k]), + z3.Not(self.vars["CorrJK"][s][i][j][k]), + ), + z3.Or( + z3.Not(self.vars["ExistK"][i][j][k]), + z3.Not(self.vars["CorrKJ"][s][i][j][k]), + ), + ] + if j - 1 >= 0: + no_pipe_or_with_corr.append( + z3.Or( + z3.Not(self.vars["ExistJ"][i][j - + 1][k]), + self.vars["CorrJK"][s][i][j - 1][k], + )) + no_pipe_or_no_corr.append( + z3.Or( + z3.Not(self.vars["ExistJ"][i][j - + 1][k]), + z3.Not( + self.vars["CorrJK"][s][i][j - + 1][k]), + )) + if k - 1 >= 0: + no_pipe_or_with_corr.append( + z3.Or( + z3.Not(self.vars["ExistK"][i][j][k - + 1]), + self.vars["CorrKJ"][s][i][j][k - 1], + )) + no_pipe_or_no_corr.append( + z3.Or( + z3.Not(self.vars["ExistK"][i][j][k - + 1]), + z3.Not( + self.vars["CorrKJ"][s][i][j][k - + 1]), + )) + self.goal.add( + z3.Implies( + normal, + z3.Or( + z3.And(no_pipe_or_with_corr), + z3.And(no_pipe_or_no_corr), + ), + )) + + # if normal is J + normal = z3.And( + z3.Not(self.vars["NodeY"][i][j][k]), + z3.Not(self.vars["ExistJ"][i][j][k]), + ) + if j - 1 >= 0: + normal = z3.And( + normal, + z3.Not(self.vars["ExistJ"][i][j - 1][k])) + no_pipe_or_with_corr = [ + z3.Or( + z3.Not(self.vars["ExistI"][i][j][k]), + self.vars["CorrIK"][s][i][j][k], + ), + z3.Or( + z3.Not(self.vars["ExistK"][i][j][k]), + self.vars["CorrKI"][s][i][j][k], + ), + ] + no_pipe_or_no_corr = [ + z3.Or( + z3.Not(self.vars["ExistI"][i][j][k]), + z3.Not(self.vars["CorrIK"][s][i][j][k]), + ), + z3.Or( + z3.Not(self.vars["ExistK"][i][j][k]), + z3.Not(self.vars["CorrKI"][s][i][j][k]), + ), + ] + if i - 1 >= 0: + no_pipe_or_with_corr.append( + z3.Or( + z3.Not(self.vars["ExistI"][i - + 1][j][k]), + self.vars["CorrIK"][s][i - 1][j][k], + )) + no_pipe_or_no_corr.append( + z3.Or( + z3.Not(self.vars["ExistI"][i - + 1][j][k]), + z3.Not( + self.vars["CorrIK"][s][i - + 1][j][k]), + )) + if k - 1 >= 0: + no_pipe_or_with_corr.append( + z3.Or( + z3.Not(self.vars["ExistK"][i][j][k - + 1]), + self.vars["CorrKI"][s][i][j][k - 1], + )) + no_pipe_or_no_corr.append( + z3.Or( + z3.Not(self.vars["ExistK"][i][j][k - + 1]), + z3.Not( + self.vars["CorrKI"][s][i][j][k - + 1]), + )) + self.goal.add( + z3.Implies( + normal, + z3.Or( + z3.And(no_pipe_or_with_corr), + z3.And(no_pipe_or_no_corr), + ), + )) + + def constraint_corr_para(self) -> None: + """for corr surf parallel to the normal , even number of them exist.""" + for s in range(self.n_s): + for i in range(self.n_i): + for j in range(self.n_j): + for k in range(self.n_k): + if (i, j, k) not in self.port_cubes: + # only X or Z spiders, if normal is K + normal = z3.And( + z3.Not(self.vars["NodeY"][i][j][k]), + z3.Not(self.vars["ExistK"][i][j][k]), + ) + if k - 1 >= 0: + normal = z3.And( + normal, + z3.Not(self.vars["ExistK"][i][j][k - 1])) + + # unlike in constraint_corr_perp, we only care + # about the cases where the pipe exists and the + # correlation surface parallel to K also is present + # so we build intermediate expressions as below + pipe_with_corr = [ + z3.And( + self.vars["ExistI"][i][j][k], + self.vars["CorrIK"][s][i][j][k], + ), + z3.And( + self.vars["ExistJ"][i][j][k], + self.vars["CorrJK"][s][i][j][k], + ), + ] + + # add (i-1,j,k)-(i,j,k) to the expression + if i - 1 >= 0: + pipe_with_corr.append( + z3.And( + self.vars["ExistI"][i - 1][j][k], + self.vars["CorrIK"][s][i - 1][j][k], + )) + + # add (i,j-1,k)-(i,j,k) to the expression + if j - 1 >= 0: + pipe_with_corr.append( + z3.And( + self.vars["ExistJ"][i][j - 1][k], + self.vars["CorrJK"][s][i][j - 1][k], + )) + + # parity of the expressions must be even + self.goal.add( + z3.Implies( + normal, + cnf_even_parity_upto4(pipe_with_corr))) + + # if normal is I + normal = z3.And( + z3.Not(self.vars["NodeY"][i][j][k]), + z3.Not(self.vars["ExistI"][i][j][k]), + ) + if i - 1 >= 0: + normal = z3.And( + normal, + z3.Not(self.vars["ExistI"][i - 1][j][k])) + pipe_with_corr = [ + z3.And( + self.vars["ExistJ"][i][j][k], + self.vars["CorrJI"][s][i][j][k], + ), + z3.And( + self.vars["ExistK"][i][j][k], + self.vars["CorrKI"][s][i][j][k], + ), + ] + if j - 1 >= 0: + pipe_with_corr.append( + z3.And( + self.vars["ExistJ"][i][j - 1][k], + self.vars["CorrJI"][s][i][j - 1][k], + )) + if k - 1 >= 0: + pipe_with_corr.append( + z3.And( + self.vars["ExistK"][i][j][k - 1], + self.vars["CorrKI"][s][i][j][k - 1], + )) + self.goal.add( + z3.Implies( + normal, + cnf_even_parity_upto4(pipe_with_corr))) + + # if normal is J + normal = z3.And( + z3.Not(self.vars["NodeY"][i][j][k]), + z3.Not(self.vars["ExistJ"][i][j][k]), + ) + if j - 1 >= 0: + normal = z3.And( + normal, + z3.Not(self.vars["ExistJ"][i][j - 1][k])) + pipe_with_corr = [ + z3.And( + self.vars["ExistI"][i][j][k], + self.vars["CorrIJ"][s][i][j][k], + ), + z3.And( + self.vars["ExistK"][i][j][k], + self.vars["CorrKJ"][s][i][j][k], + ), + ] + if i - 1 >= 0: + pipe_with_corr.append( + z3.And( + self.vars["ExistI"][i - 1][j][k], + self.vars["CorrIJ"][s][i - 1][j][k], + )) + if k - 1 >= 0: + pipe_with_corr.append( + z3.And( + self.vars["ExistK"][i][j][k - 1], + self.vars["CorrKJ"][s][i][j][k - 1], + )) + self.goal.add( + z3.Implies( + normal, + cnf_even_parity_upto4(pipe_with_corr))) + + def check_z3(self, print_progress: bool = True) -> bool: + """check whether the built goal in self.goal is satisfiable. + + Args: + print_progress (bool, optional): if print out the progress made. + + Returns: + bool: True if SAT, False if UNSAT + """ + if print_progress: + print("Construct a Z3 SMT model and solve...") + start_time = time.time() + self.solver = z3.Solver() + self.solver.add(self.goal) + ifsat = self.solver.check() + elapsed = time.time() - start_time + if print_progress: + print("elapsed time: {:2f}s".format(elapsed)) + if ifsat == z3.sat: + if print_progress: + print("Z3 SAT") + return True + else: + if print_progress: + print("Z3 UNSAT") + return False + + def check_kissat( + self, + kissat_dir: str, + dimacs_file_name: Optional[str] = None, + sat_log_file_name: Optional[str] = None, + print_progress: bool = True, + ) -> bool: + """check whether there is a solution with Kissat + + Args: + kissat_dir (str): directory containing an executable named kissat + dimacs_file_name (str, optional): Defaults to None. Then, the + dimacs file is in a tmp directory. If specified, the dimacs + will be saved to that path. + sat_log_file_name (str, optional): Defaults to None. Then, the + sat log file is in a tmp directory. If specified, the sat log + will be saved to that path. + print_progress (bool, optional): whether print the SAT solving + process on screen. Defaults to True. + + Raises: + ValueError: kissat_dir is not a directory + ValueError: there is no executable kissat in kissat_dir + ValueError: the return code to kissat is neither SAT nor UNSAT + + Returns: + bool: True if SAT, False if UNSAT + """ + if not os.path.isdir(kissat_dir): + raise ValueError(f"{kissat_dir} is not a directory.") + if kissat_dir.endswith("/"): + solver_cmd = kissat_dir + "kissat" + else: + solver_cmd = kissat_dir + "/kissat" + if not os.path.isfile(solver_cmd): + raise ValueError(f"There is no kissat in {kissat_dir}.") + + if_solved = False + with tempfile.TemporaryDirectory() as tmp_dir: + # open a tmp directory as workspace + + # dimacs and sat log are either in the tmp dir, or as user specify + tmp_dimacs_file_name = (dimacs_file_name + ".dimacs" if dimacs_file_name else + tmp_dir + "/tmp.dimacs") + tmp_sat_log_file_name = (sat_log_file_name + ".kissat" if sat_log_file_name + else tmp_dir + "/tmp.sat") + + if self.write_cnf(tmp_dimacs_file_name, + print_progress=print_progress): + # continue if the CNF is non-trivial, i.e., write_cnf is True + kissat_start_time = time.time() + + with open(tmp_sat_log_file_name, "w") as log: + # use tmp_sat_log_file_name to record stdout of kissat + + kissat_return_code = -100 + # -100 if the return code is not updated later on. + + import random + with subprocess.Popen( + [ + solver_cmd, f'--seed={random.randrange(1000000)}', + tmp_dimacs_file_name + ], + stdout=subprocess.PIPE, + bufsize=1, + universal_newlines=True, + ) as run_kissat: + for line in run_kissat.stdout: + log.write(line) + if print_progress: + sys.stdout.write(line) + get_return_code = run_kissat.communicate()[0] + kissat_return_code = run_kissat.returncode + + if kissat_return_code == 10: + # 10 means SAT in Kissat + if_solved = True + if print_progress: + print( + f"kissat runtime: {time.time()-kissat_start_time}") + print("kissat SAT!") + + # we read the Kissat solution from the SAT log, then, plug + # those into the Z3 model and solved inside Z3 again. + # The reason is that Z3 did some simplification of the + # problem so not every variable appear in the DIMACS given + # to Kissat. We still need to know their value. + result = self.read_kissat_result( + tmp_dimacs_file_name, + tmp_sat_log_file_name, + ) + self.plugin_arrs(result) + self.check_z3(print_progress) + + elif kissat_return_code == 20: + if print_progress: + print(f"{solver_cmd} UNSAT") + + elif kissat_return_code == -100: + print("Did not get Kissat return code.") + + else: + raise ValueError( + f"Kissat return code {kissat_return_code} is neither" + " SAT nor UNSAT. Maybe you should add print_process=" + "True to enable the Kissat printout message to see " + "what is going on.") + # closing the tmp directory, the files and itself are removed + + return if_solved + + def write_cnf(self, + output_file_name: str, + print_progress: bool = False) -> bool: + """generate CNF for the problem. + + Args: + output_file_name (str): file to write CNF. + + Returns: + bool: False if the CNF is trivial, True otherwise + """ + cnf_start_time = time.time() + simplified = z3.Tactic("simplify")(self.goal)[0] + simplified = z3.Tactic("propagate-values")(simplified)[0] + cnf = z3.Tactic("tseitin-cnf")(simplified)[0] + dimacs = cnf.dimacs() + if print_progress: + print(f"CNF generation time: {time.time() - cnf_start_time}") + + with open(output_file_name, "w") as output_f: + output_f.write(cnf.dimacs()) + if dimacs.startswith("p cnf 1 1"): + print("Generated CNF is trivial meaning z3 concludes the instance" + " UNSAT during simplification.") + return False + else: + return True + + def read_kissat_result(self, dimacs_file: str, + result_file: str) -> Mapping[str, Any]: + """read result from external SAT solver + + Args: + dimacs_file (str): + result_file (str): log from Kissat containing SAT assignments + + Raises: + ValueError: in the dimacs file, the last lines are comments that + records the mapping from SAT variable indices to the variable + names in Z3. If the coordinates in this name is incorrect. + + Returns: + Mapping[str, Any]: variable assignment in arrays. All the one with + a corresponding SAT variable are read off from the SAT log. + The others are left with -1. + """ + results = { + "ExistI": [[[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i)], + "ExistJ": [[[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i)], + "ExistK": [[[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i)], + "ColorI": [[[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i)], + "ColorJ": [[[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i)], + "NodeY": [[[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i)], + "CorrIJ": [[[[-1 for _ in range(self.n_k)] + for _ in range(self.n_j)] for _ in range(self.n_i)] + for _ in range(self.n_s)], + "CorrIK": [[[[-1 for _ in range(self.n_k)] + for _ in range(self.n_j)] for _ in range(self.n_i)] + for _ in range(self.n_s)], + "CorrJK": [[[[-1 for _ in range(self.n_k)] + for _ in range(self.n_j)] for _ in range(self.n_i)] + for _ in range(self.n_s)], + "CorrJI": [[[[-1 for _ in range(self.n_k)] + for _ in range(self.n_j)] for _ in range(self.n_i)] + for _ in range(self.n_s)], + "CorrKI": [[[[-1 for _ in range(self.n_k)] + for _ in range(self.n_j)] for _ in range(self.n_i)] + for _ in range(self.n_s)], + "CorrKJ": [[[[-1 for _ in range(self.n_k)] + for _ in range(self.n_j)] for _ in range(self.n_i)] + for _ in range(self.n_s)], + } + + # in this file, the assigments are lines starting with "v" like + # v -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 ... + # the vars starts from 1 and - means it's False; otherwise, it's True + # we scan through all these lines, and save the assignments to `sat` + with open(result_file, "r") as f: + sat_output = f.readlines() + sat = {} + for line in sat_output: + if line.startswith("v"): + assignments = line[1:].strip().split(" ") + for assignment in assignments: + tmp = int(assignment) + if tmp < 0: + sat[str(-tmp)] = 0 + elif tmp > 0: + sat[str(tmp)] = 1 + + # in the dimacs generated by Z3, there are lines starting with "c" like + # c 8804 CorrIJ(1,0,3,4) or c 60053 k!44404 + # which records the mapping from our variables to variables in dimacs + # the ones starting with k! are added in the translation, we don"t care + with open(dimacs_file, "r") as f: + dimacs = f.readlines() + for line in dimacs: + if line.startswith("c"): + _, index, name = line.strip().split(" ") + if name.startswith(( + "NodeY", + "ExistI", + "ExistJ", + "ExistK", + "ColorI", + "ColorJ", + "CorrIJ", + "CorrIK", + "CorrJI", + "CorrJK", + "CorrKI", + "CorrKJ", + )): + arr, tmp = name[:-1].split("(") + coords = [int(num) for num in tmp.split(",")] + if len(coords) == 3: + results[arr][coords[0]][coords[1]][ + coords[2]] = sat[index] + elif len(coords) == 4: + results[arr][coords[0]][coords[1]][coords[2]][ + coords[3]] = sat[index] + else: + raise ValueError("number of coord should be 3 or 4!") + + return results + + def get_result(self) -> Mapping[str, Any]: + """get the variable values. + + Returns: + Mapping[str, Any]: output in the LaSRe format + """ + model = self.solver.model() + data = { + "n_i": + self.n_i, + "n_j": + self.n_j, + "n_k": + self.n_k, + "n_p": + self.n_p, + "n_s": + self.n_s, + "ports": + self.ports, + "stabs": + self.stabs, + "port_cubes": + self.port_cubes, + "optional": + self.optional, + "ExistI": [[[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i)], + "ExistJ": [[[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i)], + "ExistK": [[[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i)], + "ColorI": [[[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i)], + "ColorJ": [[[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i)], + "NodeY": [[[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] + for _ in range(self.n_i)], + "CorrIJ": [[[[-1 for _ in range(self.n_k)] + for _ in range(self.n_j)] for _ in range(self.n_i)] + for _ in range(self.n_s)], + "CorrIK": [[[[-1 for _ in range(self.n_k)] + for _ in range(self.n_j)] for _ in range(self.n_i)] + for _ in range(self.n_s)], + "CorrJK": [[[[-1 for _ in range(self.n_k)] + for _ in range(self.n_j)] for _ in range(self.n_i)] + for _ in range(self.n_s)], + "CorrJI": [[[[-1 for _ in range(self.n_k)] + for _ in range(self.n_j)] for _ in range(self.n_i)] + for _ in range(self.n_s)], + "CorrKI": [[[[-1 for _ in range(self.n_k)] + for _ in range(self.n_j)] for _ in range(self.n_i)] + for _ in range(self.n_s)], + "CorrKJ": [[[[-1 for _ in range(self.n_k)] + for _ in range(self.n_j)] for _ in range(self.n_i)] + for _ in range(self.n_s)], + } + arrs = [ + "NodeY", + "ExistI", + "ExistJ", + "ExistK", + ] + if self.color_ij: + arrs += [ + "ColorI", + "ColorJ", + ] + for s in range(self.n_s): + for i in range(self.n_i): + for j in range(self.n_j): + for k in range(self.n_k): + if s == 0: # Exist, Node, and Color vars + for arr in arrs: + data[arr][i][j][k] = ( + 1 if model[self.vars[arr][i][j][k]] else 0) + + # Corr vars + for arr in [ + "CorrIJ", + "CorrIK", + "CorrJI", + "CorrJK", + "CorrKI", + "CorrKJ", + ]: + data[arr][s][i][j][k] = ( + 1 if model[self.vars[arr][s][i][j][k]] else 0) + return data diff --git a/glue/lattice_surgery/lassynth/tools/__init__.py b/glue/lattice_surgery/lassynth/tools/__init__.py new file mode 100644 index 000000000..e69de29bb diff --git a/glue/lattice_surgery/lassynth/tools/verify_stabilizers.py b/glue/lattice_surgery/lassynth/tools/verify_stabilizers.py new file mode 100644 index 000000000..25fba0b81 --- /dev/null +++ b/glue/lattice_surgery/lassynth/tools/verify_stabilizers.py @@ -0,0 +1,38 @@ +from typing import Sequence +import stim +import stimzx + + +def verify_stabilizers( + specified_paulistrings: Sequence[str], + result_networkx, + print_stabilizers: bool = False, +) -> bool: + result_stabilizers = [ + stab.output + for stab in stimzx.zx_graph_to_external_stabilizers(result_networkx) + ] + specified_stabilizers = [ + stim.PauliString(paulistring) for paulistring in specified_paulistrings + ] + if print_stabilizers: + print("specified:") + for s in specified_stabilizers: + print(s) + print("==============================================================") + print("resulting:") + for s in result_stabilizers: + print(s) + print("==============================================================") + + for s in result_stabilizers: + for ss in specified_stabilizers: + if not ss.commutes(s): + print(f"result stabilizer {s} not commuting with " + f"specified stabilizer {ss}") + if print_stabilizers: + print("specified and resulting stabilizers not equivalent") + return False + if print_stabilizers: + print("specified and resulting stabilizers are equivalent.") + return True diff --git a/glue/lattice_surgery/lassynth/translators/__init__.py b/glue/lattice_surgery/lassynth/translators/__init__.py new file mode 100644 index 000000000..e93e0abc4 --- /dev/null +++ b/glue/lattice_surgery/lassynth/translators/__init__.py @@ -0,0 +1 @@ +from lassynth.translators.zx_grid_graph import ZXGridGraph diff --git a/glue/lattice_surgery/lassynth/translators/gltf_generator.py b/glue/lattice_surgery/lassynth/translators/gltf_generator.py new file mode 100644 index 000000000..20ce69be7 --- /dev/null +++ b/glue/lattice_surgery/lassynth/translators/gltf_generator.py @@ -0,0 +1,2622 @@ +"""generating a 3D modelling file in gltf format from our LaSRe.""" + +import json +from typing import Any, Mapping, Optional, Sequence, Tuple + +# constants +SQ2 = 0.707106769085 # square root of 2 +THICKNESS = 0.01 # half separation of front and back sides of each face +AXESTHICKNESS = 0.1 + +def float_to_little_endian_hex(f): + from struct import pack + + # Pack the float into a binary string using the little-endian format + binary_data = pack(" Mapping[str, Any]: + """generate basic gltf contents, i.e., independent from the LaS + + Args: + tubelen (float, optional): ratio of the length of the pipe with respect + to the length of a cube. Defaults to 2.0. + + Returns: + Mapping[str, Any]: gltf with everything here. + """ + # floats as hex, little endian + floats = { + "0": "00000000", + "1": "0000803F", + "-1": "000080BF", + "0.5": "0000003F", + "0.45": "6666E63E", + } + floats["tube"] = float_to_little_endian_hex(tubelen) + floats["+SQ2"] = float_to_little_endian_hex(SQ2) + floats["-SQ2"] = float_to_little_endian_hex(-SQ2) + floats["+T"] = float_to_little_endian_hex(THICKNESS) + floats["-T"] = float_to_little_endian_hex(-THICKNESS) + floats["1-T"] = float_to_little_endian_hex(1 - THICKNESS) + floats["T-1"] = float_to_little_endian_hex(THICKNESS - 1) + floats["0.5+T"] = float_to_little_endian_hex(0.5 + THICKNESS) + floats["0.5-T"] = float_to_little_endian_hex(0.5 - THICKNESS) + + # integers as hex + ints = ["0000", "0100", "0200", "0300", "0400", "0500", "0600", "0700"] + + gltf = { + "asset": { + "generator": "LaSRe CodeGen by Daniel Bochen Tan", + "version": "2.0" + }, + "scene": 0, + "scenes": [{ + "name": "Scene", + "nodes": [0] + }], + "nodes": [{ + "name": "Lattice Surgery Subroutine", + "children": [] + }], + } + gltf["accessors"] = [] + gltf["buffers"] = [] + gltf["bufferViews"] = [] + + # materials are the colors. baseColorFactor is (R, G, B, alpha) + gltf["materials"] = [ + { + "name": "0-blue", + "pbrMetallicRoughness": { + "baseColorFactor": [0, 0, 1, 1] + }, + "doubleSided": False, + }, + { + "name": "1-red", + "pbrMetallicRoughness": { + "baseColorFactor": [1, 0, 0, 1] + }, + "doubleSided": False, + }, + { + "name": "2-green", + "pbrMetallicRoughness": { + "baseColorFactor": [0, 1, 0, 1] + }, + "doubleSided": False, + }, + { + "name": "3-gray", + "pbrMetallicRoughness": { + "baseColorFactor": [0.5, 0.5, 0.5, 1] + }, + "doubleSided": False, + }, + { + "name": "4-cyan.3", + "pbrMetallicRoughness": { + "baseColorFactor": [0, 1, 1, 0.3] + }, + "doubleSided": False, + "alphaMode": "BLEND", + }, + { + "name": "5-black", + "pbrMetallicRoughness": { + "baseColorFactor": [0, 0, 0, 1] + }, + "doubleSided": False, + }, + { + "name": "6-yellow", + "pbrMetallicRoughness": { + "baseColorFactor": [1, 1, 0, 1] + }, + "doubleSided": False, + }, + { + "name": "7-white", + "pbrMetallicRoughness": { + "baseColorFactor": [1, 1, 1, 1] + }, + "doubleSided": False, + }, + ] + + # for a 3D coordinate (X,Y,Z), the convention of VEC3 in GLTF is (X,Z,-Y) + # below are the data we store into the embedded binary in the GLTF. + # For each data, we create a buffer, there is one and only one bufferView + # for this buffer, and there is one and only one accessor for this + # bufferView. This is for simplicity. So in what follows, we always gather + # the string corresponding to the data, whether they're a list of floats or + # a list of integers. Then, we append a buffer, a bufferView, and an + # accessor to the GLTF. This part is quite machinary. + + # GLTF itself support doubleside color in materials, but this can lead to + # problems when converting to other formats. So, for each face of a cube or + # a pipe, we will make it two sides, front and back. The POSITION of + # vertices of these two are shifted on the Z axis by 2*THICKNESS. Since we + # need their color to both facing outside, the back side require opposite + # NORMAL vectors, and the index order needs to be reversed. We begin with + # definition for the front sides. + + # 0, positions of square: [(+T,+T,-T),(1-T,+T,-T),(+T,1-T,-T),(1-T,1-T,-T)] + s = (floats["+T"] + floats["-T"] + floats["-T"] + floats["1-T"] + + floats["-T"] + floats["-T"] + floats["+T"] + floats["-T"] + + floats["T-1"] + floats["1-T"] + floats["-T"] + floats["T-1"]) + gltf["buffers"].append({"byteLength": 48, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 0, + "byteLength": 48, + "byteOffset": 0, + "target": 34962 + }) + gltf["accessors"].append({ + "bufferView": 0, + "componentType": 5126, + "type": "VEC3", + "count": 4, + "max": [1 - THICKNESS, -THICKNESS, -THICKNESS], + "min": [THICKNESS, -THICKNESS, THICKNESS - 1], + }) + + # 1, positions of rectangle: [(0,0,-T),(L,0,-T),(0,1,-T),(L,1,-T)] + s = (floats["0"] + floats["-T"] + floats["0"] + floats["tube"] + + floats["-T"] + floats["0"] + floats["0"] + floats["-T"] + + floats["-1"] + floats["tube"] + floats["-T"] + floats["-1"]) + gltf["buffers"].append({"byteLength": 48, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 1, + "byteLength": 48, + "byteOffset": 0, + "target": 34962 + }) + gltf["accessors"].append({ + "bufferView": 1, + "componentType": 5126, + "type": "VEC3", + "count": 4, + "max": [tubelen, -THICKNESS, 0], + "min": [0, -THICKNESS, -1], + }) + + # 2, normals of rect/sqr: (0,0,-1)*4 + s = (floats["0"] + floats["-1"] + floats["0"] + floats["0"] + + floats["-1"] + floats["0"] + floats["0"] + floats["-1"] + + floats["0"] + floats["0"] + floats["-1"] + floats["0"]) + gltf["buffers"].append({"byteLength": 48, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 2, + "byteLength": 48, + "byteOffset": 0, + "target": 34962 + }) + gltf["accessors"].append({ + "bufferView": 2, + "componentType": 5126, + "type": "VEC3", + "count": 4 + }) + + # 3, vertices of rect/sqr: [1,0,3, 3,0,2] + s = ints[1] + ints[0] + ints[3] + ints[3] + ints[0] + ints[2] + gltf["buffers"].append({"byteLength": 12, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 3, + "byteLength": 12, + "byteOffset": 0, + "target": 34963 + }) + gltf["accessors"].append({ + "bufferView": 3, + "componentType": 5123, + "type": "SCALAR", + "count": 6 + }) + + # 4, positions of tilted rect: [(0,0,1/2+T),(1/2,0,+T),(0,1,1/2+T),(1/2,1,+T)] + s = (floats["0"] + floats["0.5+T"] + floats["0"] + floats["0.5"] + + floats["+T"] + floats["0"] + floats["0"] + floats["0.5+T"] + + floats["-1"] + floats["0.5"] + floats["+T"] + floats["-1"]) + gltf["buffers"].append({"byteLength": 48, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 4, + "byteLength": 48, + "byteOffset": 0, + "target": 34962 + }) + gltf["accessors"].append({ + "bufferView": 4, + "componentType": 5126, + "type": "VEC3", + "count": 4, + "max": [0.5, 0.5 + THICKNESS, 0], + "min": [0, THICKNESS, -1], + }) + + # 5, normals of tilted rect: (-sqrt(2)/2, 0, -sqrt(2)/2)*4 + s = (floats["-SQ2"] + floats["-SQ2"] + floats["0"] + floats["-SQ2"] + + floats["-SQ2"] + floats["0"] + floats["-SQ2"] + floats["-SQ2"] + + floats["0"] + floats["-SQ2"] + floats["-SQ2"] + floats["0"]) + gltf["buffers"].append({"byteLength": 48, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 5, + "byteLength": 48, + "byteOffset": 0, + "target": 34962 + }) + gltf["accessors"].append({ + "bufferView": 5, + "componentType": 5126, + "type": "VEC3", + "count": 4 + }) + + # 6, positions of Hadamard rectangle: [(0,0,-T),(15/32L,0,-T),(15/32L,1,-T), + # (15/32L,1,-T),(17/32L,0,-T),(17/32L,1,-T),(L,0,-T),(L,1,-T)] + floats["left"] = float_to_little_endian_hex(tubelen * 15 / 32) + floats["right"] = float_to_little_endian_hex(tubelen * 17 / 32) + s = (floats["0"] + floats["-T"] + floats["0"] + floats["left"] + + floats["-T"] + floats["0"] + floats["0"] + floats["-T"] + + floats["-1"] + floats["left"] + floats["-T"] + floats["-1"] + + floats["right"] + floats["-T"] + floats["0"] + floats["right"] + + floats["-T"] + floats["-1"] + floats["tube"] + floats["-T"] + + floats["0"] + floats["tube"] + floats["-T"] + floats["-1"]) + gltf["buffers"].append({"byteLength": 96, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 6, + "byteLength": 96, + "byteOffset": 0, + "target": 34962 + }) + gltf["accessors"].append({ + "bufferView": 6, + "componentType": 5126, + "type": "VEC3", + "count": 8, + "max": [tubelen, -THICKNESS, 0], + "min": [0, -THICKNESS, -1], + }) + + # 7, normals of Hadamard rect (0,0,-1)*8 + s = (floats["0"] + floats["-1"] + floats["0"] + floats["0"] + + floats["-1"] + floats["0"] + floats["0"] + floats["-1"] + + floats["0"] + floats["0"] + floats["-1"] + floats["0"] + floats["0"] + + floats["-1"] + floats["0"] + floats["0"] + floats["-1"] + + floats["0"] + floats["0"] + floats["-1"] + floats["0"] + floats["0"] + + floats["-1"] + floats["0"]) + gltf["buffers"].append({"byteLength": 96, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 7, + "byteLength": 96, + "byteOffset": 0, + "target": 34962 + }) + gltf["accessors"].append({ + "bufferView": 7, + "componentType": 5126, + "type": "VEC3", + "count": 8 + }) + + # 8, vertices of middle rect in Hadamard rect: [4,1,5, 5,1,3] + s = ints[4] + ints[1] + ints[5] + ints[5] + ints[1] + ints[3] + gltf["buffers"].append({"byteLength": 12, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 8, + "byteLength": 12, + "byteOffset": 0, + "target": 34963 + }) + gltf["accessors"].append({ + "bufferView": 8, + "componentType": 5123, + "type": "SCALAR", + "count": 6 + }) + + # 9, vertices of upper rect in Hadamard rect: [6,4,7, 7,4,5] + s = ints[6] + ints[4] + ints[7] + ints[7] + ints[4] + ints[5] + gltf["buffers"].append({"byteLength": 12, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 9, + "byteLength": 12, + "byteOffset": 0, + "target": 34963 + }) + gltf["accessors"].append({ + "bufferView": 9, + "componentType": 5123, + "type": "SCALAR", + "count": 6 + }) + + # 10, vertices of lines around a face: [0,1, 0,2, 2,3, 3,1] + # GLTF supports drawing lines, but there may be a problem converting to + # other formats. We have thus not used these data. + s = (ints[0] + ints[1] + ints[0] + ints[2] + ints[2] + ints[3] + ints[3] + + ints[1]) + gltf["buffers"].append({"byteLength": 16, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 10, + "byteLength": 16, + "byteOffset": 0, + "target": 34963 + }) + gltf["accessors"].append({ + "bufferView": 10, + "componentType": 5123, + "type": "SCALAR", + "count": 8 + }) + + # 11, positions of half-distance rectangle: [(0,0,-T),(0.45,0,-T),(0,1,-T),(0.45,1,-T)] + s = (floats["0"] + floats["-T"] + floats["0"] + floats["0.45"] + + floats["-T"] + floats["0"] + floats["0"] + floats["-T"] + + floats["-1"] + floats["0.45"] + floats["-T"] + floats["-1"]) + gltf["buffers"].append({"byteLength": 48, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 11, + "byteLength": 48, + "byteOffset": 0, + "target": 34962 + }) + gltf["accessors"].append({ + "bufferView": 11, + "componentType": 5126, + "type": "VEC3", + "count": 4, + "max": [0.45, -THICKNESS, 0], + "min": [0, -THICKNESS, -1], + }) + + # 12, backside, positions of square: [(+T,+T,+T),(1-T,+T,+T),(+T,1-T,+T),(1-T,1-T,+T)] + s = (floats["+T"] + floats["+T"] + floats["-T"] + floats["1-T"] + + floats["+T"] + floats["-T"] + floats["+T"] + floats["+T"] + + floats["T-1"] + floats["1-T"] + floats["+T"] + floats["T-1"]) + gltf["buffers"].append({"byteLength": 48, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 12, + "byteLength": 48, + "byteOffset": 0, + "target": 34962 + }) + gltf["accessors"].append({ + "bufferView": 12, + "componentType": 5126, + "type": "VEC3", + "count": 4, + "max": [1 - THICKNESS, THICKNESS, -THICKNESS], + "min": [THICKNESS, THICKNESS, THICKNESS - 1], + }) + + # 13, backside, normals of rect/sqr: (0,0,1)*4 + s = (floats["0"] + floats["1"] + floats["0"] + floats["0"] + floats["1"] + + floats["0"] + floats["0"] + floats["1"] + floats["0"] + floats["0"] + + floats["1"] + floats["0"]) + gltf["buffers"].append({"byteLength": 48, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 13, + "byteLength": 48, + "byteOffset": 0, + "target": 34962 + }) + gltf["accessors"].append({ + "bufferView": 13, + "componentType": 5126, + "type": "VEC3", + "count": 4 + }) + + # For the cubes, we want to draw black lines around its boundaries to help + # people identify them visually. However, drawing lines in GLTF may become + # a problem when converting to other formats. Here, we define super thin + # rectangles at the boundaries of squares which will be seen as lines. + + # 14, frontside, positions of edge 0: [(+T,0,-T),(1-T,0,-T),(+T,+T,-T),(1-T,+T,-T)] + s = (floats["+T"] + floats["-T"] + floats["0"] + floats["1-T"] + + floats["-T"] + floats["0"] + floats["+T"] + floats["-T"] + + floats["-T"] + floats["1-T"] + floats["-T"] + floats["-T"]) + gltf["buffers"].append({"byteLength": 48, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 14, + "byteLength": 48, + "byteOffset": 0, + "target": 34962 + }) + gltf["accessors"].append({ + "bufferView": 14, + "componentType": 5126, + "type": "VEC3", + "count": 4, + "max": [1 - THICKNESS, -THICKNESS, 0], + "min": [THICKNESS, -THICKNESS, -THICKNESS], + }) + + # 15, frontside, positions of edge 1: [(1-T,+T,-T),(1,+T,-T),(1-T,1-T,-T),(1,1-T,-T)] + s = (floats["1-T"] + floats["-T"] + floats["-T"] + floats["1"] + + floats["-T"] + floats["-T"] + floats["1-T"] + floats["-T"] + + floats["T-1"] + floats["1"] + floats["-T"] + floats["T-1"]) + gltf["buffers"].append({"byteLength": 48, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 15, + "byteLength": 48, + "byteOffset": 0, + "target": 34962 + }) + gltf["accessors"].append({ + "bufferView": 15, + "componentType": 5126, + "type": "VEC3", + "count": 4, + "max": [1, -THICKNESS, -THICKNESS], + "min": [1 - THICKNESS, -THICKNESS, THICKNESS - 1], + }) + + # 16, frontside, positions of edge 2: [(0,+T,-T),(+T,+T,-T),(0,1-T,-T),(+T,1-T,-T)] + s = (floats["0"] + floats["-T"] + floats["-T"] + floats["+T"] + + floats["-T"] + floats["-T"] + floats["0"] + floats["-T"] + + floats["T-1"] + floats["+T"] + floats["-T"] + floats["T-1"]) + gltf["buffers"].append({"byteLength": 48, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 16, + "byteLength": 48, + "byteOffset": 0, + "target": 34962 + }) + gltf["accessors"].append({ + "bufferView": 16, + "componentType": 5126, + "type": "VEC3", + "count": 4, + "max": [THICKNESS, -THICKNESS, -THICKNESS], + "min": [0, -THICKNESS, THICKNESS - 1], + }) + + # 17, frontside, positions of edge 3: [(+T,1-T,-T),(1-T,1-T,-T),(+T,1,-T),(1-T,1,-T)] + s = (floats["+T"] + floats["-T"] + floats["T-1"] + floats["1-T"] + + floats["-T"] + floats["T-1"] + floats["+T"] + floats["-T"] + + floats["-1"] + floats["1-T"] + floats["-T"] + floats["-1"]) + gltf["buffers"].append({"byteLength": 48, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 17, + "byteLength": 48, + "byteOffset": 0, + "target": 34962 + }) + gltf["accessors"].append({ + "bufferView": 17, + "componentType": 5126, + "type": "VEC3", + "count": 4, + "max": [1 - THICKNESS, -THICKNESS, THICKNESS - 1], + "min": [THICKNESS, -THICKNESS, -1], + }) + + # 18, backside, positions of edge 0: [(+T,0,+T),(1-T,0,+T),(+T,+T,+T),(1-T,+T,+T)] + s = (floats["+T"] + floats["+T"] + floats["0"] + floats["1-T"] + + floats["+T"] + floats["0"] + floats["+T"] + floats["+T"] + + floats["-T"] + floats["1-T"] + floats["+T"] + floats["-T"]) + gltf["buffers"].append({"byteLength": 48, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 18, + "byteLength": 48, + "byteOffset": 0, + "target": 34962 + }) + gltf["accessors"].append({ + "bufferView": 18, + "componentType": 5126, + "type": "VEC3", + "count": 4, + "max": [1 - THICKNESS, THICKNESS, 0], + "min": [THICKNESS, THICKNESS, -THICKNESS], + }) + + # 19, backside, positions of edge 1: [(1-T,+T,+T),(1,+T,+T),(1-T,1-T,+T),(1,1-T,+T)] + s = (floats["1-T"] + floats["+T"] + floats["-T"] + floats["1"] + + floats["+T"] + floats["-T"] + floats["1-T"] + floats["+T"] + + floats["T-1"] + floats["1"] + floats["+T"] + floats["T-1"]) + gltf["buffers"].append({"byteLength": 48, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 19, + "byteLength": 48, + "byteOffset": 0, + "target": 34962 + }) + gltf["accessors"].append({ + "bufferView": 19, + "componentType": 5126, + "type": "VEC3", + "count": 4, + "max": [1, THICKNESS, -THICKNESS], + "min": [1 - THICKNESS, THICKNESS, THICKNESS - 1], + }) + + # 20, backside, positions of edge 2: [(0,+T,+T),(+T,+T,+T),(0,1-T,+T),(+T,1-T,+T)] + s = (floats["0"] + floats["+T"] + floats["-T"] + floats["+T"] + + floats["+T"] + floats["-T"] + floats["0"] + floats["+T"] + + floats["T-1"] + floats["+T"] + floats["+T"] + floats["T-1"]) + gltf["buffers"].append({"byteLength": 48, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 20, + "byteLength": 48, + "byteOffset": 0, + "target": 34962 + }) + gltf["accessors"].append({ + "bufferView": 20, + "componentType": 5126, + "type": "VEC3", + "count": 4, + "max": [THICKNESS, THICKNESS, -THICKNESS], + "min": [0, THICKNESS, THICKNESS - 1], + }) + + # 21, backside, positions of edge 3: [(+T,1-T,+T),(1-T,1-T,+T),(+T,1,+T),(1-T,1,+T)] + s = (floats["+T"] + floats["+T"] + floats["T-1"] + floats["1-T"] + + floats["+T"] + floats["T-1"] + floats["+T"] + floats["+T"] + + floats["-1"] + floats["1-T"] + floats["+T"] + floats["-1"]) + gltf["buffers"].append({"byteLength": 48, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 21, + "byteLength": 48, + "byteOffset": 0, + "target": 34962 + }) + gltf["accessors"].append({ + "bufferView": 21, + "componentType": 5126, + "type": "VEC3", + "count": 4, + "max": [1 - THICKNESS, THICKNESS, THICKNESS - 1], + "min": [THICKNESS, THICKNESS, -1], + }) + + # 22, backside vertices of rect/sqr: [1,3,0, 3,2,0] + s = ints[1] + ints[3] + ints[0] + ints[3] + ints[2] + ints[0] + gltf["buffers"].append({"byteLength": 12, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 22, + "byteLength": 12, + "byteOffset": 0, + "target": 34963 + }) + gltf["accessors"].append({ + "bufferView": 22, + "componentType": 5123, + "type": "SCALAR", + "count": 6 + }) + + # 23, backside, positions of rectangle: [(0,0,+T),(L,0,+T),(0,1,+T),(L,1,+T)] + s = (floats["0"] + floats["+T"] + floats["0"] + floats["tube"] + + floats["+T"] + floats["0"] + floats["0"] + floats["+T"] + + floats["-1"] + floats["tube"] + floats["+T"] + floats["-1"]) + gltf["buffers"].append({"byteLength": 48, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 23, + "byteLength": 48, + "byteOffset": 0, + "target": 34962 + }) + gltf["accessors"].append({ + "bufferView": 23, + "componentType": 5126, + "type": "VEC3", + "count": 4, + "max": [tubelen, THICKNESS, 0], + "min": [0, THICKNESS, -1], + }) + + # 24, backside, positions of half-distance rectangle: [(0,0,+T),(0.45,0,+T),(0,1,+T),(0.45,1,+T)] + s = (floats["0"] + floats["+T"] + floats["0"] + floats["0.45"] + + floats["+T"] + floats["0"] + floats["0"] + floats["+T"] + + floats["-1"] + floats["0.45"] + floats["+T"] + floats["-1"]) + gltf["buffers"].append({"byteLength": 48, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 24, + "byteLength": 48, + "byteOffset": 0, + "target": 34962 + }) + gltf["accessors"].append({ + "bufferView": 24, + "componentType": 5126, + "type": "VEC3", + "count": 4, + "max": [0.45, THICKNESS, 0], + "min": [0, THICKNESS, -1], + }) + + # 25, backside, positions of Hadamard rectangle: [(0,0,+T),(15/32L,0,+T),(15/32L,1,+T), + # (15/32L,1,+T),(17/32L,0,+T),(17/32L,1,+T),(L,0,+T),(L,1,+T)] + floats["left"] = float_to_little_endian_hex(tubelen * 15 / 32) + floats["right"] = float_to_little_endian_hex(tubelen * 17 / 32) + s = (floats["0"] + floats["+T"] + floats["0"] + floats["left"] + + floats["+T"] + floats["0"] + floats["0"] + floats["+T"] + + floats["-1"] + floats["left"] + floats["+T"] + floats["-1"] + + floats["right"] + floats["+T"] + floats["0"] + floats["right"] + + floats["+T"] + floats["-1"] + floats["tube"] + floats["+T"] + + floats["0"] + floats["tube"] + floats["+T"] + floats["-1"]) + gltf["buffers"].append({"byteLength": 96, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 25, + "byteLength": 96, + "byteOffset": 0, + "target": 34962 + }) + gltf["accessors"].append({ + "bufferView": 25, + "componentType": 5126, + "type": "VEC3", + "count": 8, + "max": [tubelen, THICKNESS, 0], + "min": [0, THICKNESS, -1], + }) + + # 26, backside, normals of Hadamard rect (0,0,1)*8 + s = (floats["0"] + floats["1"] + floats["0"] + floats["0"] + floats["1"] + + floats["0"] + floats["0"] + floats["1"] + floats["0"] + floats["0"] + + floats["1"] + floats["0"] + floats["0"] + floats["1"] + floats["0"] + + floats["0"] + floats["1"] + floats["0"] + floats["0"] + floats["1"] + + floats["0"] + floats["0"] + floats["1"] + floats["0"]) + gltf["buffers"].append({"byteLength": 96, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 26, + "byteLength": 96, + "byteOffset": 0, + "target": 34962 + }) + gltf["accessors"].append({ + "bufferView": 26, + "componentType": 5126, + "type": "VEC3", + "count": 8 + }) + + # 27, backside, vertices of middle rect in Hadamard rect: [4,5,1, 5,3,1] + s = ints[4] + ints[5] + ints[1] + ints[5] + ints[3] + ints[1] + gltf["buffers"].append({"byteLength": 12, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 27, + "byteLength": 12, + "byteOffset": 0, + "target": 34963 + }) + gltf["accessors"].append({ + "bufferView": 27, + "componentType": 5123, + "type": "SCALAR", + "count": 6 + }) + + # 28, backside, vertices of upper rect in Hadamard rect: [6,7,4, 7,5,4] + s = ints[6] + ints[7] + ints[4] + ints[7] + ints[5] + ints[4] + gltf["buffers"].append({"byteLength": 12, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 28, + "byteLength": 12, + "byteOffset": 0, + "target": 34963 + }) + gltf["accessors"].append({ + "bufferView": 28, + "componentType": 5123, + "type": "SCALAR", + "count": 6 + }) + + # 29, backside, positions of tilted rect: [(0,0,1/2+T),(1/2,0,+T),(0,1,1/2+T),(1/2,1,+T)] + s = (floats["0"] + floats["0.5-T"] + floats["0"] + floats["0.5"] + + floats["-T"] + floats["0"] + floats["0"] + floats["0.5-T"] + + floats["-1"] + floats["0.5"] + floats["-T"] + floats["-1"]) + gltf["buffers"].append({"byteLength": 48, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 29, + "byteLength": 48, + "byteOffset": 0, + "target": 34962 + }) + gltf["accessors"].append({ + "bufferView": 29, + "componentType": 5126, + "type": "VEC3", + "count": 4, + "max": [0.5, 0.5 - THICKNESS, 0], + "min": [0, -THICKNESS, -1], + }) + + # 30, backside, normals of tilted rect: (sqrt(2)/2, 0, sqrt(2)/2)*4 + s = (floats["+SQ2"] + floats["+SQ2"] + floats["0"] + floats["+SQ2"] + + floats["+SQ2"] + floats["0"] + floats["+SQ2"] + floats["+SQ2"] + + floats["0"] + floats["+SQ2"] + floats["+SQ2"] + floats["0"]) + gltf["buffers"].append({"byteLength": 48, "uri": hex_to_bin(s)}) + gltf["bufferViews"].append({ + "buffer": 30, + "byteLength": 48, + "byteOffset": 0, + "target": 34962 + }) + gltf["accessors"].append({ + "bufferView": 30, + "componentType": 5126, + "type": "VEC3", + "count": 4 + }) + + # finished creating the binary + + # Now we create meshes. These are the real constructors of the 3D diagram. + # a mesh can contain multiple primitives. A primitive can be defined by a + # set of vertices POSITION, their NORMAL vectors, the order of going around + # these vertices, and the color (material) for the triangles defined by + # going around the vertices. `mode:4` means color these triangles. + gltf["meshes"] = [ + { + "name": + "0-square-blue", + "primitives": [ + # front side + { + "attributes": { + "NORMAL": 2, + "POSITION": 0 + }, + "indices": 3, + "material": 0, + "mode": 4, + }, + # back side + { + "attributes": { + "NORMAL": 13, + "POSITION": 12 + }, + "indices": 22, + "material": 0, + "mode": 4, + }, + # front side edge 0 + { + "attributes": { + "NORMAL": 2, + "POSITION": 14 + }, + "indices": 3, + "material": 5, + "mode": 4, + }, + # front side edge 1 + { + "attributes": { + "NORMAL": 2, + "POSITION": 15 + }, + "indices": 3, + "material": 5, + "mode": 4, + }, + # front side edge 2 + { + "attributes": { + "NORMAL": 2, + "POSITION": 16 + }, + "indices": 3, + "material": 5, + "mode": 4, + }, + # front side edge 3 + { + "attributes": { + "NORMAL": 2, + "POSITION": 17 + }, + "indices": 3, + "material": 5, + "mode": 4, + }, + # back side edge 0 + { + "attributes": { + "NORMAL": 13, + "POSITION": 18 + }, + "indices": 22, + "material": 5, + "mode": 4, + }, + # back side edge 1 + { + "attributes": { + "NORMAL": 13, + "POSITION": 19 + }, + "indices": 22, + "material": 5, + "mode": 4, + }, + # back side edge 2 + { + "attributes": { + "NORMAL": 13, + "POSITION": 20 + }, + "indices": 22, + "material": 5, + "mode": 4, + }, + # back side edge 3 + { + "attributes": { + "NORMAL": 13, + "POSITION": 21 + }, + "indices": 22, + "material": 5, + "mode": 4, + }, + ], + }, + { + "name": + "1-square-red", + "primitives": [ + # front side + { + "attributes": { + "NORMAL": 2, + "POSITION": 0 + }, + "indices": 3, + "material": 1, + "mode": 4, + }, + # back side + { + "attributes": { + "NORMAL": 13, + "POSITION": 12 + }, + "indices": 22, + "material": 1, + "mode": 4, + }, + # front side edge 0 + { + "attributes": { + "NORMAL": 2, + "POSITION": 14 + }, + "indices": 3, + "material": 5, + "mode": 4, + }, + # front side edge 1 + { + "attributes": { + "NORMAL": 2, + "POSITION": 15 + }, + "indices": 3, + "material": 5, + "mode": 4, + }, + # front side edge 2 + { + "attributes": { + "NORMAL": 2, + "POSITION": 16 + }, + "indices": 3, + "material": 5, + "mode": 4, + }, + # front side edge 3 + { + "attributes": { + "NORMAL": 2, + "POSITION": 17 + }, + "indices": 3, + "material": 5, + "mode": 4, + }, + # back side edge 0 + { + "attributes": { + "NORMAL": 13, + "POSITION": 18 + }, + "indices": 22, + "material": 5, + "mode": 4, + }, + # back side edge 1 + { + "attributes": { + "NORMAL": 13, + "POSITION": 19 + }, + "indices": 22, + "material": 5, + "mode": 4, + }, + # back side edge 2 + { + "attributes": { + "NORMAL": 13, + "POSITION": 20 + }, + "indices": 22, + "material": 5, + "mode": 4, + }, + # back side edge 3 + { + "attributes": { + "NORMAL": 13, + "POSITION": 21 + }, + "indices": 22, + "material": 5, + "mode": 4, + }, + ], + }, + { + "name": + "2-square-gray", + "primitives": [ + { + "attributes": { + "NORMAL": 2, + "POSITION": 0 + }, + "indices": 3, + "material": 3, + "mode": 4, + }, + # back side + { + "attributes": { + "NORMAL": 13, + "POSITION": 12 + }, + "indices": 22, + "material": 3, + "mode": 4, + }, + ], + }, + { + "name": + "3-square-green", + "primitives": [ + { + "attributes": { + "NORMAL": 2, + "POSITION": 0 + }, + "indices": 3, + "material": 2, + "mode": 4, + }, # back side + { + "attributes": { + "NORMAL": 13, + "POSITION": 12 + }, + "indices": 22, + "material": 2, + "mode": 4, + }, + ], + }, + { + "name": + "4-rectangle-blue", + "primitives": [ + { + "attributes": { + "NORMAL": 2, + "POSITION": 1 + }, + "indices": 3, + "material": 0, + "mode": 4, + }, + # backside + { + "attributes": { + "NORMAL": 13, + "POSITION": 23 + }, + "indices": 22, + "material": 0, + "mode": 4, + } + ], + }, + { + "name": + "5-rectangle-red", + "primitives": [ + { + "attributes": { + "NORMAL": 2, + "POSITION": 1 + }, + "indices": 3, + "material": 1, + "mode": 4, + }, + # backside + { + "attributes": { + "NORMAL": 13, + "POSITION": 23 + }, + "indices": 22, + "material": 1, + "mode": 4, + } + ], + }, + { + "name": + "6-rectangle-gray", + "primitives": [ + { + "attributes": { + "NORMAL": 2, + "POSITION": 1 + }, + "indices": 3, + "material": 3, + "mode": 4, + }, + # backside + { + "attributes": { + "NORMAL": 13, + "POSITION": 23 + }, + "indices": 22, + "material": 3, + "mode": 4, + } + ], + }, + { + "name": + "7-rectangle-red/yellow/blue", + "primitives": [ + { + "attributes": { + "NORMAL": 7, + "POSITION": 6 + }, + "indices": 3, + "material": 1, + "mode": 4, + }, + { + "attributes": { + "NORMAL": 7, + "POSITION": 6 + }, + "indices": 8, + "material": 6, + "mode": 4, + }, + { + "attributes": { + "NORMAL": 7, + "POSITION": 6 + }, + "indices": 9, + "material": 0, + "mode": 4, + }, + # backside + { + "attributes": { + "NORMAL": 26, + "POSITION": 25 + }, + "indices": 22, + "material": 1, + "mode": 4, + }, + { + "attributes": { + "NORMAL": 26, + "POSITION": 25 + }, + "indices": 27, + "material": 6, + "mode": 4, + }, + { + "attributes": { + "NORMAL": 26, + "POSITION": 25 + }, + "indices": 28, + "material": 0, + "mode": 4, + }, + ], + }, + { + "name": + "8-rectangle-blue/yellow/red", + "primitives": [ + { + "attributes": { + "NORMAL": 7, + "POSITION": 6 + }, + "indices": 3, + "material": 0, + "mode": 4, + }, + { + "attributes": { + "NORMAL": 7, + "POSITION": 6 + }, + "indices": 8, + "material": 6, + "mode": 4, + }, + { + "attributes": { + "NORMAL": 7, + "POSITION": 6 + }, + "indices": 9, + "material": 1, + "mode": 4, + }, + # backside + { + "attributes": { + "NORMAL": 26, + "POSITION": 25 + }, + "indices": 22, + "material": 0, + "mode": 4, + }, + { + "attributes": { + "NORMAL": 26, + "POSITION": 25 + }, + "indices": 27, + "material": 6, + "mode": 4, + }, + { + "attributes": { + "NORMAL": 26, + "POSITION": 25 + }, + "indices": 28, + "material": 1, + "mode": 4, + }, + ], + }, + { + "name": + "9-square-cyan.3", + "primitives": [ + { + "attributes": { + "NORMAL": 2, + "POSITION": 0 + }, + "indices": 3, + "material": 4, + "mode": 4, + }, # back side + { + "attributes": { + "NORMAL": 13, + "POSITION": 12 + }, + "indices": 22, + "material": 4, + "mode": 4, + }, + ], + }, + { + "name": + "10-rectangle-cyan.3", + "primitives": [ + { + "attributes": { + "NORMAL": 2, + "POSITION": 1 + }, + "indices": 3, + "material": 4, + "mode": 4, + }, + # backside + { + "attributes": { + "NORMAL": 13, + "POSITION": 23 + }, + "indices": 22, + "material": 4, + "mode": 4, + } + ], + }, + { + "name": + "11-tilted-cyan.3", + "primitives": [ + { + "attributes": { + "NORMAL": 5, + "POSITION": 4 + }, + "indices": 3, + "material": 4, + "mode": 4, + }, + # backside + { + "attributes": { + "NORMAL": 30, + "POSITION": 29 + }, + "indices": 22, + "material": 4, + "mode": 4, + }, + ], + }, + { + "name": + "12-half-distance-rectangle-green", + "primitives": [ + { + "attributes": { + "NORMAL": 2, + "POSITION": 11 + }, + "indices": 3, + "material": 2, + "mode": 4, + }, + # back side + { + "attributes": { + "NORMAL": 13, + "POSITION": 24 + }, + "indices": 22, + "material": 2, + "mode": 4, + }, + ], + }, + { + "name": + "13-square-black", + "primitives": [ + { + "attributes": { + "NORMAL": 2, + "POSITION": 0 + }, + "indices": 3, + "material": 5, + "mode": 4, + }, # back side + { + "attributes": { + "NORMAL": 13, + "POSITION": 12 + }, + "indices": 22, + "material": 5, + "mode": 4, + }, + ], + }, + { + "name": + "14-half-distance-rectangle-black", + "primitives": [ + { + "attributes": { + "NORMAL": 2, + "POSITION": 11 + }, + "indices": 3, + "material": 5, + "mode": 4, + }, + # back side + { + "attributes": { + "NORMAL": 13, + "POSITION": 24 + }, + "indices": 22, + "material": 5, + "mode": 4, + }, + ], + }, + ] + + return gltf + + +def axes_gen(SEP: float, max_i: int, max_j: int, + max_k: int) -> Sequence[Mapping[str, Any]]: + rectangles = [] + + # I axis, red + rectangles += [ + { + "name": f"axisI:-K", + "mesh": 5, + "translation": [-0.5, -0.5, 0.5], + "scale": [SEP * max_i / (SEP - 1), AXESTHICKNESS, AXESTHICKNESS], + }, + { + "name": f"axisI:+K", + "mesh": 5, + "translation": [-0.5, -0.5 + AXESTHICKNESS, 0.5], + "scale": [SEP * max_i / (SEP - 1), AXESTHICKNESS, AXESTHICKNESS], + }, + { + "name": f"axisI:-J", + "mesh": 5, + "translation": [-0.5, -0.5, 0.5], + "rotation": [SQ2, 0, 0, SQ2], + "scale": [SEP * max_i / (SEP - 1), AXESTHICKNESS, AXESTHICKNESS], + }, + { + "name": f"axisI:+J", + "mesh": 5, + "translation": [-0.5, -0.5, 0.5 - AXESTHICKNESS], + "rotation": [SQ2, 0, 0, SQ2], + "scale": [SEP * max_i / (SEP - 1), AXESTHICKNESS, AXESTHICKNESS], + }, + ] + + # J axis, green + rectangles += [ + { + "name": f"axisJ:-K", + "rotation": [0, SQ2, 0, SQ2], + "translation": [-0.5 + AXESTHICKNESS, -0.5, 0.5], + "mesh": 3, + "scale": [SEP * max_j, AXESTHICKNESS, AXESTHICKNESS], + }, + { + "name": f"axisJ:+K", + "rotation": [0, SQ2, 0, SQ2], + "translation": [ + -0.5 + AXESTHICKNESS, + -0.5 + AXESTHICKNESS, + 0.5, + ], + "mesh": 3, + "scale": [SEP * max_j, AXESTHICKNESS, AXESTHICKNESS], + }, + { + "name": f"axisJ:-I", + "rotation": [0.5, 0.5, -0.5, 0.5], + "translation": [-0.5, -0.5, 0.5], + "mesh": 3, + "scale": [SEP * max_j, AXESTHICKNESS, AXESTHICKNESS], + }, + { + "name": f"axisJ:+I", + "rotation": [0.5, 0.5, -0.5, 0.5], + "translation": [-0.5 + AXESTHICKNESS, -0.5, 0.5], + "mesh": 3, + "scale": [SEP * max_j, AXESTHICKNESS, AXESTHICKNESS], + }, + ] + + # K axis, blue + rectangles += [ + { + "name": f"axisK:-I", + "mesh": 4, + "rotation": [0, 0, SQ2, SQ2], + "translation": [-0.5, -0.5 + AXESTHICKNESS, 0.5], + "scale": [SEP * max_k / (SEP - 1), AXESTHICKNESS, AXESTHICKNESS], + }, + { + "name": f"axisK:+I", + "mesh": 4, + "rotation": [0, 0, SQ2, SQ2], + "translation": [-0.5 + AXESTHICKNESS, -0.5 + AXESTHICKNESS, 0.5], + "scale": [SEP * max_k / (SEP - 1), AXESTHICKNESS, AXESTHICKNESS], + }, + { + "name": f"axisK:-J", + "mesh": 4, + "rotation": [0.5, 0.5, 0.5, 0.5], + "translation": [-0.5 + AXESTHICKNESS, -0.5 + AXESTHICKNESS, 0.5], + "scale": [SEP * max_k / (SEP - 1), AXESTHICKNESS, AXESTHICKNESS], + }, + { + "name": + f"axisK:+J", + "mesh": + 4, + "rotation": [0.5, 0.5, 0.5, 0.5], + "translation": [ + -0.5 + AXESTHICKNESS, + -0.5 + AXESTHICKNESS, + 0.5 - AXESTHICKNESS, + ], + "scale": [SEP * max_k / (SEP - 1), AXESTHICKNESS, AXESTHICKNESS], + }, + ] + + return rectangles + + +def tube_gen(SEP: float, loc: Tuple[int, int, int], dir: str, color: int, + stabilizer: int, corr: Tuple[int, int], noColor: bool, + rm_dir: str) -> Sequence[Mapping[str, Any]]: + """compute the GLTF nodes for a pipe. This can include its four faces and + correlation surface inside, minus the face to remove specified by rm_dir. + + Args: + SEP (float): the distance, e.g., from I-pipe(i,j,k) to I-pipe(i+1,j,k). + loc (Tuple[int, int, int]): 3D coordinate of the pipe. + dir (str): direction of the pipe, "I", "J", or "K". + color (int): color variable of the pipe, can be -1(unknown), 0, or 1. + stabilizer (int): index of the stabilizer. + corr (Tuple[int, int]): two bits for two possible corr surface inside. + noColor (bool): K-pipe are not colored if this is True. + rm_dir (str): the direction of face to remove. if a stabilier is shown. + + Returns: + Sequence[Mapping[str, Any]]: list of constructed GLTF nodes, typically + 4 or 5 contiguous nodes in the list corredpond to one pipe. + """ + rectangles = [] + if dir == "I": + rectangles = [ + { + "name": f"edgeI{loc}:-K", + "mesh": 4 if color else 5, + "translation": [1 + SEP * loc[0], SEP * loc[2], -SEP * loc[1]], + }, + { + "name": f"edgeI{loc}:+K", + "mesh": 4 if color else 5, + "translation": + [1 + SEP * loc[0], 1 + SEP * loc[2], -SEP * loc[1]], + }, + { + "name": f"edgeI{loc}:-J", + "mesh": 5 if color else 4, + "translation": [1 + SEP * loc[0], SEP * loc[2], -SEP * loc[1]], + "rotation": [SQ2, 0, 0, SQ2], + }, + { + "name": f"edgeI{loc}:+J", + "mesh": 5 if color else 4, + "translation": + [1 + SEP * loc[0], SEP * loc[2], -1 - SEP * loc[1]], + "rotation": [SQ2, 0, 0, SQ2], + }, + ] + if corr[0]: + rectangles.append({ + "name": + f"edgeI{loc}:CorrIJ", + "mesh": + 10, + "translation": [ + 1 + SEP * loc[0], + 0.5 + SEP * loc[2], + -SEP * loc[1], + ], + }) + if corr[1]: + rectangles.append({ + "name": + f"edgeI{loc}:CorrIK", + "mesh": + 10, + "translation": [ + 1 + SEP * loc[0], + SEP * loc[2], + -0.5 - SEP * loc[1], + ], + "rotation": [SQ2, 0, 0, SQ2], + }) + elif dir == "J": + rectangles = [ + { + "name": f"edgeJ{loc}:-K", + "rotation": [0, SQ2, 0, SQ2], + "translation": + [1 + SEP * loc[0], SEP * loc[2], -1 - SEP * loc[1]], + "mesh": 5 if color else 4, + }, + { + "name": + f"edgeJ{loc}:+K", + "rotation": [0, SQ2, 0, SQ2], + "translation": [ + 1 + SEP * loc[0], + 1 + SEP * loc[2], + -1 - SEP * loc[1], + ], + "mesh": + 5 if color else 4, + }, + { + "name": f"edgeJ{loc}:-I", + "rotation": [0.5, 0.5, -0.5, 0.5], + "translation": [SEP * loc[0], SEP * loc[2], -1 - SEP * loc[1]], + "mesh": 4 if color else 5, + }, + { + "name": f"edgeJ{loc}:+I", + "rotation": [0.5, 0.5, -0.5, 0.5], + "translation": + [1 + SEP * loc[0], SEP * loc[2], -1 - SEP * loc[1]], + "mesh": 4 if color else 5, + }, + ] + if corr[0]: + rectangles.append({ + "name": + f"edgeJ{loc}:CorrJK", + "mesh": + 10, + "rotation": [0.5, 0.5, -0.5, 0.5], + "translation": [ + 0.5 + SEP * loc[0], + SEP * loc[2], + -1 - SEP * loc[1], + ], + }) + if corr[1]: + rectangles.append({ + "name": + f"edgeJ{loc}:CorrJI", + "mesh": + 10, + "rotation": [0, SQ2, 0, SQ2], + "translation": [ + 1 + SEP * loc[0], + 0.5 + SEP * loc[2], + -1 - SEP * loc[1], + ], + }) + + elif dir == "K": + colorKM = color // 7 + colorKP = color % 7 + rectangles = [ + { + "name": f"edgeJ{loc}:-I", + "mesh": 6, + "rotation": [0, 0, SQ2, SQ2], + "translation": [SEP * loc[0], 1 + SEP * loc[2], -SEP * loc[1]], + }, + { + "name": f"edgeJ{loc}:+I", + "mesh": 6, + "rotation": [0, 0, SQ2, SQ2], + "translation": + [1 + SEP * loc[0], 1 + SEP * loc[2], -SEP * loc[1]], + }, + { + "name": f"edgeK{loc}:-J", + "mesh": 6, + "rotation": [0.5, 0.5, 0.5, 0.5], + "translation": + [1 + SEP * loc[0], 1 + SEP * loc[2], -SEP * loc[1]], + }, + { + "name": + f"edgeJ{loc}:+J", + "mesh": + 6, + "rotation": [0.5, 0.5, 0.5, 0.5], + "translation": [ + 1 + SEP * loc[0], + 1 + SEP * loc[2], + -1 - SEP * loc[1], + ], + }, + ] + if not noColor: + if colorKM == 0 and colorKP == 0: + rectangles[0]["mesh"] = 4 + rectangles[1]["mesh"] = 4 + rectangles[2]["mesh"] = 5 + rectangles[3]["mesh"] = 5 + if colorKM == 1 and colorKP == 1: + rectangles[0]["mesh"] = 5 + rectangles[1]["mesh"] = 5 + rectangles[2]["mesh"] = 4 + rectangles[3]["mesh"] = 4 + if colorKM == 1 and colorKP == 0: + rectangles[0]["mesh"] = 7 + rectangles[1]["mesh"] = 7 + rectangles[2]["mesh"] = 8 + rectangles[3]["mesh"] = 8 + if colorKM == 0 and colorKP == 1: + rectangles[0]["mesh"] = 8 + rectangles[1]["mesh"] = 8 + rectangles[2]["mesh"] = 7 + rectangles[3]["mesh"] = 7 + + if corr[0]: + rectangles.append({ + "name": + f"edgeK{loc}:CorrKI", + "mesh": + 10, + "rotation": [0.5, 0.5, 0.5, 0.5], + "translation": [ + 1 + SEP * loc[0], + 1 + SEP * loc[2], + -0.5 - SEP * loc[1], + ], + }) + if corr[1]: + rectangles.append({ + "name": + f"edgeK{loc}:CorrKJ", + "mesh": + 10, + "rotation": [0, 0, SQ2, SQ2], + "translation": [ + 0.5 + SEP * loc[0], + 1 + SEP * loc[2], + -SEP * loc[1], + ], + }) + + rectangles = [rect for rect in rectangles if rm_dir not in rect["name"]] + if stabilizer == -1: + rectangles = [ + rect for rect in rectangles if "Corr" not in rect["name"] + ] + return rectangles + + +def cube_gen( + SEP: float, + loc: Tuple[int, int, int], + exists: Mapping[str, int], + colors: Mapping[str, int], + stabilizer: int, + corr: Mapping[str, Tuple[int, int]], + noColor: bool, + rm_dir: str, +) -> Sequence[Mapping[str, Any]]: + """compute the GLTF nodes for a cube. This can include its faces and + correlation surface inside, minus the face to remove specified by rm_dir. + + Args: + SEP (float): the distance, e.g., from cube(i,j,k) to cube(i+1,j,k). + loc (Tuple[int, int, int]): 3D coordinate of the pipe. + exists (Mapping[str, int]): whether there is a pipe in the 6 directions + to this cube. (+|-)(I|J|K). + colors (Mapping[str, int]): color variable of the pipe, can be + -1(unknown), 0, or 1. + stabilizer (int): index of the stabilizer. + corr (Mapping[str, Tuple[int, int]]): two bits for two possible + correlation surface inside a pipe. These info for all 6 pipes. + noColor (bool): K-pipe are not colored if this is True. + rm_dir (str): the direction of face to remove. if a stabilier is shown. + + Returns: + Sequence[Mapping[str, Any]]: list of constructed GLTF nodes. + """ + squares = [] + for face in ["-K", "+K"]: + if exists[face] == 0: + squares.append({ + "name": + f"spider{loc}:{face}", + "mesh": + 2, + "translation": [ + SEP * loc[0], + (1 if face == "+K" else 0) + SEP * loc[2], + -SEP * loc[1], + ], + }) + for dir in ["+I", "-I", "+J", "-J"]: + if exists[dir]: + if dir == "+I" or dir == "-I": + if colors[dir] == 1: + squares[-1]["mesh"] = 0 + else: + squares[-1]["mesh"] = 1 + else: + if colors[dir] == 0: + squares[-1]["mesh"] = 0 + else: + squares[-1]["mesh"] = 1 + break + for face in ["-I", "+I"]: + if exists[face] == 0: + squares.append({ + "name": + f"spider{loc}:{face}", + "mesh": + 2, + "translation": [ + (1 if face == "+I" else 0) + SEP * loc[0], + SEP * loc[2], + -SEP * loc[1], + ], + "rotation": [0, 0, SQ2, SQ2], + }) + for dir in ["+J", "-J", "+K", "-K"]: + if exists[dir]: + if dir == "+J" or dir == "-J": + if colors[dir] == 1: + squares[-1]["mesh"] = 0 + else: + squares[-1]["mesh"] = 1 + elif not noColor: + if colors[dir] == 1: + squares[-1]["mesh"] = 1 + elif colors[dir] == 0: + squares[-1]["mesh"] = 0 + for face in ["-J", "+J"]: + if exists[face] == 0: + squares.append({ + "name": + f"spider{loc}:{face}", + "mesh": + 2, + "translation": [ + 1 + SEP * loc[0], + SEP * loc[2], + (-1 if face == "+J" else 0) - SEP * loc[1], + ], + "rotation": [0.5, 0.5, 0.5, 0.5], + }) + for dir in ["+I", "-I", "+K", "-K"]: + if exists[dir]: + if dir == "+I" or dir == "-I": + if colors[dir] == 0: + squares[-1]["mesh"] = 0 + else: + squares[-1]["mesh"] = 1 + elif not noColor: + if colors[dir] == 1: + squares[-1]["mesh"] = 0 + elif colors[dir] == 0: + squares[-1]["mesh"] = 1 + + degree = sum([v for (k, v) in exists.items()]) + normal = {"I": 0, "J": 0, "K": 0} + if exists["-I"] == 0 and exists["+I"] == 0: + normal["I"] = 1 + if exists["-J"] == 0 and exists["+J"] == 0: + normal["J"] = 1 + if exists["-K"] == 0 and exists["+K"] == 0: + normal["K"] = 1 + if degree > 1: + if (exists["-I"] and exists["+I"] and exists["-J"] == 0 + and exists["+J"] == 0 and exists["-K"] == 0 + and exists["+K"] == 0): + if corr["-I"][0]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 9, + "translation": [ + SEP * loc[0], + 0.5 + SEP * loc[2], + -SEP * loc[1], + ], + }) + if corr["-I"][1]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 9, + "translation": [ + 1 + SEP * loc[0], + SEP * loc[2], + -0.5 - SEP * loc[1], + ], + "rotation": [0.5, 0.5, 0.5, 0.5], + }) + elif (exists["-I"] == 0 and exists["+I"] == 0 and exists["-J"] + and exists["+J"] and exists["-K"] == 0 and exists["+K"] == 0): + if corr["-J"][0]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 9, + "translation": [ + 0.5 + SEP * loc[0], + SEP * loc[2], + -SEP * loc[1], + ], + "rotation": [0, 0, SQ2, SQ2], + }) + if corr["-J"][1]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 9, + "translation": [ + SEP * loc[0], + 0.5 + SEP * loc[2], + -SEP * loc[1], + ], + }) + elif (exists["-I"] == 0 and exists["+I"] == 0 and exists["-J"] == 0 + and exists["+J"] == 0 and exists["-K"] and exists["+K"]): + if corr["-K"][0]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 9, + "translation": [ + 1 + SEP * loc[0], + SEP * loc[2], + -0.5 - SEP * loc[1], + ], + "rotation": [0.5, 0.5, 0.5, 0.5], + }) + if corr["-K"][1]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 9, + "translation": [ + 0.5 + SEP * loc[0], + SEP * loc[2], + -SEP * loc[1], + ], + "rotation": [0, 0, SQ2, SQ2], + }) + else: + if normal["I"]: + if corr["-J"][0] or corr["+J"][0] or corr["-K"][1] or corr[ + "+K"][1]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 9, + "translation": [ + 0.5 + SEP * loc[0], + SEP * loc[2], + -SEP * loc[1], + ], + "rotation": [0, 0, SQ2, SQ2], + }) + + if corr["-J"][1] and corr["+J"][1] and corr["-K"][0] and corr[ + "+K"][0]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 11, + "translation": [ + SEP * loc[0], + SEP * loc[2], + -1 - SEP * loc[1], + ], + "rotation": [0, -SQ2, 0, SQ2], + }) + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 11, + "translation": [ + SEP * loc[0], + 0.5 + SEP * loc[2], + -0.5 - SEP * loc[1], + ], + "rotation": [0, -SQ2, 0, SQ2], + }) + elif corr["-J"][1] and corr["+J"][1]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 9, + "translation": [ + SEP * loc[0], + 0.5 + SEP * loc[2], + -SEP * loc[1], + ], + }) + elif corr["-K"][0] and corr["+K"][0]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 9, + "translation": [ + 1 + SEP * loc[0], + SEP * loc[2], + -0.5 - SEP * loc[1], + ], + "rotation": [0.5, 0.5, 0.5, 0.5], + }) + elif corr["-J"][1] and corr["-K"][0]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 11, + "translation": [ + 1 + SEP * loc[0], + SEP * loc[2], + -SEP * loc[1], + ], + "rotation": [0, SQ2, 0, SQ2], + }) + elif corr["+J"][1] and corr["+K"][0]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 11, + "translation": [ + 1 + SEP * loc[0], + 0.5 + SEP * loc[2], + -0.5 - SEP * loc[1], + ], + "rotation": [0, SQ2, 0, SQ2], + }) + elif corr["+J"][1] and corr["-K"][0]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 11, + "translation": [ + SEP * loc[0], + SEP * loc[2], + -1 - SEP * loc[1], + ], + "rotation": [0, -SQ2, 0, SQ2], + }) + elif corr["-J"][1] and corr["+K"][0]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 11, + "translation": [ + SEP * loc[0], + 0.5 + SEP * loc[2], + -0.5 - SEP * loc[1], + ], + "rotation": [0, -SQ2, 0, SQ2], + }) + elif normal["J"]: + if corr["-K"][0] or corr["+K"][0] or corr["-I"][1] or corr[ + "+I"][1]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 9, + "translation": [ + 1 + SEP * loc[0], + SEP * loc[2], + -0.5 - SEP * loc[1], + ], + "rotation": [0.5, 0.5, 0.5, 0.5], + }) + + if corr["-K"][1] and corr["+K"][1] and corr["-I"][0] and corr[ + "+I"][0]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 11, + "translation": [ + 0.5 + SEP * loc[0], + 0.5 + SEP * loc[2], + -SEP * loc[1], + ], + "rotation": [0, 0, SQ2, SQ2], + }) + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 11, + "translation": [ + 1 + SEP * loc[0], + SEP * loc[2], + -SEP * loc[1], + ], + "rotation": [0, 0, SQ2, SQ2], + }) + elif corr["-K"][1] and corr["+K"][1]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 9, + "translation": [ + 0.5 + SEP * loc[0], + SEP * loc[2], + -SEP * loc[1], + ], + "rotation": [0, 0, SQ2, SQ2], + }) + elif corr["-I"][0] and corr["+I"][0]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 9, + "translation": [ + SEP * loc[0], + 0.5 + SEP * loc[2], + -SEP * loc[1], + ], + }) + elif corr["-K"][1] and corr["-I"][0]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 11, + "translation": + [SEP * loc[0], SEP * loc[2], -SEP * loc[1]], + }) + elif corr["+K"][1] and corr["+I"][0]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 11, + "translation": [ + 0.5 + SEP * loc[0], + 0.5 + SEP * loc[2], + -SEP * loc[1], + ], + }) + elif corr["+K"][1] and corr["-I"][0]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 11, + "translation": [ + 0.5 + SEP * loc[0], + 0.5 + SEP * loc[2], + -SEP * loc[1], + ], + "rotation": [0, 0, SQ2, SQ2], + }) + elif corr["-K"][1] and corr["+I"][0]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 11, + "translation": [ + 1 + SEP * loc[0], + SEP * loc[2], + -SEP * loc[1], + ], + "rotation": [0, 0, SQ2, SQ2], + }) + else: + if corr["-I"][0] or corr["+I"][0] or corr["-J"][1] or corr[ + "+J"][1]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 9, + "translation": [ + SEP * loc[0], + 0.5 + SEP * loc[2], + -SEP * loc[1], + ], + }) + + if corr["-I"][1] and corr["+I"][1] and corr["-J"][0] and corr[ + "+J"][0]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 11, + "translation": [ + 0.5 + SEP * loc[0], + SEP * loc[2], + -0.5 - SEP * loc[1], + ], + "rotation": [SQ2, 0, 0, SQ2], + }) + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 11, + "translation": [ + SEP * loc[0], + SEP * loc[2], + -1 - SEP * loc[1], + ], + "rotation": [SQ2, 0, 0, SQ2], + }) + elif corr["-I"][1] and corr["+I"][1]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 9, + "translation": [ + 1 + SEP * loc[0], + SEP * loc[2], + -0.5 - SEP * loc[1], + ], + "rotation": [0.5, 0.5, 0.5, 0.5], + }) + elif corr["-J"][0] and corr["+J"][0]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 9, + "translation": [ + 0.5 + SEP * loc[0], + SEP * loc[2], + -SEP * loc[1], + ], + "rotation": [0, 0, SQ2, SQ2], + }) + elif corr["-I"][1] and corr["-J"][0]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 11, + "translation": [ + SEP * loc[0], + 1 + SEP * loc[2], + -SEP * loc[1], + ], + "rotation": [-SQ2, 0, 0, SQ2], + }) + elif corr["+I"][1] and corr["+J"][0]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 11, + "translation": [ + 0.5 + SEP * loc[0], + 1 + SEP * loc[2], + -0.5 - SEP * loc[1], + ], + "rotation": [-SQ2, 0, 0, SQ2], + }) + elif corr["+I"][1] and corr["-J"][0]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 11, + "translation": [ + 0.5 + SEP * loc[0], + SEP * loc[2], + -0.5 - SEP * loc[1], + ], + "rotation": [SQ2, 0, 0, SQ2], + }) + elif corr["-I"][1] and corr["+J"][0]: + squares.append({ + "name": + f"spider{loc}:Corr", + "mesh": + 11, + "translation": [ + SEP * loc[0], + SEP * loc[2], + -1 - SEP * loc[1], + ], + "rotation": [SQ2, 0, 0, SQ2], + }) + + squares = [sqar for sqar in squares if rm_dir not in sqar["name"]] + if stabilizer == -1: + squares = [sqar for sqar in squares if "Corr" not in sqar["name"]] + return squares + + +def special_gen( + SEP: float, + loc: Tuple[int, int, int], + exists: Mapping[str, int], + type: str, + stabilizer: int, + rm_dir: str, +) -> Sequence[Mapping[str, Any]]: + """compute the GLTF nodes for special cubes. Currently Ycube and Tinjection + + Args: + SEP (float): the distance, e.g., from cube(i,j,k) to cube(i+1,j,k). + loc (Tuple[int, int, int]): 3D coordinate of the pipe. + exists (Mapping[str, int]): whether there is a pipe in the 6 directions + to this cube. (+|-)(I|J|K). + stabilizer (int): index of the stabilizer. + noColor (bool): K-pipe are not colored if this is True. + rm_dir (str): the direction of face to remove. if a stabilier is shown. + + Returns: + Sequence[Mapping[str, Any]]: list of constructed GLTF nodes. + """ + if type == "Y": + square_mesh = 3 + half_dist_mesh = 12 + elif type == "T": + square_mesh = 13 + half_dist_mesh = 14 + else: + square_mesh = -1 + half_dist_mesh = -1 + + shapes = [] + if exists["+K"]: + # need connect to top + shapes.append({ + "name": + f"spider{loc}:top:-K", + "mesh": + square_mesh, + "translation": [ + SEP * loc[0], + 0.55 + SEP * loc[2], + -SEP * loc[1], + ], + }) + shapes.append({ + "name": + f"spider{loc}:top:-I", + "mesh": + half_dist_mesh, + "rotation": [0, 0, SQ2, SQ2], + "translation": [SEP * loc[0], 0.55 + SEP * loc[2], -SEP * loc[1]], + }) + shapes.append({ + "name": + f"spider{loc}:top:+I", + "mesh": + half_dist_mesh, + "rotation": [0, 0, SQ2, SQ2], + "translation": + [1 + SEP * loc[0], 0.55 + SEP * loc[2], -SEP * loc[1]], + }) + shapes.append({ + "name": + f"spider{loc}:top:-J", + "mesh": + half_dist_mesh, + "rotation": [0.5, 0.5, 0.5, 0.5], + "translation": + [1 + SEP * loc[0], 0.55 + SEP * loc[2], -SEP * loc[1]], + }) + shapes.append({ + "name": + f"spider{loc}:top:+J", + "mesh": + half_dist_mesh, + "rotation": [0.5, 0.5, 0.5, 0.5], + "translation": [ + 1 + SEP * loc[0], + 0.55 + SEP * loc[2], + -SEP * loc[1] - 1, + ], + }) + + if exists["-K"]: + # need connect to bottom + shapes.append({ + "name": + f"spider{loc}:bottom:+K", + "mesh": + square_mesh, + "translation": [ + SEP * loc[0], + 0.45 + SEP * loc[2], + -SEP * loc[1], + ], + }) + shapes.append({ + "name": + f"spider{loc}:bottom:-I", + "mesh": + half_dist_mesh, + "rotation": [0, 0, SQ2, SQ2], + "translation": [SEP * loc[0], SEP * loc[2], -SEP * loc[1]], + }) + shapes.append({ + "name": + f"spider{loc}:bottom:+I", + "mesh": + half_dist_mesh, + "rotation": [0, 0, SQ2, SQ2], + "translation": [1 + SEP * loc[0], SEP * loc[2], -SEP * loc[1]], + }) + shapes.append({ + "name": + f"spider{loc}:bottom:-J", + "mesh": + half_dist_mesh, + "rotation": [0.5, 0.5, 0.5, 0.5], + "translation": [1 + SEP * loc[0], SEP * loc[2], -SEP * loc[1]], + }) + shapes.append({ + "name": + f"spider{loc}:bottom:+J", + "mesh": + half_dist_mesh, + "rotation": [0.5, 0.5, 0.5, 0.5], + "translation": [ + 1 + SEP * loc[0], + SEP * loc[2], + -SEP * loc[1] - 1, + ], + }) + + shapes = [shp for shp in shapes if rm_dir not in shp["name"]] + return shapes + + +def gltf_generator(lasre: Mapping[str, Any], + stabilizer: int = -1, + tube_len: float = 2.0, + no_color_z: bool = False, + attach_axes: bool = False, + rm_dir: Optional[str] = None) -> Mapping[str, Any]: + """generate gltf in a dict and write to a json file with extension .gltf + + Args: + lasre (Mapping[str, Any]): LaSRe of the LaS. + stabilizer (int, optional): index of the stabilizer. The correlation + surfaces corresponding to it will be drawn. Defaults to -1, which + means do not draw any correlation surfaces. + tube_len (float, optional): ratio of the length of the pipes compared + to the length of the cubes. Defaults to 2.0. + no_color_z (bool, optional): do not color the Z-pipes. Defaults to + False, which means by default Z-pipes are colored. + attach_axes (bool, optional): attach an IJK axes. Defaults to False. + rm_dir (str, optional): the direction of faces to remove to reveal + the correlation surfaces. Defaults to None. + + Raises: + ValueError: rm_dir is not any one of :(+|-)(I|J|K) + ValueError: the index of stabilizer is not -1 nor in [0, n_stabilizer) + + Returns: + Mapping[str, Any]: the constructed gltf in a dict. + """ + s, tubelen, noColor = ( + stabilizer, + tube_len, + no_color_z, + ) + if rm_dir is None: + rm_dir = ":II" + elif rm_dir not in [":+I", ":-I", ":+J", ":-J", ":+K", ":-K"]: + raise ValueError("rm_dir is not one of :+I, :-I, :+J, :-J, :+K, :-K") + + gltf = base_gen(tubelen) + + i_bound = lasre["n_i"] + j_bound = lasre["n_j"] + k_bound = lasre["n_k"] + NodeY = lasre["NodeY"] + ExistI = lasre["ExistI"] + ColorI = lasre["ColorI"] + ExistJ = lasre["ExistJ"] + ColorJ = lasre["ColorJ"] + ExistK = lasre["ExistK"] + if "CorrIJ" in lasre: + CorrIJ = lasre["CorrIJ"] + CorrIK = lasre["CorrIK"] + CorrJI = lasre["CorrJI"] + CorrJK = lasre["CorrJK"] + CorrKI = lasre["CorrKI"] + CorrKJ = lasre["CorrKJ"] + s_bound = len(CorrIJ) + if "ColorKP" not in lasre: + ColorKP = [[[-1 for _ in range(k_bound)] for _ in range(j_bound)] + for _ in range(i_bound)] + else: + ColorKP = lasre["ColorKP"] + if "ColorKM" not in lasre: + ColorKM = [[[-1 for _ in range(k_bound)] for _ in range(j_bound)] + for _ in range(i_bound)] + else: + ColorKM = lasre["ColorKM"] + port_cubes = lasre["port_cubes"] + t_injections = (lasre["optional"]["t_injections"] + if "t_injections" in lasre["optional"] else []) + + if s < -1 or (s_bound > 0 and s not in range(-1, s_bound)): + raise ValueError(f"No such stabilizer index {s}.") + + for i in range(i_bound): + for j in range(j_bound): + for k in range(k_bound): + if ExistI[i][j][k]: + gltf["nodes"] += tube_gen( + tubelen + 1.0, + (i, j, k), + "I", + ColorI[i][j][k], + s, + (CorrIJ[s][i][j][k], + CorrIK[s][i][j][k]) if s_bound else (0, 0), + noColor, + rm_dir, + ) + if ExistJ[i][j][k]: + gltf["nodes"] += tube_gen( + tubelen + 1.0, + (i, j, k), + "J", + ColorJ[i][j][k], + s, + (CorrJK[s][i][j][k], + CorrJI[s][i][j][k]) if s_bound else (0, 0), + noColor, + rm_dir, + ) + if ExistK[i][j][k]: + gltf["nodes"] += tube_gen( + tubelen + 1.0, + (i, j, k), + "K", + 7 * ColorKM[i][j][k] + ColorKP[i][j][k], + s, + (CorrKI[s][i][j][k], + CorrKJ[s][i][j][k]) if s_bound else (0, 0), + noColor, + rm_dir, + ) + + for i in range(i_bound): + for j in range(j_bound): + for k in range(k_bound): + exists = {"-I": 0, "+I": 0, "-K": 0, "+K": 0, "-J": 0, "+J": 0} + colors = {} + corr = { + "-I": (0, 0), + "+I": (0, 0), + "-J": (0, 0), + "+J": (0, 0), + "-K": (0, 0), + "+K": (0, 0), + } + if i > 0 and ExistI[i - 1][j][k]: + exists["-I"] = 1 + colors["-I"] = ColorI[i - 1][j][k] + corr["-I"] = (CorrIJ[s][i - 1][j][k], + CorrIK[s][i - 1][j][k]) if s_bound else (0, + 0) + if ExistI[i][j][k]: + exists["+I"] = 1 + colors["+I"] = ColorI[i][j][k] + corr["+I"] = (CorrIJ[s][i][j][k], + CorrIK[s][i][j][k]) if s_bound else (0, 0) + if j > 0 and ExistJ[i][j - 1][k]: + exists["-J"] = 1 + colors["-J"] = ColorJ[i][j - 1][k] + corr["-J"] = (CorrJK[s][i][j - 1][k], + CorrJI[s][i][j - 1][k]) if s_bound else (0, + 0) + if ExistJ[i][j][k]: + exists["+J"] = 1 + colors["+J"] = ColorJ[i][j][k] + corr["+J"] = (CorrJK[s][i][j][k], + CorrJI[s][i][j][k]) if s_bound else (0, 0) + if k > 0 and ExistK[i][j][k - 1]: + exists["-K"] = 1 + colors["-K"] = ColorKP[i][j][k - 1] + corr["-K"] = (CorrKI[s][i][j][k - 1], + CorrKJ[s][i][j][k - 1]) if s_bound else (0, + 0) + if ExistK[i][j][k]: + exists["+K"] = 1 + colors["+K"] = ColorKM[i][j][k] + corr["+K"] = (CorrKI[s][i][j][k], + CorrKJ[s][i][j][k]) if s_bound else (0, 0) + if sum([v for (k, v) in exists.items()]) > 0: + if (i, j, k) not in port_cubes: + if NodeY[i][j][k]: + gltf["nodes"] += special_gen( + tubelen + 1.0, + (i, j, k), + exists, + "Y", + s, + rm_dir, + ) + else: + gltf["nodes"] += cube_gen( + tubelen + 1.0, + (i, j, k), + exists, + colors, + s, + corr, + noColor, + rm_dir, + ) + elif [i, j, k] in t_injections: + gltf["nodes"] += special_gen( + tubelen + 1.0, + (i, j, k), + exists, + "T", + s, + rm_dir, + ) + + if attach_axes: + gltf["nodes"] += axes_gen(tube_len + 1.0, i_bound, j_bound, k_bound) + + gltf["nodes"][0]["children"] = list(range(1, len(gltf["nodes"]))) + + return gltf diff --git a/glue/lattice_surgery/lassynth/translators/networkx_generator.py b/glue/lattice_surgery/lassynth/translators/networkx_generator.py new file mode 100644 index 000000000..4003f75c4 --- /dev/null +++ b/glue/lattice_surgery/lassynth/translators/networkx_generator.py @@ -0,0 +1,53 @@ +"""generate a annotated networkx.Graph corresponding to the LaS.""" + +import networkx +from lassynth.translators import ZXGridGraph +import stimzx +from typing import Mapping, Any + + +def networkx_generator(lasre: Mapping[str, Any]) -> networkx.Graph: + n_i, n_j, n_k = lasre["n_i"], lasre["n_j"], lasre["n_k"] + port_cubes = lasre["port_cubes"] + zxgridgraph = ZXGridGraph(lasre) + edges = zxgridgraph.edges + nodes = zxgridgraph.nodes + + zx_nx_graph = networkx.Graph() + type_to_str = {"X": "X", "Z": "Z", "Pi": "in", "Po": "out", "I": "X"} + cnt = 0 + for (i, j, k) in port_cubes: + node = nodes[i][j][k] + zx_nx_graph.add_node(cnt, value=stimzx.ZxType(type_to_str[node.type])) + node.node_id = cnt + cnt += 1 + + for i in range(n_i + 1): + for j in range(n_j + 1): + for k in range(n_k + 1): + node = nodes[i][j][k] + if node.type not in ["N", "Po", "Pi"]: + zx_nx_graph.add_node(cnt, + value=stimzx.ZxType( + type_to_str[node.type])) + node.node_id = cnt + cnt += 1 + if node.y_tail_minus: + zx_nx_graph.add_node(cnt, value=stimzx.ZxType("Z", 1)) + zx_nx_graph.add_edge(node.node_id, cnt) + cnt += 1 + if node.y_tail_plus: + zx_nx_graph.add_node(cnt, value=stimzx.ZxType("Z", 3)) + zx_nx_graph.add_edge(node.node_id, cnt) + cnt += 1 + + for edge in edges: + if edge.type != "h": + zx_nx_graph.add_edge(edge.node0.node_id, edge.node1.node_id) + else: + zx_nx_graph.add_node(cnt, value=stimzx.ZxType("H")) + zx_nx_graph.add_edge(cnt, edge.node0.node_id) + zx_nx_graph.add_edge(cnt, edge.node1.node_id) + cnt += 1 + + return zx_nx_graph diff --git a/glue/lattice_surgery/lassynth/translators/textfig_generator.py b/glue/lattice_surgery/lassynth/translators/textfig_generator.py new file mode 100644 index 000000000..1024b46f2 --- /dev/null +++ b/glue/lattice_surgery/lassynth/translators/textfig_generator.py @@ -0,0 +1,217 @@ +"""Generate text figures of 2D time slices of the LaS.""" + +from lassynth.translators import ZXGridGraph + + +class TextLayer: + pad_i = 1 + pad_j = 1 + sep_i = 4 + sep_j = 4 + + def __init__(self, zx_graph: ZXGridGraph, k: int, if_middle: bool) -> None: + self.n_i, self.n_j, self.n_k = ( + zx_graph.n_i, + zx_graph.n_j, + zx_graph.n_k, + ) + self.chars = [[ + " " for _ in range(2 * TextLayer.pad_i + + (self.n_i - 1) * TextLayer.sep_i + 1) + ] + ["\n"] for _ in range(2 * TextLayer.pad_j + + (self.n_j - 1) * TextLayer.sep_j + 1)] + if if_middle: + self.compute_middle(zx_graph, k) + else: + self.compute_normal(zx_graph, k) + + def set_char(self, j: int, i: int, character): + self.chars[j][i] = character + + def compute_normal(self, zx_graph: ZXGridGraph, k: int): + """a normal layer corresponds to a layer of cubes in LaS, e.g., + / / + X X + | / + | + |/ + Z . + / + There are 2x2 tiles of surface codes. The bottom right one is not being + used, represented by a `.`; the top right one is identity in because + it has degree 2, but our convention is that these spiders have type `X` + The top left one is like that, too. The bottom left is a Z-spider with + three edges, which is non trivial. `-` and `|` I-pipes and J-pipes. + `/` are K-pipes. The `/` on the bottom left corner of a spider connects + to the previous moment. The `/` on the top right corner of a spider + connects to the next moment. + + Args: + zx_graph (ZXGridGraph): + k (int): the height of this layer. + """ + for i in range(self.n_i): + for j in range(self.n_j): + spider = zx_graph.nodes[i][j][k] + + if spider.type in ["N", "Pi", "Po"]: + self.set_char( + TextLayer.pad_j + j * TextLayer.sep_j, + TextLayer.pad_i + i * TextLayer.sep_i, + ".", + ) + continue + elif spider.type == "I": + self.set_char( + TextLayer.pad_j + j * TextLayer.sep_j, + TextLayer.pad_i + i * TextLayer.sep_i, + "X", + ) + else: + self.set_char( + TextLayer.pad_j + j * TextLayer.sep_j, + TextLayer.pad_i + i * TextLayer.sep_i, + spider.type, + ) + + # I pipes + if spider.exists["+I"]: + for offset in range(1, TextLayer.sep_i): + self.set_char( + TextLayer.pad_j + j * TextLayer.sep_j, + TextLayer.pad_i + i * TextLayer.sep_i + offset, + "-", + ) + + # J pipes + if spider.exists["+J"]: + for offset in range(1, TextLayer.sep_i): + self.set_char( + TextLayer.pad_j + j * TextLayer.sep_j + offset, + TextLayer.pad_i + i * TextLayer.sep_i, + "|", + ) + + # K pipes + if spider.exists["+K"]: + self.set_char( + TextLayer.pad_j + j * TextLayer.sep_j - 1, + TextLayer.pad_i + i * TextLayer.sep_i + 1, + "/", + ) + if spider.exists["-K"]: + self.set_char( + TextLayer.pad_j + j * TextLayer.sep_j + 1, + TextLayer.pad_i + i * TextLayer.sep_i - 1, + "/", + ) + + def compute_middle(self, zx_graph: ZXGridGraph, k: int): + """a middle layer is either a Hadmard edge or a normal edge, e.g., + / + . X + / + + / + H . + / + These layers cannot have `-` or `|`. It only has `/` which are K-pipes. + The node is either `H` meaning the edge is a Hadamard edge, or `X` + meaning the edge is a normal edge. We use `X` for identity here. + + Args: + zx_graph (ZXGridGraph): + k (int): the height of this layer. There is a middle layer after a + normal layer. + """ + for i in range(self.n_i): + for j in range(self.n_j): + self.set_char( + TextLayer.pad_j + j * TextLayer.sep_j, + TextLayer.pad_i + i * TextLayer.sep_i, + ".", + ) + spider = zx_graph.nodes[i][j][k] + color_sum = -1 + if k == self.n_k - 1: + try: + for port in zx_graph.lasre["ports"]: + if (port["i"], port["j"], port["k"]) == (i, j, k): + color_sum = port["c"] + spider.colors["+K"] + break + except ValueError: + print( + f"KPipe({i},{j},{k}) connect outside but not port." + ) + else: + upper_spider = zx_graph.nodes[i][j][k + 1] + if spider.exists["+K"] == 1 and upper_spider.exists[ + "-K"] == 1: + color_sum = spider.colors["+K"] + upper_spider.colors[ + "-K"] + if spider.exists["+K"] == 0 and upper_spider.exists[ + "-K"] == 1: + try: + for port in zx_graph.lasre["ports"]: + if (port["i"], port["j"], port["k"]) == (i, j, + k): + color_sum = port[ + "c"] + upper_spider.colors["-K"] + break + except ValueError: + print(f"KPipe({i},{j},{k})- should be a port.") + if spider.exists["+K"] == 1 and upper_spider.exists[ + "-K"] == 0: + try: + for port in zx_graph.lasre["ports"]: + if (port["i"], port["j"], + port["k"]) == (i, j, k + 1): + color_sum = port["c"] + spider.colors["+K"] + break + except ValueError: + print(f"KPipe({i},{j},{k + 1})- should be a port") + + if color_sum != -1: + self.set_char( + TextLayer.pad_j + j * TextLayer.sep_j - 1, + TextLayer.pad_i + i * TextLayer.sep_i + 1, + "/", + ) + self.set_char( + TextLayer.pad_j + j * TextLayer.sep_j + 1, + TextLayer.pad_i + i * TextLayer.sep_i - 1, + "/", + ) + if color_sum == 1: + self.set_char( + TextLayer.pad_j + j * TextLayer.sep_j, + TextLayer.pad_i + i * TextLayer.sep_i, + "H", + ) + else: + self.set_char( + TextLayer.pad_j + j * TextLayer.sep_j, + TextLayer.pad_i + i * TextLayer.sep_i, + "X", + ) + + def get_text(self): + text = "" + for j in range(2 * TextLayer.pad_j + (self.n_j - 1) * TextLayer.sep_j + + 1): + for i in range(2 * TextLayer.pad_i + + (self.n_i - 1) * TextLayer.sep_i + 1): + text += self.chars[j][i] + text += "\n" + return text + + +def textfig_generator(lasre: dict): + text = "======================================\n" + zx_graph = ZXGridGraph(lasre) + for k in range(lasre["n_k"] - 1, -1, -1): + text += TextLayer(zx_graph, k, True).get_text() + text += "======================================\n" + text += TextLayer(zx_graph, k, False).get_text() + text += "======================================\n" + return text diff --git a/glue/lattice_surgery/lassynth/translators/zx_grid_graph.py b/glue/lattice_surgery/lassynth/translators/zx_grid_graph.py new file mode 100644 index 000000000..4586e6df5 --- /dev/null +++ b/glue/lattice_surgery/lassynth/translators/zx_grid_graph.py @@ -0,0 +1,292 @@ +"""Classes ZXGridEdge, ZXGridSpider, and ZXGridGraph. ZXGridGraph is a graph +where nodes are the cubes in LaS and edges are pipes in LaS. +""" + +from typing import Any, Mapping, Sequence, Tuple, Optional + + +class ZXGridNode: + + def __init__(self, coord3: Tuple[int, int, int], + connectivity: Mapping[str, Mapping[str, int]]) -> None: + """initialize ZXGridNode for a cube in the LaS. + + self.type: type of ZX spider, 'N': no spider, 'X'/'Z': X/Z-spider, + 'S': Y cube, 'I': identity, 'Pi': input port, 'Po': output port. + self.i/j/k: 3D corrdinates of the cube in the LaS. + self.exists is a dictionary with six keys corresponding to whether a + pipe exist in the six directions to a cube in the LaS. + self.colors are the colors of these possible pipes. + self.y_tail_plus: if this node connects a Y on the top. + self.y_tail_minus: if this node connects a Y on the bottom. + + Args: + coord3 (Tuple[int, int, int]): 3D coordinate of the cube. + connectivity (Mapping[str, Mapping[str, int]]): contains exists + and colors of the six possible pipes to a cube + """ + self.i, self.j, self.k = coord3 + self.y_tail_plus = False + self.y_tail_minus = False + self.node_id = -1 + self.exists = connectivity["exists"] + self.colors = connectivity["colors"] + self.compute_type() + + def compute_type(self) -> None: + """decide the type of a ZXGridNoe + + Raises: + ValueError: node has degree=1, which should be forbidden earlier. + ValueError: node has degree>4, which should be forbidden earlier. + """ + deg = sum([v for (k, v) in self.exists.items()]) + if deg == 0: + self.type = "N" + return + elif deg == 1: + raise ValueError("There should not be deg-1 Z or X spiders.") + elif deg == 2: + self.type = "I" + elif deg >= 5: + raise ValueError("deg > 4: 3D corner exists") + else: # degree = 3 or 4 + if self.exists["-I"] == 0 and self.exists["+I"] == 0: + if self.exists["-J"]: + if self.colors["-J"] == 0: + self.type = "X" + else: + self.type = "Z" + else: # must exist +J + if self.colors["+J"] == 0: + self.type = "X" + else: + self.type = "Z" + + if self.exists["-J"] == 0 and self.exists["+J"] == 0: + if self.exists["-I"]: + if self.colors["-I"] == 0: + self.type = "Z" + else: + self.type = "X" + else: # must exist +I + if self.colors["+I"] == 0: + self.type = "Z" + else: + self.type = "X" + + if self.exists["-K"] == 0 and self.exists["+K"] == 0: + if self.exists["-I"]: + if self.colors["-I"] == 0: + self.type = "X" + else: + self.type = "Z" + else: # must exist +I + if self.colors["+I"] == 0: + self.type = "X" + else: + self.type = "Z" + + def zigxag_xy(self, n_j: int) -> Tuple[int, int]: + return (self.k * (n_j + 2) + self.j, -(n_j + 1) * self.i + self.j) + + def zigxag_str(self, n_j: int) -> str: + zigxag_type = { + 'Z': '@', + 'X': 'O', + 'S': 's', + 'W': 'w', + 'I': 'O', + 'Pi': 'in', + 'Po': 'out', + } + (x, y) = self.zigxag_xy(n_j) + return str(-y) + ',' + str(-x) + ',' + str(zigxag_type[self.type]) + + +class ZXGridEdge: + + def __init__(self, if_h: bool, node0: ZXGridNode, + node1: ZXGridNode) -> None: + """initialize ZXGridEdge for a pipe in the LaS. + + Args: + if_h (bool): if this edge is a Hadamard edge. + node0 (ZXGridNode): one end of the edge. + node1 (ZXGridNode): the other end of the edge. + + Raises: + ValueError: the two spiders are the same. + ValueError: the two spiders are not neighbors. + """ + + dist = abs(node0.i - node1.i) + abs(node0.j - node1.j) + abs(node0.k - + node1.k) + if dist == 0: + raise ValueError(f"{node0} and {node1} are the same.") + if dist > 1: + raise ValueError(f"{node0} and {node1} are not neighbors.") + self.node0, self.node1 = node0, node1 + self.type = "h" if if_h else "-" + + def zigxag_str(self, n_j: int) -> str: + (xa, ya) = self.node0.zigxag_xy(n_j) + (xb, yb) = self.node1.zigxag_xy(n_j) + return (str(-ya) + ',' + str(-xa) + ',' + str(-yb) + ',' + str(-xb) + + ',' + self.type) + + +class ZXGridGraph: + + def __init__(self, lasre: Mapping[str, Any]) -> None: + self.lasre = lasre + self.n_i, self.n_j, self.n_k = ( + lasre["n_i"], + lasre["n_j"], + lasre["n_k"], + ) + self.nodes = [[[ + ZXGridNode((i, j, k), self.gather_cube_connectivity(i, j, k)) + for k in range(self.n_k + 1) + ] for j in range(self.n_j + 1)] for i in range(self.n_i + 1)] + for (i, j, k) in self.lasre["port_cubes"]: + self.nodes[i][j][k].type = 'Po' + self.append_y_tails() + self.edges = [] + self.derive_edges() + + def gather_cube_connectivity(self, i: int, j: int, + k: int) -> Mapping[str, Mapping[str, int]]: + # exists and colors for no cube + exists = {"-I": 0, "+I": 0, "-K": 0, "+K": 0, "-J": 0, "+J": 0} + colors = { + "-I": -1, + "+I": -1, + "-K": -1, + "+K": -1, + "-J": -1, + "+J": -1, + } + if i in range(self.n_i) and j in range(self.n_j) and k in range( + self.n_k) and ((i, j, k) not in self.lasre["port_cubes"]) and ( + self.lasre["NodeY"][i][j][k] == 0): + if i > 0 and self.lasre["ExistI"][i - 1][j][k]: + exists["-I"] = 1 + colors["-I"] = self.lasre["ColorI"][i - 1][j][k] + if self.lasre["ExistI"][i][j][k]: + exists["+I"] = 1 + colors["+I"] = self.lasre["ColorI"][i][j][k] + if j > 0 and self.lasre["ExistJ"][i][j - 1][k]: + exists["-J"] = 1 + colors["-J"] = self.lasre["ColorJ"][i][j - 1][k] + if self.lasre["ExistJ"][i][j][k]: + exists["+J"] = 1 + colors["+J"] = self.lasre["ColorJ"][i][j][k] + if k > 0 and self.lasre["ExistK"][i][j][k - 1]: + exists["-K"] = 1 + colors["-K"] = self.lasre["ColorKP"][i][j][k - 1] + if self.lasre["ExistK"][i][j][k]: + exists["+K"] = 1 + colors["+K"] = self.lasre["ColorKM"][i][j][k] + return {"exists": exists, "colors": colors} + + def append_y_tails(self) -> None: + for i in range(self.n_i): + for j in range(self.n_j): + for k in range(self.n_k): + if self.lasre["NodeY"][i][j][k]: + if (k - 1 >= 0 and self.lasre["ExistK"][i][j][k - 1] + and (not self.lasre["NodeY"][i][j][k - 1])): + self.nodes[i][j][k - 1].y_tail_plus = True + if (k + 1 < self.n_k and self.lasre["ExistK"][i][j][k] + and (not self.lasre["NodeY"][i][j][k + 1])): + self.nodes[i][j][k + 1].y_tail_minus = True + + def derive_edges(self): + valid_types = ["Z", "X", "S", "I", "Pi", "Po"] + for i in range(self.n_i): + for j in range(self.n_j): + for k in range(self.n_k): + if (self.lasre["ExistI"][i][j][k] == 1 + and self.nodes[i][j][k].type in valid_types + and self.nodes[i + 1][j][k].type in valid_types): + self.edges.append( + ZXGridEdge(0, self.nodes[i][j][k], + self.nodes[i + 1][j][k])) + + if (self.lasre["ExistJ"][i][j][k] == 1 + and self.nodes[i][j][k].type in valid_types + and self.nodes[i][j + 1][k].type in valid_types): + self.edges.append( + ZXGridEdge(0, self.nodes[i][j][k], + self.nodes[i][j + 1][k])) + + if (self.lasre["ExistK"][i][j][k] == 1 + and self.nodes[i][j][k].type in valid_types + and self.nodes[i][j][k + 1].type in valid_types): + self.edges.append( + ZXGridEdge( + abs(self.lasre["ColorKM"][i][j][k] - + self.lasre["ColorKP"][i][j][k]), + self.nodes[i][j][k], + self.nodes[i][j][k + 1], + )) + + def to_zigxag_url(self, io_spec: Optional[Sequence[str]] = None) -> str: + """generate a url for ZigXag + + Args: + io_spec (Sequence[str], optional): specify whether each port is an + input port or an output port. + + Raises: + ValueError: len(io_spec) is not the same with the number of ports. + + Returns: + str: zigxag url + """ + if io_spec is not None: + if len(io_spec) != len(self.lasre["port_cubes"]): + raise ValueError( + f"io_spec has length {len(io_spec)} but there are " + f"{len(self.lasre['port_cubes'])} ports.") + for w, (i, j, k) in enumerate(self.lasre["port_cubes"]): + self.nodes[i][j][k].type = io_spec[w] + + valid_types = ["Z", "X", "S", "W", "I", "Pi", "Po"] + nodes_str = "" + first = True + for i in range(self.n_i + 1): + for j in range(self.n_j + 1): + for k in range(self.n_k + 1): + if self.nodes[i][j][k].type in valid_types: + if not first: + nodes_str += ";" + nodes_str += self.nodes[i][j][k].zigxag_str(self.n_j) + first = False + + edges_str = "" + for i, edge in enumerate(self.edges): + if i > 0: + edges_str += ";" + edges_str += edge.zigxag_str(self.n_j) + + # add nodes and edges for Y cubes + for i in range(self.n_i): + for j in range(self.n_j): + for k in range(self.n_k): + (x, y) = self.nodes[i][j][k].zigxag_xy(self.n_j) + if self.nodes[i][j][k].y_tail_plus: + nodes_str += (";" + str(x + self.n_j - j) + "," + + str(y) + ",s") + edges_str += (";" + str(x + self.n_j - j) + "," + + str(y) + "," + str(x) + "," + str(y) + + ",-") + if self.nodes[i][j][k].y_tail_minus: + nodes_str += (";" + str(x - j - 1) + "," + str(y) + + ",s") + edges_str += (";" + str(x - j - 1) + "," + str(y) + + "," + str(x) + "," + str(y) + ",-") + + zigxag_str = "https://algassert.com/zigxag#" + nodes_str + ":" + edges_str + return zigxag_str diff --git a/glue/lattice_surgery/olssco/__init__.py b/glue/lattice_surgery/olssco/__init__.py deleted file mode 100644 index 42e9d2075..000000000 --- a/glue/lattice_surgery/olssco/__init__.py +++ /dev/null @@ -1,2 +0,0 @@ -from .lattice_surgery_compiler import LatticeSurgeryProblem -from .lattice_surgery_compiler import LatticeSurgerySolution diff --git a/glue/lattice_surgery/olssco/lattice_surgery_compiler.py b/glue/lattice_surgery/olssco/lattice_surgery_compiler.py deleted file mode 100644 index 80f604709..000000000 --- a/glue/lattice_surgery/olssco/lattice_surgery_compiler.py +++ /dev/null @@ -1,460 +0,0 @@ -"""Two wrapper classes fpr OLSSSol, rewrite passes, and translators.""" - -import functools -import itertools -import json -import multiprocessing -import random -from typing import Any, Literal, Mapping, Optional, Sequence -from olssco.rewrite_passes.attach_fixups import attach_fixups -from olssco.rewrite_passes.color_z import color_z -from olssco.rewrite_passes.remove_unconnected import remove_unconnected -from olssco.sat_lattice_surgery_solver import OptimalLatticeSurgerySubroutineSolver -from olssco.tools.verify_stabilizers import verify_stabilizers -from olssco.translators.gltf_generator import gltf_generator -from olssco.translators.networkx_generator import networkx_generator -from olssco.translators.textfig_generator import textfig_generator -from olssco.translators.zigxag_generator import zigxag_generator - - -class LatticeSurgerySolution: - """A class for the result of compilation lattice surgery subroutine (LSS). - - It internally saves an LaSSIR (Lattice Surgery Subroutine Intermediate - Representation) and we can apply rewrite passes to it, or use translators to - derive other formats of the LSS solution - """ - - def __init__( - self, - *, - lassir: Mapping[str, Any], - ) -> None: - """initialization for LatticeSurgerySubroutine - - Args: - lassir (Mapping[str, Any]): LaSSIR - """ - self.lassir = lassir - - def get_depth(self) -> int: - """get the depth/height of the LSS in LaSSIR. - - Returns: - int: depth/height of the LSS in LaSSIR - """ - return self.lassir["n_k"] - - def after_removing_disconnected_pieces(self): - """remove_unconnected.""" - return LatticeSurgerySolution(lassir=remove_unconnected(self.lassir)) - - def after_color_k_pipes(self): - """coloring K pipes.""" - return LatticeSurgerySolution(lassir=color_z(self.lassir)) - - def after_default_optimizations(self): - """default optimizations: remove unconnected, and then color K pipes.""" - solution = LatticeSurgerySolution(lassir=remove_unconnected(self.lassir)) - solution = LatticeSurgerySolution(lassir=color_z(solution.lassir)) - return solution - - def after_t_factory_default_optimizations(self): - """default optimization for T-factories.""" - solution = LatticeSurgerySolution(lassir=remove_unconnected(self.lassir)) - solution = LatticeSurgerySolution(lassir=color_z(solution.lassir)) - solution = LatticeSurgerySolution(lassir=attach_fixups(solution.lassir)) - return solution - - def save_lassir(self, file_name: str) -> None: - """save the current LaSSIR to a file. - - Args: - file_name (str): file to save the current LaSSIR - """ - with open(file_name, "w") as f: - json.dump(self.lassir, f) - - def to_3d_model_gltf( - self, - output_file_name: str, - stabilizer: int = -1, - tube_len: float = 2.0, - no_color_z: bool = False, - ) -> None: - """generate gltf file (for 3D modelling). - - Args: - output_file_name (str): - stabilizer (int, optional): Defaults to -1 meaning do not draw - correlation surfaces. If the value is in [0, n_s), the correlation - surfaces corresponding to that stabilizer are drawn and faces in one - of the directions are revealed to unveil the correlation surfaces. - tube_len (float, optional): Length of the pipe comapred to the cube. - Defaults to 2.0. - no_color_z (bool, optional): Do not color the K pipes. Defaults to - False. - """ - gltf_generator( - self.lassir, - output_file=output_file_name, - stabilizer=stabilizer, - tube_len=tube_len, - no_color_z=no_color_z, - ) - - def to_zigxag_url( - self, - io_spec: Optional[Sequence[str]] = None, - ) -> str: - """generate a link that leads to a ZigXag figure. - - Args: - io_spec (Optional[Sequence[str]], optional): Specify whether each port - is an input or an output. Length must be the same with the number of - ports. Defaults to None, which means all ports are outputs. - - Returns: - str: the ZigXag link - """ - return zigxag_generator(self.lassir, io_spec=io_spec) - - def to_text_diagram( - self, - ) -> str: - """generate the text figure of LSS time slices. - - Returns: - str: text figure of the LSS - """ - return textfig_generator(self.lassir) - - def generate_networkx(self): - """generate a annotated networkx.Graph correponding to the LSS. - - Returns: - networkx.Graph: - """ - return networkx_generator(self.lassir) - - def verify_stabilizers_stimzx(self, print_stabilizers: bool = False) -> bool: - """verify the stabilizer of the LSS. - - Use Stim ZX to deduce the stabilizers from the annotated networkx graph. - Then use Stim to ensure that this set of stabilizers and the set of - stabilizers specified in the input are equivalent. - - Args: - print_stabilizers (bool, optional): If True, print the two sets of - stabilizers. Defaults to False. - - Returns: - bool: True if the two sets are equivalent; otherwise False. - """ - paulistrings = [ - paulistring.replace(".", "_") - for paulistring in self.lassir["specification"]["stabilizers"] - ] - return verify_stabilizers( - paulistrings, - self.generate_networkx(), - print_stabilizers=print_stabilizers, - ) - - -class LatticeSurgeryProblem: - """A class to provide the input specification of LSS and solve it.""" - - def __init__( - self, - specification: Optional[Mapping[str, Any]] = None, - solver: Literal["kissat", "z3"] = "z3", - kissat_dir: Optional[str] = None, - ) -> None: - """initialize LatticeSurgeryCompiler. - - Args: - specification (Optional[Mapping[str, Any]], optional): the LSS - specification to solve. Defaults to None. - solver (Literal["kissat", "z3"], optional): the solver to use. Defaults - to "z3". "kissat" is recommended. - kissat_dir (Optional[str], optional): directory of the kissat - executable. Defaults to None. - """ - self.specification = specification - self.result = None - self.solver = solver - self.kissat_dir = kissat_dir - - def solve( - self, - specification: Optional[Mapping[str, Any]] = None, - given_arrs: Optional[Mapping[str, Any]] = None, - given_vals: Optional[Sequence[Mapping[str, Any]]] = None, - print_detail: bool = False, - dimacs_file_name: Optional[str] = None, - sat_log_file_name: Optional[str] = None, - ) -> Optional[LatticeSurgerySolution]: - """solve an LSS compilation problem. - - Args: - specification (Optional[Mapping[str, Any]], optional): the LSS - specification to solve. Defaults to None. - given_arrs (Optional[Mapping[str, Any]], optional): given array of known - values to plug in. Defaults to None. - given_vals (Optional[Sequence[Mapping[str, Any]]], optional): given - known values to plug in. Defaults to None. Format should be a sequence - of dicts. Each one contains three fields: 'array', the name of the - array, e.g., 'ExistI'; 'indices', a sequence of the indices, e.g., [0, - 0, 0]; and 'value', 0 or 1. - print_detail (bool, optional): whether to print details in SAT solving. - Defaults to False. - dimacs_file_name (Optional[str], optional): file to save the DIMACS. - Defaults to None. - sat_log_file_name (Optional[str], optional): file to save the SAT solver - log. Defaults to None. - - Returns: - Optional[LatticeSurgerySubroutine]: if the problem is unsatisfiable, - this is None; otherwise, an object initialized by the compiled result. - """ - olsssol = OptimalLatticeSurgerySubroutineSolver( - input_dict=specification if specification else self.specification, - given_arrs=given_arrs, - given_vals=given_vals, - ) - - if self.solver == "z3": - if_sat = olsssol.check_z3(print_progress=print_detail) - else: - if_sat = olsssol.check_external_solver( - dimacs_file_name=dimacs_file_name, - sat_log_file_name=sat_log_file_name, - print_progress=print_detail, - kissat_dir=self.kissat_dir, - ) - - if if_sat: - solver_result = olsssol.get_result() - self.result = LatticeSurgerySolution(lassir=solver_result) - return self.result - else: - return None - - def optimize_depth( - self, - start_depth: int, - print_detail: bool = False, - dimacs_file_name_prefix: Optional[str] = None, - sat_log_file_name_prefix: Optional[str] = None, - ) -> LatticeSurgerySolution: - """find the optimal solution in terms of depth/height of the LSS. - - Args: - start_depth (int): starting depth of the exploration - print_detail (bool, optional): whether to print details in SAT solving. - Defaults to False. - dimacs_file_name_prefix (Optional[str], optional): file prefix to save - the DIMACS. The full file name will contain the specific depth after - this prefix. Defaults to None. - sat_log_file_name_prefix (Optional[str], optional): file prefix to save - the SAT log. The full file name will contain the specific depth after - this prefix. Defaults to None. - result_file_name_prefix (Optional[str], optional): file prefix to save - the variable assignments. The full file name will contain the specific - depth after this prefix. Defaults to None. - post_optimization (str, optional): optimization to perform when - initializing the LatticeSurgerySubroutine object for the result. - Defaults to "default". - - Raises: - ValueError: starting depth is too low. - - Returns: - LatticeSurgerySubroutine: compiled result with the optimal depth. - """ - depth = int(start_depth) - if depth < 2: - raise ValueError("depth too low.") - - checked_depth = {} - while True: - # the ports on the top floor will still be on the top floor when we - # increase the height. This is an assumption. Adapt to your use cases. - for port in self.specification["ports"]: - if port["location"][2] == self.specification["max_k"]: - port["location"][2] = depth - self.specification["max_k"] = depth - - result = self.solve( - print_detail=print_detail, - dimacs_file_name=dimacs_file_name_prefix + f"_d={depth}" - if dimacs_file_name_prefix - else None, - sat_log_file_name=sat_log_file_name_prefix + f"_d={depth}" - if sat_log_file_name_prefix - else None, - ) - if result is None: - checked_depth[str(depth)] = "UNSAT" - if str(depth + 1) in checked_depth: - # since this depth leads to UNSAT, we need to increase the depth, - # but if depth+1 is already checked, we can stop - break - else: - depth += 1 - else: - checked_depth[str(depth)] = "SAT" - self.sat_result = LatticeSurgerySolution(lassir=result.lassir) - if str(depth - 1) in checked_depth: - # since this depth leads to SAT, we need to try decreasing the depth, - # but if depth-1 is already checked, we can stop - break - else: - depth -= 1 - - return self.sat_result - - def with_permuted_ports(self, perm): - # say permutation is [0,3,2], then original is in order, i.e., [0,2,3] - # the full permutation is 0,1,2,3 -> 0,1,3,2 - original = sorted(perm) - this_input = dict(self.specification) - new_ports = [] - for p, port in enumerate(self.specification["ports"]): - if p not in perm: - # the p-th port is not involved in the permutation, e.g., 1 is unchanged - new_ports.append(port) - - else: - # after the permutation, the index of the p-th port is the k-th port in - # `perm` where k is the place of p in `original`. In this example, when - # p=0 and 1, nothing changed. When p=2, we find `place` to be 1, and - # perm[place]=3, so we attach port_3. When p=3, we end up attach port_2 - place = original.index(p) - new_ports.append(self.specification["ports"][perm[place]]) - this_input["ports"] = new_ports - return LatticeSurgeryProblem(this_input) - - def try_one_permutation( - self, - perm: Sequence[int], - print_detail: bool = False, - dimacs_file_name_prefix: Optional[str] = None, - sat_log_file_name_prefix: Optional[str] = None, - result_file_name_prefix: Optional[str] = None, - ) -> Optional[LatticeSurgerySolution]: - """check after the given permutation of ports, if the problem is satisfiable. - - Args: - perm (Sequence[int]): the given permutation, which is an integer tuple - of length n (n being the number of ports permuted). - print_detail (bool, optional): whether to print details in SAT solving. - Defaults to False. - dimacs_file_name_prefix (Optional[str], optional): file prefix to save - the DIMACS. The full file name will contain the specific permutation - after this prefix. Defaults to None. - sat_log_file_name_prefix (Optional[str], optional): file prefix to save - the SAT log. The full file name will contain the specific permutation - after this prefix. Defaults to None. - result_file_name_prefix (Optional[str], optional): file prefix to save - the variable assignments. The full file name will contain the specific - permutation after this prefix. Defaults to None. - - Returns: - Optional[LatticeSurgerySubroutine]: if the problem is unsatisfiable, - this is None; otherwise, an object initialized by the compiled result. - """ - - # say permutation is [0,3,2], then original is in order, i.e., [0,2,3] - # the full permutation is 0,1,2,3 -> 0,1,3,2 - original = sorted(perm) - this_input = dict(self.specification) - new_ports = [] - for p, port in enumerate(self.specification["ports"]): - if p not in perm: - # the p-th port is not involved in the permutation, e.g., 1 is unchanged - new_ports.append(port) - - else: - # after the permutation, the index of the p-th port is the k-th port in - # `perm` where k is the place of p in `original`. In this example, when - # p=0 and 1, nothing changed. When p=2, we find `place` to be 1, and - # perm[place]=3, so we attach port_3. When p=3, we end up attach port_2 - place = original.index(p) - new_ports.append(self.specification["ports"][perm[place]]) - this_input["ports"] = new_ports - - result = self.solve( - specification=this_input, - print_detail=print_detail, - dimacs_file_name=dimacs_file_name_prefix - + "_" - + perm.__repr__().replace(" ", "") - if dimacs_file_name_prefix - else None, - sat_log_file_name=sat_log_file_name_prefix - + "_" - + perm.__repr__().replace(" ", "") - if sat_log_file_name_prefix - else None, - ) - print(f"{perm}: {'SAT' if result else 'UNSAT'}") - return result - - def solve_all_port_permutations( - self, - permute_ports: Sequence[int], - parallelism: int = 1, - shuffle: bool = True, - **kwargs, - ) -> Mapping[str, Sequence[Sequence[int]]]: - """try all the permutations of given ports to see which ones are satisfiable. - - Notice that we do not check that the LSS after permuting the ports (we do - not permute the stabilizers accordingly) is functionally equivalent. The - users should use this method based on their judgement. Also, the number of - permutations scales exponentially with the number of ports to permute, so - this method can easily take an immense amount of time. - - Args: - permute_ports (Sequence[int]): the indices of ports to permite - parallelism (int, optional): number of parallel process. Each one try - one permutation. A New proess starts when an old one finishes. - Defaults to 1. - shuffle (bool, optional): whether using a random order to start the - processes. Defaults to True. - **kwargs: - - Returns: - Mapping[str, Sequence[Sequence[int]]]: a dict with two keys. "SAT": [.] - a list containing all the satisfiable permutations; "UNSAT": [.] - all the unsatisfiable permutations - """ - perms = list(itertools.permutations(permute_ports)) - if shuffle: - random.shuffle(perms) - - pool = multiprocessing.Pool(parallelism) - # issue the job one by one (chuck=1) - results = pool.map( - functools.partial( - self.try_one_permutation, - **kwargs, - ), - perms, - chunksize=1, - ) - - sat_perms = [] - unsat_perms = [] - for p, result in enumerate(results): - if result is None: - unsat_perms.append(perms[p]) - else: - sat_perms.append(perms[p]) - - return { - "SAT": sat_perms, - "UNSAT": unsat_perms, - } diff --git a/glue/lattice_surgery/olssco/rewrite_passes/attach_fixups.py b/glue/lattice_surgery/olssco/rewrite_passes/attach_fixups.py deleted file mode 100644 index 770e410cb..000000000 --- a/glue/lattice_surgery/olssco/rewrite_passes/attach_fixups.py +++ /dev/null @@ -1,64 +0,0 @@ -# assuming all T injections requiring fixup are on the top floor. The output is also on the top floor - - -def attach_fixups(lasir): - n_s = len(lasir['CorrIJ']) - n_i = lasir['n_i'] - n_j = lasir['n_j'] - n_k = lasir['n_k'] - - fixup_locs = [] - for p in lasir['optional']['top_fixups']: - fixup_locs.append((lasir['ports'][p]['i'], lasir['ports'][p]['j'])) - - for i in range(n_i): - for j in range(n_j): - if (i, j) in fixup_locs: - lasir['NodeY'][i][j].append(1) - lasir['ExistK'][i][j][n_k - 1] = 1 - else: - lasir['NodeY'][i][j].append(0) - lasir['ExistK'][i][j][n_k - 1] = 0 - lasir['NodeY'][i][j].append(0) - for arr in ['ExistI', 'ExistJ', 'ExistK']: - lasir[arr][i][j].append(0) - lasir[arr][i][j].append(0) - for arr in ['ColorI', 'ColorJ', 'ColorKM', 'ColorKP']: - lasir[arr][i][j].append(-1) - lasir[arr][i][j].append(-1) - for s in range(n_s): - for arr in ['CorrIJ', 'CorrIK', 'CorrJK', 'CorrJI', 'CorrKI', 'CorrKJ']: - lasir[arr][s][i][j].append(0) - lasir[arr][s][i][j].append(0) - - for port in lasir['ports']: - if 'f' in port and port['f'] == 'output': - ii, jj = port['i'], port['j'] - lasir['ExistK'][ii][jj][n_k - 1] = 1 - lasir['ExistK'][ii][jj][n_k] = 1 - lasir['ExistK'][ii][jj][n_k + 1] = 1 - lasir['ColorKM'][ii][jj][n_k] = lasir['ColorKP'][ii][jj][n_k - 1] - lasir['ColorKM'][ii][jj][n_k + 1] = lasir['ColorKM'][ii][jj][n_k] - lasir['ColorKP'][ii][jj][n_k] = lasir['ColorKM'][ii][jj][n_k] - lasir['ColorKP'][ii][jj][n_k + 1] = lasir['ColorKP'][ii][jj][n_k] - for s in range(n_s): - lasir['CorrKI'][s][ii][jj][n_k] = lasir['CorrKI'][s][ii][jj][n_k - 1] - lasir['CorrKI'][s][ii][jj][n_k + 1] = lasir['CorrKI'][s][ii][jj][n_k] - lasir['CorrKJ'][s][ii][jj][n_k] = lasir['CorrKJ'][s][ii][jj][n_k - 1] - lasir['CorrKJ'][s][ii][jj][n_k + 1] = lasir['CorrKJ'][s][ii][jj][n_k] - port['k'] += 2 - for c in lasir['port_cubes']: - if c[0] == port['i'] and c[1] == port['j']: - c[2] = port['k'] + 1 - - t_injections = [] - for port in lasir['ports']: - if port['f'] == 'T': - if port['e'] == '+': - t_injections.append([port['i'], port['j'], port['k'] + 1]) - else: - t_injections.append([port['i'], port['j'], port['k']]) - lasir['optional']['t_injections'] = t_injections - - lasir['n_k'] += 2 - return lasir diff --git a/glue/lattice_surgery/olssco/rewrite_passes/color_z.py b/glue/lattice_surgery/olssco/rewrite_passes/color_z.py deleted file mode 100644 index ead83a445..000000000 --- a/glue/lattice_surgery/olssco/rewrite_passes/color_z.py +++ /dev/null @@ -1,176 +0,0 @@ -"""A one-line summary of the module or program, terminated by a period. - -Leave one blank line. The rest of this docstring should contain an -overall description of the module or program. Optionally, it may also -contain a brief description of exported classes and functions and/or usage -examples. - -Typical usage example: - - foo = ClassFoo() - bar = foo.FunctionBar() -""" - - -def if_uncolorK(n_i, n_j, n_k, ExistK, ColorKP, ColorKM): - for i in range(n_i): - for j in range(n_j): - for k in range(n_k): - if ExistK[i][j][k] and ( - ColorKP[i][j][k] == -1 or ColorKM[i][j][k] == -1 - ): - # print((i,j,k)) - return True - return False - - -def in_bound(n_i, n_j, n_k, i, j, k): - if i in range(n_i) and j in range(n_j) and k in range(n_k): - return True - return False - - -def propogate_IJcolor( - n_i, n_j, n_k, ExistI, ExistJ, ExistK, ColorI, ColorJ, ColorKP, ColorKM -): - for i in range(n_i): - for j in range(n_j): - for k in range(n_k): - if ExistK[i][j][k]: - if in_bound(n_i, n_j, n_k, i - 1, j, k) and ExistI[i - 1][j][k]: - ColorKM[i][j][k] = 1 - ColorI[i - 1][j][k] - if ExistI[i][j][k]: - ColorKM[i][j][k] = 1 - ColorI[i][j][k] - if in_bound(n_i, n_j, n_k, i, j - 1, k) and ExistJ[i][j - 1][k]: - ColorKM[i][j][k] = 1 - ColorJ[i][j - 1][k] - if ExistJ[i][j][k]: - ColorKM[i][j][k] = 1 - ColorJ[i][j][k] - - if ( - in_bound(n_i, n_j, n_k, i - 1, j, k + 1) - and ExistI[i - 1][j][k + 1] - ): - ColorKP[i][j][k] = 1 - ColorI[i - 1][j][k + 1] - if in_bound(n_i, n_j, n_k, i, j, k + 1) and ExistI[i][j][k + 1]: - ColorKP[i][j][k] = 1 - ColorI[i][j][k + 1] - if ( - in_bound(n_i, n_j, n_k, i, j - 1, k + 1) - and ExistJ[i][j - 1][k + 1] - ): - ColorKP[i][j][k] = 1 - ColorJ[i][j - 1][k + 1] - if in_bound(n_i, n_j, n_k, i, j, k + 1) and ExistJ[i][j][k + 1]: - ColorKP[i][j][k] = 1 - ColorJ[i][j][k + 1] - - -def propogate_Kcolor(n_i, n_j, n_k, ExistK, ColorKP, ColorKM, NodeY): - did_something = False - for i in range(n_i): - for j in range(n_j): - for k in range(n_k): - if ExistK[i][j][k]: - if in_bound(n_i, n_j, n_k, i, j, k - 1) and ExistK[i][j][k - 1]: - if ColorKP[i][j][k - 1] > -1 and ColorKM[i][j][k] == -1: - ColorKM[i][j][k] = ColorKP[i][j][k - 1] - did_something = True - if in_bound(n_i, n_j, n_k, i, j, k + 1) and ExistK[i][j][k + 1]: - if ColorKM[i][j][k + 1] > -1 and ColorKP[i][j][k] == -1: - ColorKP[i][j][k] = ColorKM[i][j][k + 1] - did_something = True - if ( - NodeY[i][j][k] - and ColorKM[i][j][k] == -1 - and ColorKP[i][j][k] > -1 - ): - ColorKM[i][j][k] = ColorKP[i][j][k] - did_something = True - if ( - in_bound(n_i, n_j, n_k, i, j, k + 1) - and NodeY[i][j][k + 1] - and ColorKM[i][j][k] > -1 - and ColorKP[i][j][k] == -1 - ): - ColorKP[i][j][k] = ColorKM[i][j][k] - did_something = True - return did_something - - -def assign_Kcolor(n_i, n_j, n_k, ExistK, ColorKP, ColorKM, NodeY): - for i in range(n_i): - for j in range(n_j): - for k in range(n_k): - if ExistK[i][j][k]: - if ColorKM[i][j][k] > -1 and ColorKP[i][j][k] == -1: - ColorKP[i][j][k] = ColorKM[i][j][k] - break - - for i in range(n_i): - for j in range(n_j): - for k in range(n_k): - if ExistK[i][j][k]: - if NodeY[i][j][k] and ColorKM[i][j][k] == -1: - ColorKM[i][j][k] = 0 - break - if ( - in_bound(n_i, n_j, n_k, i, j, k + 1) - and NodeY[i][j][k + 1] - and ColorKP[i][j][k] == -1 - ): - ColorKP[i][j][k] = 0 - break - - -def color_ports(ports, ColorKP, ColorKM): - for port in ports: - if port['d'] == 'K': - if port['e'] == '+': - ColorKP[port['i']][port['j']][port['k']] = port['c'] - else: - ColorKM[port['i']][port['j']][port['k']] = port['c'] - - -def colorZ( - n_i, - n_j, - n_k, - ExistI, - ExistJ, - ExistK, - ColorI, - ColorJ, - ports, - NodeY, - noPrune=False, -): - ColorKP = [[[-1 for _ in range(n_k)] for _ in range(n_j)] for _ in range(n_i)] - ColorKM = [[[-1 for _ in range(n_k)] for _ in range(n_j)] for _ in range(n_i)] - color_ports(ports, ColorKP, ColorKM) - propogate_IJcolor( - n_i, n_j, n_k, ExistI, ExistJ, ExistK, ColorI, ColorJ, ColorKP, ColorKM - ) - while (not noPrune) and if_uncolorK(n_i, n_j, n_k, ExistK, ColorKP, ColorKM): - if not propogate_Kcolor(n_i, n_j, n_k, ExistK, ColorKP, ColorKM, NodeY): - assign_Kcolor(n_i, n_j, n_k, ExistK, ColorKP, ColorKM, NodeY) - return ColorKP, ColorKM - - -def color_z(lasir: dict): - n_i, n_j, n_k, ExistK = ( - lasir['n_i'], - lasir['n_j'], - lasir['n_k'], - lasir['ExistK'], - ) - ExistI, ColorI, ExistJ, ColorJ = ( - lasir['ExistI'], - lasir['ColorI'], - lasir['ExistJ'], - lasir['ColorJ'], - ) - NodeY = lasir['NodeY'] - ports, port_cubes = lasir['ports'], lasir['port_cubes'] - - lasir['ColorKP'], lasir['ColorKM'] = colorZ( - n_i, n_j, n_k, ExistI, ExistJ, ExistK, ColorI, ColorJ, ports, NodeY - ) - # lasir['ColorKP'], lasir['ColorKM'] = [[[-1 for _ in range(n_k)] for _ in range(n_j)] for _ in range(n_i)], [[[-1 for _ in range(n_k)] for _ in range(n_j)] for _ in range(n_i)] - return lasir diff --git a/glue/lattice_surgery/olssco/rewrite_passes/remove_unconnected.py b/glue/lattice_surgery/olssco/rewrite_passes/remove_unconnected.py deleted file mode 100644 index 3af8695ac..000000000 --- a/glue/lattice_surgery/olssco/rewrite_passes/remove_unconnected.py +++ /dev/null @@ -1,134 +0,0 @@ -"""A one-line summary of the module or program, terminated by a period. - -Leave one blank line. The rest of this docstring should contain an -overall description of the module or program. Optionally, it may also -contain a brief description of exported classes and functions and/or usage -examples. - -Typical usage example: - - foo = ClassFoo() - bar = foo.FunctionBar() -""" - - -def check_connect(n_i, n_j, n_k, ExistI, ExistJ, ExistK, ports, NodeY): - y_nodes = [ - i * n_j * n_k + j * n_k + k - for i in range(n_i) - for j in range(n_j) - for k in range(n_k) - if NodeY[i][j][k] - ] - Connect = [[[0 for _ in range(n_k)] for _ in range(n_j)] for _ in range(n_i)] - vips = [p['i'] * n_j * n_k + p['j'] * n_k + p['k'] for p in ports] - mat = [[0 for _ in range(n_i * n_j * n_k)] for _ in range(n_i * n_j * n_k)] - adj = [[] for _ in range(n_i * n_j * n_k)] - for i in range(n_i): - for j in range(n_j): - for k in range(n_k): - if ExistI[i][j][k] and i + 1 < n_i: - adj[i * n_j * n_k + j * n_k + k].append( - (i + 1) * n_j * n_k + j * n_k + k - ) - adj[(i + 1) * n_j * n_k + j * n_k + k].append( - i * n_j * n_k + j * n_k + k - ) - if ExistJ[i][j][k] and j + 1 < n_j: - adj[i * n_j * n_k + j * n_k + k].append( - i * n_j * n_k + (j + 1) * n_k + k - ) - adj[i * n_j * n_k + (j + 1) * n_k + k].append( - i * n_j * n_k + j * n_k + k - ) - if ExistK[i][j][k] and k + 1 < n_k: - adj[i * n_j * n_k + j * n_k + k].append( - i * n_j * n_k + j * n_k + k + 1 - ) - adj[i * n_j * n_k + j * n_k + k + 1].append( - i * n_j * n_k + j * n_k + k - ) - for i in range(n_i): - for j in range(n_j): - for k in range(n_k): - queue = [ - i * n_j * n_k + j * n_k + k, - ] - if i * n_j * n_k + j * n_k + k in y_nodes: - continue - visited = [0 for _ in range(n_i * n_j * n_k)] - while len(queue) > 0: - if queue[0] in vips: - Connect[i][j][k] = 1 - break - visited[queue[0]] = 1 - for v in adj[queue[0]]: - if not visited[v] and v not in y_nodes: - queue.append(v) - queue.pop(0) - - return Connect - - -def array3DAnd(arr0, arr1): - a = len(arr0) - b = len(arr0[0]) - c = len(arr0[0][0]) - arrAnd = [[[0 for _ in range(c)] for _ in range(b)] for _ in range(a)] - for i in range(a): - for j in range(b): - for k in range(c): - if arr0[i][j][k] == 1 and arr1[i][j][k] == 1: - arrAnd[i][j][k] = 1 - return arrAnd - - -def check_edge(n_i, n_j, n_k, ExistI, ExistJ, ExistK, Connect): - EffectI = [[[0 for _ in range(n_k)] for _ in range(n_j)] for _ in range(n_i)] - EffectJ = [[[0 for _ in range(n_k)] for _ in range(n_j)] for _ in range(n_i)] - EffectK = [[[0 for _ in range(n_k)] for _ in range(n_j)] for _ in range(n_i)] - for i in range(n_i): - for j in range(n_j): - for k in range(n_k): - if ExistI[i][j][k] and ( - Connect[i][j][k] or (i + 1 < n_i and Connect[i + 1][j][k]) - ): - EffectI[i][j][k] = 1 - if ExistJ[i][j][k] and ( - Connect[i][j][k] or (j + 1 < n_j and Connect[i][j + 1][k]) - ): - EffectJ[i][j][k] = 1 - if ExistK[i][j][k] and ( - Connect[i][j][k] or (k + 1 < n_k and Connect[i][j][k + 1]) - ): - EffectK[i][j][k] = 1 - return EffectI, EffectJ, EffectK - - -def remove_unconnected(lasir: dict): - n_i, n_j, n_k, ExistK = ( - lasir['n_i'], - lasir['n_j'], - lasir['n_k'], - lasir['ExistK'], - ) - ExistI, ColorI, ExistJ, ColorJ = ( - lasir['ExistI'], - lasir['ColorI'], - lasir['ExistJ'], - lasir['ColorJ'], - ) - NodeY = lasir['NodeY'] - ports, port_cubes = lasir['ports'], lasir['port_cubes'] - Connect = check_connect(n_i, n_j, n_k, ExistI, ExistJ, ExistK, ports, NodeY) - EffectI, EffectJ, EffectK = check_edge( - n_i, n_j, n_k, ExistI, ExistJ, ExistK, Connect - ) - ExistI, ExistJ, ExistK = ( - array3DAnd(ExistI, EffectI), - array3DAnd(ExistJ, EffectJ), - array3DAnd(ExistK, EffectK), - ) - lasir['ExistI'], lasir['ExistJ'], lasir['ExistK'] = ExistI, ExistJ, ExistK - - return lasir diff --git a/glue/lattice_surgery/olssco/sat_lattice_surgery_solver.py b/glue/lattice_surgery/olssco/sat_lattice_surgery_solver.py deleted file mode 100644 index f8c294175..000000000 --- a/glue/lattice_surgery/olssco/sat_lattice_surgery_solver.py +++ /dev/null @@ -1,1805 +0,0 @@ -"""OLSSSol: Optimal Lattice Surgery Subroutine Solver - -It encodes a lattice surgery problem to SAT/SMT and checks whether there is a -solution. In this compilation problem, we are given certain spacetime volume, -certain ports, and certain stabilizers. OLSSSol encodes the constraints on -LaSSIR variables such that the resulting variable assignments consist of a valid -lattice surgery procedure with the correct functionality (satisfies all the -given stabilizers). OLSSSol finds the solution with a SAT/SMT solver. -""" - -import os -import subprocess -import sys -import tempfile -import time -from typing import Any, Mapping, Optional, Sequence -import z3 - - -def var_given( - data: dict[ - str, - Any, - ], - arr: str, - i: int, - j: int, - k: int, - l: int | None = None, -) -> bool: - """Check whether data[arr][i][j][k]([l]) is given. - - If the given indices are not found, or the number is neither 0 nor 1, return - False; otherwise return True. - - Args: - data (dict[ str, Any, ]): contain arrays - arr (str): ExistI, etc. - i (int): first index - j (int): second index - k (int): third index - l (int | None, optional): optional fourth index. Defaults to None. - - Returns: - bool: whether the variable value is given - """ - - if arr not in data: - return False - if i not in range(len(data[arr])): - return False - if j not in range(len(data[arr][i])): - return False - if k not in range(len(data[arr][i][j])): - return False - if l is None: - if data[arr][i][j][k] != 0 and data[arr][i][j][k] != 1: - return False - return True - # l is not None, then - if l not in range(len(data[arr][i][j][k])): - return False - if data[arr][i][j][k][l] != 0 and data[arr][i][j][k][l] != 1: - return False - return True - - -def port_incident_edges( - port: Mapping[str, str | int], n_i: int, n_j: int, n_k: int -) -> tuple[Sequence[str], Sequence[tuple[int, int, int]]]: - """Compute the edges incident to a port. - - A port is an edge with a dangling end. The incident edges of a port are the - five other edges connecting to that end. However, some of these edges can be - out of bound, we just want to compute those that are in bound. - - Args: - port (Mapping[str, str | int]): the port to consider - n_i (int): spatial bound on I direction - n_j (int): spatial bound on J direction - n_k (int): spatial bound on K direction - - Returns: - tuple[Sequence[str], Sequence[tuple[int, int, int]]]: - Two lists of the same length [0,6): (dirs, coords) - dirs: the direction of the incident edges, can be 'I', 'J', or 'K' - coords: the coordinates of the incident edges, each one is (i,j,k) - """ - coords = [] - dirs = [] - - # first, just consider adjancency without caring about out-of-bound - if port['d'] == 'I': - adj_dirs = ['I', 'J', 'J', 'K', 'K'] - if port['e'] == '-': # empty cube is (i,j,k) - adj_coords = [ - (port['i'] - 1, port['j'], port['k']), # (i-1,j,k)---(i,j,k) - (port['i'], port['j'] - 1, port['k']), # (i,j-1,k)---(i,j,k) - (port['i'], port['j'], port['k']), # (i,j,k)---(i+1,j,k) - (port['i'], port['j'], port['k'] - 1), # (i,j,k-1)---(i,j,k) - (port['i'], port['j'], port['k']), # (i,j,k)---(i,j,k+1) - ] - elif port['e'] == '+': # empty cube is (i+1,j,k) - adj_coords = [ - (port['i'] + 1, port['j'], port['k']), # (i+1,j,k)---(i+2,j,k) - (port['i'] + 1, port['j'] - 1, port['k']), # (i+1,j-1,k)---(i+1,j,k) - (port['i'] + 1, port['j'], port['k']), # (i+1,j,k)---(i+1,j+1,k) - (port['i'] + 1, port['j'], port['k'] - 1), # (i+1,j,k-1)---(i+1,j,k) - (port['i'] + 1, port['j'], port['k']), # (i+1,j,k)---(i+1,j,k+1) - ] - - if port['d'] == 'J': - adj_dirs = ['J', 'K', 'K', 'I', 'I'] - if port['e'] == '-': - adj_coords = [ - (port['i'], port['j'] - 1, port['k']), - (port['i'], port['j'], port['k'] - 1), - (port['i'], port['j'], port['k']), - (port['i'] - 1, port['j'], port['k']), - (port['i'], port['j'], port['k']), - ] - elif port['e'] == '+': - adj_coords = [ - (port['i'], port['j'] + 1, port['k']), - (port['i'], port['j'] + 1, port['k'] - 1), - (port['i'], port['j'] + 1, port['k']), - (port['i'] - 1, port['j'] + 1, port['k']), - (port['i'], port['j'] + 1, port['k']), - ] - - if port['d'] == 'K': - adj_dirs = ['K', 'I', 'I', 'J', 'J'] - if port['e'] == '-': - adj_coords = [ - (port['i'], port['j'], port['k'] - 1), - (port['i'] - 1, port['j'], port['k']), - (port['i'], port['j'], port['k']), - (port['i'], port['j'] - 1, port['k']), - (port['i'], port['j'], port['k']), - ] - elif port['e'] == '+': - adj_coords = [ - (port['i'], port['j'], port['k'] + 1), - (port['i'] - 1, port['j'], port['k'] + 1), - (port['i'], port['j'], port['k'] + 1), - (port['i'], port['j'] - 1, port['k'] + 1), - (port['i'], port['j'], port['k'] + 1), - ] - - # only keep the edges in bound - for i, coord in enumerate(adj_coords): - if ( - (coord[0] in range(n_i)) - and (coord[1] in range(n_j)) - and (coord[2] in range(n_k)) - ): - coords.append(adj_coords[i]) - dirs.append(adj_dirs[i]) - - return dirs, coords - - -def cnf_even_parity_upto4(eles: Sequence[Any]) -> Any: - """Compute the CNF format of parity of up to four Z3 binary variables. - - Args: - eles (Sequence[Any]): the binary variables - - Returns: - (Any) the Z3 constraint meaning the parity of the inputs is even. - """ - - if len(eles) == 1: # 1 var even parity -> this var is false - return z3.Not(eles[0]) - if len(eles) == 2: # 2 vars even pairty -> both True or both False - return z3.Or( - z3.And(z3.Not(eles[0]), z3.Not(eles[1])), z3.And(eles[0], eles[1]) - ) - if len(eles) == 3: # 3 vars even parity -> all False, or 2 True and 1 False - return z3.Or( - z3.And(z3.Not(eles[0]), z3.Not(eles[1]), z3.Not(eles[2])), - z3.And(eles[0], eles[1], z3.Not(eles[2])), - z3.And(eles[0], z3.Not(eles[1]), eles[2]), - z3.And(z3.Not(eles[0]), eles[1], eles[2]), - ) - if len(eles) == 4: # 4 vars even parity -> 0, 2, or 4 vars are True - return z3.Or( - z3.And( - z3.Not(eles[0]), z3.Not(eles[1]), z3.Not(eles[2]), z3.Not(eles[3]) - ), - z3.And(z3.Not(eles[0]), z3.Not(eles[1]), eles[2], eles[3]), - z3.And(z3.Not(eles[0]), eles[1], z3.Not(eles[2]), eles[3]), - z3.And(z3.Not(eles[0]), eles[1], eles[2], z3.Not(eles[3])), - z3.And(eles[0], z3.Not(eles[1]), z3.Not(eles[2]), eles[3]), - z3.And(eles[0], z3.Not(eles[1]), eles[2], z3.Not(eles[3])), - z3.And(eles[0], eles[1], z3.Not(eles[2]), z3.Not(eles[3])), - z3.And(eles[0], eles[1], eles[2], eles[3]), - ) - - -class OptimalLatticeSurgerySubroutineSolver: - """class of compiling LaSSIR using Z3 SMT solver.""" - - def __init__( - self, - input_dict: Mapping[str, Any], - given_arrs: Mapping[str, Any] | None = None, - given_vals: Sequence[Mapping[str, Any]] | None = None, - color_ij: bool = True, - ) -> None: - """initialization of OLSSSol objects. - - Args: - input_dict (Mapping[str, Any]): specification of LSS - given_arrs (Mapping[str, Any], optional): Arrays of values to plug in. - Defaults to None. - given_vals (Sequence[Mapping[str, Any]], optional): Values to plug in. - Defaults to None. - color_ij (bool, optional): if the color matching constraints of I and J - edges are imposed. Defaults to False. - """ - self.input_dict = input_dict - self.color_ij = color_ij - self.goal = z3.Goal() - self.process_input(input_dict) - self.build_smt_model( - given_arrs=given_arrs, given_vals=given_vals, color_ij=color_ij - ) - - def process_input(self, input_dict: Mapping[str, Any]) -> None: - """read input file, mainly translating the info of the ports. - - Args: - input_dict (Mapping[str, Any]): - - Raises: - ValueError: no input specification given - ValueError: missing key in input - ValueError: some spatial bound <= 0 - ValueError: more stabilizers than ports - ValueError: stabilizer length is not the same as the number of ports - ValueError: stabilizer contain things other than I, X, Y, or Z - ValueError: missing key in port - ValueError: port location is not a 3-tuple - ValueError: port direction is not 2-string - ValueError: port sign (which end is dangling) is not - or + - ValueError: port axis is not I, J, or K - ValueError: port Z basis direction is not I, J, or K, and not the same - with the edge - """ - data = input_dict - - if not input_dict: - raise ValueError('no input specification given.') - - for key in ['max_i', 'max_j', 'max_k', 'ports', 'stabilizers']: - if key not in data: - raise ValueError(f'missing key {key} in input.') - - # load spatial bound, check > 0 - self.n_i = data['max_i'] - self.n_j = data['max_j'] - self.n_k = data['max_k'] - if min([self.n_i, self.n_j, self.n_k]) <= 0: - raise ValueError('max_i or _j or _k <= 0.') - - self.n_p = len(data['ports']) - self.n_s = len(data['stabilizers']) - # there's at most as many stabilizers as ports - if self.n_s > self.n_p: - raise ValueError('Too many stabilizers compated to ports.') - - # stabilizers should be paulistrings of length #ports - self.paulistings = [s.replace('.', 'I') for s in data['stabilizers']] - for s in self.paulistings: - if len(s) != self.n_p: - raise ValueError(f'invalid stabilizer length {s}.') - for i in range(len(s)): - if s[i] not in ['I', 'X', 'Y', 'Z']: - raise ValueError(f'invalid stabilizer pauli {s}.') - - # transform port data - self.ports = [] - for port in data['ports']: - my_port = {} - - for key in ['location', 'direction', 'z_basis_direction']: - if key not in port: - raise ValueError(f'missing key {key} in port {port}') - - if len(port['location']) != 3: - raise ValueError(f'port with invalid location {port}.') - my_port['i'], my_port['j'], my_port['k'] = port['location'] - - if len(port['direction']) != 2: - raise ValueError(f'port with invalid direction {port}.') - if port['direction'][0] not in ['+', '-']: - raise ValueError(f'port with invalid sign {port}.') - if port['direction'][1] not in ['I', 'J', 'K']: - raise ValueError(f'port with invalid axis {port}.') - my_port['e'] = '-' if port['direction'][0] == '+' else '+' - my_port['d'] = port['direction'][1] - if my_port['e'] == '+': - # the corresponding coordinate should -1, e.g., if axis is K and - # it's minus direction, then edge should be (i,j,k-1)-(i,j,k) - my_port[my_port['d'].lower()] -= 1 - - z_dir = port['z_basis_direction'] - if z_dir not in ['I', 'J', 'K'] or z_dir == my_port['d']: - raise ValueError(f'port with invalid Z basis direction {port}.') - if my_port['d'] == 'I': - my_port['c'] = 0 if z_dir == 'J' else 1 - if my_port['d'] == 'J': - my_port['c'] = 0 if z_dir == 'K' else 1 - if my_port['d'] == 'K': - my_port['c'] = 0 if z_dir == 'I' else 1 - - if 'function' in port: - my_port['f'] = port['function'] - - self.ports.append(my_port) - - # from paulistrings to correlation surfaces - self.stabs = self.derive_corr_boundary(self.paulistings) - - self.optional = {} - self.forbidden_cubes = [] - if 'optional' in data: - self.optional = data['optional'] - - if 'forbidden_cubes' in data['optional']: - for cube in data['optional']['forbidden_cubes']: - if len(cube) != 3: - raise ValueError(f'forbid cube invalid {cube}.') - if ( - cube[0] not in range(self.n_i) - or cube[1] not in range(self.n_j) - or cube[2] not in range(self.n_k) - ): - continue - self.forbidden_cubes.append(cube) - - self.get_port_cubes() - - def derive_corr_boundary( - self, paulistrings: Sequence[str] - ) -> list[list[Mapping[str, int]]]: - """derive the boundary correlation surface variable values. - - From the color orientation of the ports and the stabilizers, we can derive - which correlation surface variables evaluates to True and which to False at - the ports for each stabilizer. - - Args: - paulistrings (Sequence[str]): stabilizers as a list of Pauli strings. - - Returns: - list[list[Mapping[str, int]]]: Outer layer list is the list of - stabilizers. Inner layer list is the situation at each port for one - specifeic stabilizer. Each port is specified with a dictionary of 2 bits - for the 2 correaltion surfaces. - """ - stabs = [] - for paulistring in paulistrings: - corr = [] - for p in range(self.n_p): - if paulistring[p] == 'I': # I -> no corr surf should be present - if self.ports[p]['d'] == 'I': - corr.append({'IJ': 0, 'IK': 0}) - if self.ports[p]['d'] == 'J': - corr.append({'JI': 0, 'JK': 0}) - if self.ports[p]['d'] == 'K': - corr.append({'KI': 0, 'KJ': 0}) - - if paulistring[p] == 'Y': # Y -> both corr surf should be present - if self.ports[p]['d'] == 'I': - corr.append({'IJ': 1, 'IK': 1}) - if self.ports[p]['d'] == 'J': - corr.append({'JI': 1, 'JK': 1}) - if self.ports[p]['d'] == 'K': - corr.append({'KI': 1, 'KJ': 1}) - - if paulistring[p] == 'X': # X -> only corr surf touching red faces - if self.ports[p]['d'] == 'I': - if self.ports[p]['c']: - corr.append({'IJ': 1, 'IK': 0}) - else: - corr.append({'IJ': 0, 'IK': 1}) - if self.ports[p]['d'] == 'J': - if self.ports[p]['c']: - corr.append({'JI': 0, 'JK': 1}) - else: - corr.append({'JI': 1, 'JK': 0}) - if self.ports[p]['d'] == 'K': - if self.ports[p]['c']: - corr.append({'KI': 1, 'KJ': 0}) - else: - corr.append({'KI': 0, 'KJ': 1}) - - if paulistring[p] == 'Z': # Z -> only corr surf touching blue faces - if self.ports[p]['d'] == 'I': - if not self.ports[p]['c']: - corr.append({'IJ': 1, 'IK': 0}) - else: - corr.append({'IJ': 0, 'IK': 1}) - if self.ports[p]['d'] == 'J': - if not self.ports[p]['c']: - corr.append({'JI': 0, 'JK': 1}) - else: - corr.append({'JI': 1, 'JK': 0}) - if self.ports[p]['d'] == 'K': - if not self.ports[p]['c']: - corr.append({'KI': 1, 'KJ': 0}) - else: - corr.append({'KI': 0, 'KJ': 1}) - stabs.append(corr) - return stabs - - def define_vars(self, color_ij: bool = True) -> None: - """define the variables in Z3 into self.vars. - - Args: - color_ij (bool, optional): if the color matching constraints of I and J - edges are imposed. Defaults to True. - """ - self.vars = { - 'ExistI': [ - [ - [z3.Bool(f'ExistI({i},{j},{k})') for k in range(self.n_k)] - for j in range(self.n_j) - ] - for i in range(self.n_i) - ], - 'ExistJ': [ - [ - [z3.Bool(f'ExistJ({i},{j},{k})') for k in range(self.n_k)] - for j in range(self.n_j) - ] - for i in range(self.n_i) - ], - 'ExistK': [ - [ - [z3.Bool(f'ExistK({i},{j},{k})') for k in range(self.n_k)] - for j in range(self.n_j) - ] - for i in range(self.n_i) - ], - 'NodeY': [ - [ - [z3.Bool(f'NodeY({i},{j},{k})') for k in range(self.n_k)] - for j in range(self.n_j) - ] - for i in range(self.n_i) - ], - 'CorrIJ': [ - [ - [ - [ - z3.Bool(f'CorrIJ({s},{i},{j},{k})') - for k in range(self.n_k) - ] - for j in range(self.n_j) - ] - for i in range(self.n_i) - ] - for s in range(self.n_s) - ], - 'CorrIK': [ - [ - [ - [ - z3.Bool(f'CorrIK({s},{i},{j},{k})') - for k in range(self.n_k) - ] - for j in range(self.n_j) - ] - for i in range(self.n_i) - ] - for s in range(self.n_s) - ], - 'CorrJK': [ - [ - [ - [ - z3.Bool(f'CorrJK({s},{i},{j},{k})') - for k in range(self.n_k) - ] - for j in range(self.n_j) - ] - for i in range(self.n_i) - ] - for s in range(self.n_s) - ], - 'CorrJI': [ - [ - [ - [ - z3.Bool(f'CorrJI({s},{i},{j},{k})') - for k in range(self.n_k) - ] - for j in range(self.n_j) - ] - for i in range(self.n_i) - ] - for s in range(self.n_s) - ], - 'CorrKI': [ - [ - [ - [ - z3.Bool(f'CorrKI({s},{i},{j},{k})') - for k in range(self.n_k) - ] - for j in range(self.n_j) - ] - for i in range(self.n_i) - ] - for s in range(self.n_s) - ], - 'CorrKJ': [ - [ - [ - [ - z3.Bool(f'CorrKJ({s},{i},{j},{k})') - for k in range(self.n_k) - ] - for j in range(self.n_j) - ] - for i in range(self.n_i) - ] - for s in range(self.n_s) - ], - } - - if color_ij: - self.vars['ColorI'] = [ - [ - [z3.Bool(f'ColorI({i},{j},{k})') for k in range(self.n_k)] - for j in range(self.n_j) - ] - for i in range(self.n_i) - ] - self.vars['ColorJ'] = [ - [ - [z3.Bool(f'ColorJ({i},{j},{k})') for k in range(self.n_k)] - for j in range(self.n_j) - ] - for i in range(self.n_i) - ] - - def plugin_arrs(self, data: Mapping[str, Any], color_ij: bool = True) -> None: - """plug in the given arrays of values. - - Args: - data (Mapping[str, Any]): contains gieven values - color_ij (bool, optional): if the color matching constraints of I and J - edges are imposed. Defaults to True. - """ - arrs = [ - 'NodeY', - 'ExistI', - 'ExistJ', - 'ExistK', - ] - if color_ij: - arrs += ['ColorI', 'ColorJ'] - - for s in range(self.n_s): - for i in range(self.n_i): - for j in range(self.n_j): - for k in range(self.n_k): - if s == 0: # Exist, Node, and Color vars - for arr in arrs: - if var_given(data, arr, i, j, k): - self.goal.add( - self.vars[arr][i][j][k] - if data[arr][i][j][k] == 1 - else z3.Not(self.vars[arr][i][j][k]) - ) - # Corr vars - for arr in [ - 'CorrIJ', - 'CorrIK', - 'CorrJI', - 'CorrJK', - 'CorrKI', - 'CorrKJ', - ]: - if var_given(data, arr, s, i, j, k): - self.goal.add( - self.vars[arr][s][i][j][k] - if data[arr][s][i][j][k] - else z3.Not(self.vars[arr][s][i][j][k]) - ) - - def plugin_vals(self, data_set: Sequence[Mapping[str, Any]]): - """plug in the given values - - Args: - data (Sequence[Mapping[str, Any]]): given values as a sequence of dicts. - Each one contains three fields: 'array', the name of the array, e.g., - 'ExistI'; 'indices', a sequence of the indices; and 'value'. - """ - for data in data_set: - (arr, idx) = data['array'], data['indices'] - if arr.startswith('Corr'): - s, i, j, k = idx - if data['value']: - self.goal.add(self.vars[arr][s][i][j][k]) - else: - self.goal.add(z3.Not(self.vars[arr][s][i][j][k])) - else: - i, j, k = idx - if data['value']: - self.goal.add(self.vars[arr][i][j][k]) - else: - self.goal.add(z3.Not(self.vars[arr][i][j][k])) - - def get_port_cubes(self) -> None: - """calculate which cubes are empty serving as ports.""" - self.port_cubes = [] - for p in self.ports: - # if e=-, (i,j,k); otherwise, +1 in the proper direction - if p['e'] == '-': - self.port_cubes.append((p['i'], p['j'], p['k'])) - elif p['d'] == 'I': - self.port_cubes.append((p['i'] + 1, p['j'], p['k'])) - elif p['d'] == 'J': - self.port_cubes.append((p['i'], p['j'] + 1, p['k'])) - elif p['d'] == 'K': - self.port_cubes.append((p['i'], p['j'], p['k'] + 1)) - - def constraint_forbid_cube(self) -> None: - """forbid a list of cubes.""" - for cube in self.forbidden_cubes: - (i, j, k) = cube[0], cube[1], cube[2] - if ( - len(cube) != 3 - or i not in range(self.n_i) - or j not in range(self.n_j) - or k not in range(self.n_k) - ): - continue - self.goal.add(z3.Not(self.vars['NodeY'][i][j][k])) - if i > 0: - self.goal.add(z3.Not(self.vars['ExistI'][i - 1][j][k])) - self.goal.add(z3.Not(self.vars['ExistI'][i][j][k])) - if j > 0: - self.goal.add(z3.Not(self.vars['ExistJ'][i][j - 1][k])) - self.goal.add(z3.Not(self.vars['ExistJ'][i][j][k])) - # if k > 0: - # self.model.add(z3.Not(self.vars['ExistK'][i][j][k - 1])) - # self.model.add(z3.Not(self.vars['ExistK'][i][j][k])) - - def constraint_port(self, color_ij: bool = True) -> None: - """structural constraints at ports: some edges must exist and some must not. - - Args: - color_ij (bool, optional): if the color matching constraints of I and J - edges are imposed. Defaults to True. - """ - for port in self.ports: - # the edge specified by the port exists - self.goal.add( - self.vars[f'Exist{port["d"]}'][port['i']][port['j']][port['k']] - ) - # if I- or J-edge exist, set the color value too to the given one - if color_ij: - if port['d'] != 'K': - if port['c'] == 1: - self.goal.add( - self.vars[f'Color{port["d"]}'][port['i']][port['j']][port['k']] - ) - else: - self.goal.add( - z3.Not( - self.vars[f'Color{port["d"]}'][port['i']][port['j']][ - port['k'] - ] - ) - ) - - # collect the edges touching the port to forbid them - dirs, coords = port_incident_edges(port, self.n_i, self.n_j, self.n_k) - for i, coord in enumerate(coords): - self.goal.add( - z3.Not(self.vars[f'Exist{dirs[i]}'][coord[0]][coord[1]][coord[2]]) - ) - - def constraint_connect_outside(self) -> None: - """no edge should cross the spatial bound except for ports.""" - for i in range(self.n_i): - for j in range(self.n_j): - # consider K-edges crossing K-bound and not a port - if (i, j, self.n_k) not in self.port_cubes: - self.goal.add(z3.Not(self.vars['ExistK'][i][j][self.n_k - 1])) - for i in range(self.n_i): - for k in range(self.n_k): - if (i, self.n_j, k) not in self.port_cubes: - self.goal.add(z3.Not(self.vars['ExistJ'][i][self.n_j - 1][k])) - for j in range(self.n_j): - for k in range(self.n_k): - if (self.n_i, j, k) not in self.port_cubes: - self.goal.add(z3.Not(self.vars['ExistI'][self.n_i - 1][j][k])) - - def constraint_timelike_y(self) -> None: - """Y-spiders must be timelike, i.e., forbid all I- and J- edges to them.""" - for i in range(self.n_i): - for j in range(self.n_j): - for k in range(self.n_k): - if (i, j, k) not in self.port_cubes: - self.goal.add( - z3.Implies( - self.vars['NodeY'][i][j][k], - z3.Not(self.vars['ExistI'][i][j][k]), - ) - ) - self.goal.add( - z3.Implies( - self.vars['NodeY'][i][j][k], - z3.Not(self.vars['ExistJ'][i][j][k]), - ) - ) - if i - 1 >= 0: - self.goal.add( - z3.Implies( - self.vars['NodeY'][i][j][k], - z3.Not(self.vars['ExistI'][i - 1][j][k]), - ) - ) - if j - 1 >= 0: - self.goal.add( - z3.Implies( - self.vars['NodeY'][i][j][k], - z3.Not(self.vars['ExistJ'][i][j - 1][k]), - ) - ) - - def constraint_no_deg1(self) -> None: - """forbid degree-1 X or Z spiders by considering incident edges.""" - for i in range(self.n_i): - for j in range(self.n_j): - for k in range(self.n_k): - for d in ['I', 'J', 'K']: - for e in ['-', '+']: - cube = {'I': i, 'J': j, 'K': k} - cube[d] += 1 if e == '+' else 0 - - # construct fake ports to get incident edges - p0 = {'i': i, 'j': j, 'k': k, 'd': d, 'e': e, 'c': 0} - found_p0 = False - for port in self.ports: - if ( - i == port['i'] - and j == port['j'] - and k == port['k'] - and d == port['d'] - ): - found_p0 = True - - # only non-port edges need to consider - if ( - not found_p0 - and cube['I'] < self.n_i - and cube['J'] < self.n_j - and cube['K'] < self.n_k - ): - # only cubes inside bound need to consider - dirs, coords = port_incident_edges( - p0, self.n_i, self.n_j, self.n_k - ) - edges = [ - self.vars[f'Exist{dirs[l]}'][coord[0]][coord[1]][coord[2]] - for l, coord in enumerate(coords) - ] - # if the cube is not Y and the edge exist, then - # at least one of its incident edges exists. - self.goal.add( - z3.Implies( - z3.And( - z3.Not( - self.vars['NodeY'][cube['I']][cube['J']][ - cube['K'] - ] - ), - self.vars[f'Exist{d}'][i][j][k], - ), - z3.Or(edges), - ) - ) - - def constraint_ij_color(self) -> None: - """color matching for I- and J-edges.""" - for i in range(self.n_i): - for j in range(self.n_j): - for k in range(self.n_k): - if i >= 1 and j >= 1: - # (i-1,j,k)-(i,j,k) and (i,j-1,k)-(i,j,k) - self.goal.add( - z3.Implies( - z3.And( - self.vars['ExistI'][i - 1][j][k], - self.vars['ExistJ'][i][j - 1][k], - ), - z3.Or( - z3.And( - self.vars['ColorI'][i - 1][j][k], - z3.Not(self.vars['ColorJ'][i][j - 1][k]), - ), - z3.And( - z3.Not(self.vars['ColorI'][i - 1][j][k]), - self.vars['ColorJ'][i][j - 1][k], - ), - ), - ) - ) - - if i >= 1: - # (i-1,j,k)-(i,j,k) and (i,j,k)-(i,j+1,k) - self.goal.add( - z3.Implies( - z3.And( - self.vars['ExistI'][i - 1][j][k], - self.vars['ExistJ'][i][j][k], - ), - z3.Or( - z3.And( - self.vars['ColorI'][i - 1][j][k], - z3.Not(self.vars['ColorJ'][i][j][k]), - ), - z3.And( - z3.Not(self.vars['ColorI'][i - 1][j][k]), - self.vars['ColorJ'][i][j][k], - ), - ), - ) - ) - # (i-1,j,k)-(i,j,k) and (i,j,k)-(i+1,j,k) - self.goal.add( - z3.Implies( - z3.And( - self.vars['ExistI'][i - 1][j][k], - self.vars['ExistI'][i][j][k], - ), - z3.Or( - z3.And( - self.vars['ColorI'][i - 1][j][k], - self.vars['ColorI'][i][j][k], - ), - z3.And( - z3.Not(self.vars['ColorI'][i - 1][j][k]), - z3.Not(self.vars['ColorI'][i][j][k]), - ), - ), - ) - ) - - if j >= 1: - # (i,j,k)-(i+1,j,k) and (i,j-1,k)-(i,j,k) - self.goal.add( - z3.Implies( - z3.And( - self.vars['ExistI'][i][j][k], - self.vars['ExistJ'][i][j - 1][k], - ), - z3.Or( - z3.And( - self.vars['ColorI'][i][j][k], - z3.Not(self.vars['ColorJ'][i][j - 1][k]), - ), - z3.And( - z3.Not(self.vars['ColorI'][i][j][k]), - self.vars['ColorJ'][i][j - 1][k], - ), - ), - ) - ) - # (i,j-1,k)-(i,j,k) and (i,j,k)-(i,j+1,k) - self.goal.add( - z3.Implies( - z3.And( - self.vars['ExistJ'][i][j - 1][k], - self.vars['ExistJ'][i][j][k], - ), - z3.Or( - z3.And( - self.vars['ColorJ'][i][j - 1][k], - self.vars['ColorJ'][i][j][k], - ), - z3.And( - z3.Not(self.vars['ColorJ'][i][j - 1][k]), - z3.Not(self.vars['ColorJ'][i][j][k]), - ), - ), - ) - ) - - # (i,j,k)-(i+1,j,k) and (i,j,k)-(i,j+1,k) - self.goal.add( - z3.Implies( - z3.And( - self.vars['ExistI'][i][j][k], self.vars['ExistJ'][i][j][k] - ), - z3.Or( - z3.And( - self.vars['ColorI'][i][j][k], - z3.Not(self.vars['ColorJ'][i][j][k]), - ), - z3.And( - z3.Not(self.vars['ColorI'][i][j][k]), - self.vars['ColorJ'][i][j][k], - ), - ), - ) - ) - - def constraint_3d_corner(self) -> None: - """forbid 3D corners by saying at least in one direction, both edges nonexist.""" - for i in range(self.n_i): - for j in range(self.n_j): - for k in range(self.n_k): - i_edges = [ - self.vars['ExistI'][i][j][k], - ] - if i - 1 >= 0: - i_edges.append(self.vars['ExistI'][i - 1][j][k]) - j_edges = [ - self.vars['ExistJ'][i][j][k], - ] - if j - 1 >= 0: - j_edges.append(self.vars['ExistJ'][i][j - 1][k]) - k_edges = [ - self.vars['ExistK'][i][j][k], - ] - if k - 1 >= 0: - k_edges.append(self.vars['ExistK'][i][j][k - 1]) - - # at least one of the three terms is true. The first term is that - # both I-edges connecting to (i,j,k) do not exist - self.goal.add( - z3.Or( - z3.Not(z3.Or(i_edges)), - z3.Not(z3.Or(j_edges)), - z3.Not(z3.Or(k_edges)), - ) - ) - - def constraint_corr_ports(self) -> None: - """plug in the correlation surface values at the ports.""" - for s, stab in enumerate(self.stabs): - for p, corrs in enumerate(stab): - for k, v in corrs.items(): - if v == 1: - self.goal.add( - self.vars[f'Corr{k}'][s][self.ports[p]['i']][ - self.ports[p]['j'] - ][self.ports[p]['k']] - ) - else: - self.goal.add( - z3.Not( - self.vars[f'Corr{k}'][s][self.ports[p]['i']][ - self.ports[p]['j'] - ][self.ports[p]['k']] - ) - ) - - def constraint_corr_y(self) -> None: - """correlation surfaces at Y-spider should both exist or nonexist.""" - for s in range(self.n_s): - for i in range(self.n_i): - for j in range(self.n_j): - for k in range(self.n_k): - self.goal.add( - z3.Or( - z3.Not(self.vars['NodeY'][i][j][k]), - z3.Or( - z3.And( - self.vars['CorrKI'][s][i][j][k], - self.vars['CorrKJ'][s][i][j][k], - ), - z3.And( - z3.Not(self.vars['CorrKI'][s][i][j][k]), - z3.Not(self.vars['CorrKJ'][s][i][j][k]), - ), - ), - ) - ) - if k - 1 >= 0: - self.goal.add( - z3.Or( - z3.Not(self.vars['NodeY'][i][j][k]), - z3.Or( - z3.And( - self.vars['CorrKI'][s][i][j][k - 1], - self.vars['CorrKJ'][s][i][j][k - 1], - ), - z3.And( - z3.Not(self.vars['CorrKI'][s][i][j][k - 1]), - z3.Not(self.vars['CorrKJ'][s][i][j][k - 1]), - ), - ), - ) - ) - - def constraint_corr_perp(self) -> None: - """for corr surf perpendicular to normal vector, all exist or nonexist.""" - for s in range(self.n_s): - for i in range(self.n_i): - for j in range(self.n_j): - for k in range(self.n_k): - if (i, j, k) not in self.port_cubes: # only internal spider - # only consider X or Z spider - # if normal is K meaning meaning both (i,j,k)-(i,j,k+1) and - # (i,j,k)-(i,j,k-1) are out of range, or in range but nonexistent - normal = z3.And( - z3.Not(self.vars['NodeY'][i][j][k]), - z3.Not(self.vars['ExistK'][i][j][k]), - ) - if k - 1 >= 0: - normal = z3.And( - normal, z3.Not(self.vars['ExistK'][i][j][k - 1]) - ) - - # for other edges, need to build intermediate expression - # for (i,j,k)-(i+1,j,k) and (i,j,k)-(i,j+1,k), build expression - # meaning the edge is nonexistent or exist and has the correlation - # surface perpendicular to the normal vector in them. - no_edge_or_with_corr = [ - z3.Or( - z3.Not(self.vars['ExistI'][i][j][k]), - self.vars['CorrIJ'][s][i][j][k], - ), - z3.Or( - z3.Not(self.vars['ExistJ'][i][j][k]), - self.vars['CorrJI'][s][i][j][k], - ), - ] - - # for (i,j,k)-(i+1,j,k) and (i,j,k)-(i,j+1,k), build expression - # meaning the edge is nonexistent or exist and does not have the - # correlation surface perpendicular to the normal vector in them. - no_edge_or_no_corr = [ - z3.Or( - z3.Not(self.vars['ExistI'][i][j][k]), - z3.Not(self.vars['CorrIJ'][s][i][j][k]), - ), - z3.Or( - z3.Not(self.vars['ExistJ'][i][j][k]), - z3.Not(self.vars['CorrJI'][s][i][j][k]), - ), - ] - - if i - 1 >= 0: - # build intermediate expression for (i-1,j,k)-(i,j,k) - no_edge_or_with_corr.append( - z3.Or( - z3.Not(self.vars['ExistI'][i - 1][j][k]), - self.vars['CorrIJ'][s][i - 1][j][k], - ) - ) - no_edge_or_no_corr.append( - z3.Or( - z3.Not(self.vars['ExistI'][i - 1][j][k]), - z3.Not(self.vars['CorrIJ'][s][i - 1][j][k]), - ) - ) - - if j - 1 >= 0: - # build intermediate expression for (i,j-1,k)-(i,j,k) - no_edge_or_with_corr.append( - z3.Or( - z3.Not(self.vars['ExistJ'][i][j - 1][k]), - self.vars['CorrJI'][s][i][j - 1][k], - ) - ) - no_edge_or_no_corr.append( - z3.Or( - z3.Not(self.vars['ExistJ'][i][j - 1][k]), - z3.Not(self.vars['CorrJI'][s][i][j - 1][k]), - ) - ) - - # if normal vector is K, then in all its incident edges that exist - # all correlation surface in I-J plane exist or nonexist - self.goal.add( - z3.Implies( - normal, - z3.Or( - z3.And(no_edge_or_with_corr), - z3.And(no_edge_or_no_corr), - ), - ) - ) - - # if normal is I - normal = z3.And( - z3.Not(self.vars['NodeY'][i][j][k]), - z3.Not(self.vars['ExistI'][i][j][k]), - ) - if i - 1 >= 0: - normal = z3.And( - normal, z3.Not(self.vars['ExistI'][i - 1][j][k]) - ) - no_edge_or_with_corr = [ - z3.Or( - z3.Not(self.vars['ExistJ'][i][j][k]), - self.vars['CorrJK'][s][i][j][k], - ), - z3.Or( - z3.Not(self.vars['ExistK'][i][j][k]), - self.vars['CorrKJ'][s][i][j][k], - ), - ] - no_edge_or_no_corr = [ - z3.Or( - z3.Not(self.vars['ExistJ'][i][j][k]), - z3.Not(self.vars['CorrJK'][s][i][j][k]), - ), - z3.Or( - z3.Not(self.vars['ExistK'][i][j][k]), - z3.Not(self.vars['CorrKJ'][s][i][j][k]), - ), - ] - if j - 1 >= 0: - no_edge_or_with_corr.append( - z3.Or( - z3.Not(self.vars['ExistJ'][i][j - 1][k]), - self.vars['CorrJK'][s][i][j - 1][k], - ) - ) - no_edge_or_no_corr.append( - z3.Or( - z3.Not(self.vars['ExistJ'][i][j - 1][k]), - z3.Not(self.vars['CorrJK'][s][i][j - 1][k]), - ) - ) - if k - 1 >= 0: - no_edge_or_with_corr.append( - z3.Or( - z3.Not(self.vars['ExistK'][i][j][k - 1]), - self.vars['CorrKJ'][s][i][j][k - 1], - ) - ) - no_edge_or_no_corr.append( - z3.Or( - z3.Not(self.vars['ExistK'][i][j][k - 1]), - z3.Not(self.vars['CorrKJ'][s][i][j][k - 1]), - ) - ) - self.goal.add( - z3.Implies( - normal, - z3.Or( - z3.And(no_edge_or_with_corr), - z3.And(no_edge_or_no_corr), - ), - ) - ) - - # if normal is J - normal = z3.And( - z3.Not(self.vars['NodeY'][i][j][k]), - z3.Not(self.vars['ExistJ'][i][j][k]), - ) - if j - 1 >= 0: - normal = z3.And( - normal, z3.Not(self.vars['ExistJ'][i][j - 1][k]) - ) - no_edge_or_with_corr = [ - z3.Or( - z3.Not(self.vars['ExistI'][i][j][k]), - self.vars['CorrIK'][s][i][j][k], - ), - z3.Or( - z3.Not(self.vars['ExistK'][i][j][k]), - self.vars['CorrKI'][s][i][j][k], - ), - ] - no_edge_or_no_corr = [ - z3.Or( - z3.Not(self.vars['ExistI'][i][j][k]), - z3.Not(self.vars['CorrIK'][s][i][j][k]), - ), - z3.Or( - z3.Not(self.vars['ExistK'][i][j][k]), - z3.Not(self.vars['CorrKI'][s][i][j][k]), - ), - ] - if i - 1 >= 0: - no_edge_or_with_corr.append( - z3.Or( - z3.Not(self.vars['ExistI'][i - 1][j][k]), - self.vars['CorrIK'][s][i - 1][j][k], - ) - ) - no_edge_or_no_corr.append( - z3.Or( - z3.Not(self.vars['ExistI'][i - 1][j][k]), - z3.Not(self.vars['CorrIK'][s][i - 1][j][k]), - ) - ) - if k - 1 >= 0: - no_edge_or_with_corr.append( - z3.Or( - z3.Not(self.vars['ExistK'][i][j][k - 1]), - self.vars['CorrKI'][s][i][j][k - 1], - ) - ) - no_edge_or_no_corr.append( - z3.Or( - z3.Not(self.vars['ExistK'][i][j][k - 1]), - z3.Not(self.vars['CorrKI'][s][i][j][k - 1]), - ) - ) - self.goal.add( - z3.Implies( - normal, - z3.Or( - z3.And(no_edge_or_with_corr), - z3.And(no_edge_or_no_corr), - ), - ) - ) - - def constraint_corr_para(self) -> None: - """for corr surf parallel to the normal vector, even number of them exist.""" - for s in range(self.n_s): - for i in range(self.n_i): - for j in range(self.n_j): - for k in range(self.n_k): - if (i, j, k) not in self.port_cubes: # only internal spiders - # only X or Z spiders, if normal is K - normal = z3.And( - z3.Not(self.vars['NodeY'][i][j][k]), - z3.Not(self.vars['ExistK'][i][j][k]), - ) - if k - 1 >= 0: - normal = z3.And( - normal, z3.Not(self.vars['ExistK'][i][j][k - 1]) - ) - - # unlike in constraint_corr_perp, we only care about the cases - # where the edge exists and the correlation surface parallel to - # K also is present, so we build intermediate expressions as below - edge_with_corr = [ - z3.And( - self.vars['ExistI'][i][j][k], - self.vars['CorrIK'][s][i][j][k], - ), - z3.And( - self.vars['ExistJ'][i][j][k], - self.vars['CorrJK'][s][i][j][k], - ), - ] - - # build the intermediate expression for (i-1,j,k)-(i,j,k) - if i - 1 >= 0: - edge_with_corr.append( - z3.And( - self.vars['ExistI'][i - 1][j][k], - self.vars['CorrIK'][s][i - 1][j][k], - ) - ) - - # build the intermediate expression for (i,j-1,k)-(i,j,k) - if j - 1 >= 0: - edge_with_corr.append( - z3.And( - self.vars['ExistJ'][i][j - 1][k], - self.vars['CorrJK'][s][i][j - 1][k], - ) - ) - - # the parity of the intermediate expressions must be even - self.goal.add( - z3.Implies(normal, cnf_even_parity_upto4(edge_with_corr)) - ) - - # if normal is I - normal = z3.And( - z3.Not(self.vars['NodeY'][i][j][k]), - z3.Not(self.vars['ExistI'][i][j][k]), - ) - if i - 1 >= 0: - normal = z3.And( - normal, z3.Not(self.vars['ExistI'][i - 1][j][k]) - ) - edge_with_corr = [ - z3.And( - self.vars['ExistJ'][i][j][k], - self.vars['CorrJI'][s][i][j][k], - ), - z3.And( - self.vars['ExistK'][i][j][k], - self.vars['CorrKI'][s][i][j][k], - ), - ] - if j - 1 >= 0: - edge_with_corr.append( - z3.And( - self.vars['ExistJ'][i][j - 1][k], - self.vars['CorrJI'][s][i][j - 1][k], - ) - ) - if k - 1 >= 0: - edge_with_corr.append( - z3.And( - self.vars['ExistK'][i][j][k - 1], - self.vars['CorrKI'][s][i][j][k - 1], - ) - ) - self.goal.add( - z3.Implies(normal, cnf_even_parity_upto4(edge_with_corr)) - ) - - # if normal is J - normal = z3.And( - z3.Not(self.vars['NodeY'][i][j][k]), - z3.Not(self.vars['ExistJ'][i][j][k]), - ) - if j - 1 >= 0: - normal = z3.And( - normal, z3.Not(self.vars['ExistJ'][i][j - 1][k]) - ) - edge_with_corr = [ - z3.And( - self.vars['ExistI'][i][j][k], - self.vars['CorrIJ'][s][i][j][k], - ), - z3.And( - self.vars['ExistK'][i][j][k], - self.vars['CorrKJ'][s][i][j][k], - ), - ] - if i - 1 >= 0: - edge_with_corr.append( - z3.And( - self.vars['ExistI'][i - 1][j][k], - self.vars['CorrIJ'][s][i - 1][j][k], - ) - ) - if k - 1 >= 0: - edge_with_corr.append( - z3.And( - self.vars['ExistK'][i][j][k - 1], - self.vars['CorrKJ'][s][i][j][k - 1], - ) - ) - self.goal.add( - z3.Implies(normal, cnf_even_parity_upto4(edge_with_corr)) - ) - - def build_smt_model( - self, - given_arrs: Mapping[str, Any] = None, - given_vals: Sequence[Mapping[str, Any]] = None, - color_ij: bool = True, - ) -> None: - """build the SMT model with variables and constraints. - - Args: - given_arrs (Mapping[str, Any], optional): given arrays of values to plug - in. Defaults to None. - given_vals (Sequence[Mapping[str, Any]], optional): given values to plug - in. Defaults to None. - color_ij (bool, optional): if the color matching constraints of I and J - edges are imposed. Defaults to True. - """ - self.define_vars(color_ij=color_ij) - if given_arrs: - self.plugin_arrs(given_arrs, color_ij=color_ij) - if given_vals: - self.plugin_vals(given_vals) - - # baseline order - self.constraint_forbid_cube() - self.constraint_port(color_ij=color_ij) - self.constraint_connect_outside() - self.constraint_timelike_y() - self.constraint_no_deg1() - if color_ij: - self.constraint_ij_color() - self.constraint_3d_corner() - - self.constraint_corr_ports() - self.constraint_corr_y() - self.constraint_corr_perp() - self.constraint_corr_para() - - def check_z3(self, print_progress: bool = True) -> bool: - """check whether the built goal in self.goal is satisfiable. - - Args: - print_progress (bool, optional): if print out the progress made. - - Returns: - bool: True if SAT, False if UNSAT - """ - if print_progress: - print('Construct a Z3 SMT model and solve...') - start_time = time.time() - self.solver = z3.Solver() - self.solver.add(self.goal) - ifsat = self.solver.check() - elapsed = time.time() - start_time - if print_progress: - print('elapsed time: {:2f}s'.format(elapsed)) - if ifsat == z3.sat: - if print_progress: - print('Z3 SAT') - return True - else: - if print_progress: - print('Z3 UNSAT') - return False - - def get_result(self) -> Mapping[str, Any]: - """get the variable values. - - Returns: - Mapping[str, Any]: output in the LaSSIR format - """ - model = self.solver.model() - data = { - 'specification': self.input_dict, - 'n_i': self.n_i, - 'n_j': self.n_j, - 'n_k': self.n_k, - 'n_p': self.n_p, - 'n_s': self.n_s, - 'ports': self.ports, - 'stabs': self.stabs, - 'port_cubes': self.port_cubes, - 'optional': self.optional, - 'ExistI': [ - [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] - for _ in range(self.n_i) - ], - 'ExistJ': [ - [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] - for _ in range(self.n_i) - ], - 'ExistK': [ - [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] - for _ in range(self.n_i) - ], - 'ColorI': [ - [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] - for _ in range(self.n_i) - ], - 'ColorJ': [ - [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] - for _ in range(self.n_i) - ], - 'NodeY': [ - [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] - for _ in range(self.n_i) - ], - 'CorrIJ': [ - [ - [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] - for _ in range(self.n_i) - ] - for _ in range(self.n_s) - ], - 'CorrIK': [ - [ - [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] - for _ in range(self.n_i) - ] - for _ in range(self.n_s) - ], - 'CorrJK': [ - [ - [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] - for _ in range(self.n_i) - ] - for _ in range(self.n_s) - ], - 'CorrJI': [ - [ - [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] - for _ in range(self.n_i) - ] - for _ in range(self.n_s) - ], - 'CorrKI': [ - [ - [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] - for _ in range(self.n_i) - ] - for _ in range(self.n_s) - ], - 'CorrKJ': [ - [ - [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] - for _ in range(self.n_i) - ] - for _ in range(self.n_s) - ], - } - arrs = [ - 'NodeY', - 'ExistI', - 'ExistJ', - 'ExistK', - ] - if self.color_ij: - arrs += [ - 'ColorI', - 'ColorJ', - ] - for s in range(self.n_s): - for i in range(self.n_i): - for j in range(self.n_j): - for k in range(self.n_k): - if s == 0: # Exist, Node, and Color vars - for arr in arrs: - data[arr][i][j][k] = 1 if model[self.vars[arr][i][j][k]] else 0 - - # Corr vars - for arr in [ - 'CorrIJ', - 'CorrIK', - 'CorrJI', - 'CorrJK', - 'CorrKI', - 'CorrKJ', - ]: - data[arr][s][i][j][k] = ( - 1 if model[self.vars[arr][s][i][j][k]] else 0 - ) - return data - - def write_cnf(self, output_file_name: str) -> bool: - """generate CNF for the problem. - - Args: - output_file_name (str): file to write CNF. - - Returns: - bool: False if the CNF is trivial, True otherwise - """ - simplified = z3.Tactic('simplify')(self.goal)[0] - simplified = z3.Tactic('propagate-values')(simplified)[0] - cnf = z3.Tactic('tseitin-cnf')(simplified)[0] - dimacs = cnf.dimacs() - - with open(output_file_name, 'w') as output_f: - output_f.write(cnf.dimacs()) - if dimacs.startswith('p cnf 1 1'): - print( - 'Generated CNF is trivial meaning z3 concludes the instance UNSAT' - ' during simplification.' - ) - return False - else: - return True - - def read_external_result( - self, dimacs_file: str, result_file: str - ) -> Mapping[str, Any]: - """read result from external SAT solver - - Args: - dimacs_file (str): - result_file (str): log, e.g., from Kissat containing SAT assignments - - Raises: - ValueError: in the dimacs file, the last lines are comments that records - the mapping from SAT variable indices to the variable names in Z3. If - the coordinates in this name is incorrect, this error is raised. - - Returns: - Mapping[str, Any]: variable assignment in arrays. All the one with a - corresponding SAT variable are read off from the SAT log. The others - are left with -1. - """ - results = { - 'ExistI': [ - [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] - for _ in range(self.n_i) - ], - 'ExistJ': [ - [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] - for _ in range(self.n_i) - ], - 'ExistK': [ - [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] - for _ in range(self.n_i) - ], - 'ColorI': [ - [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] - for _ in range(self.n_i) - ], - 'ColorJ': [ - [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] - for _ in range(self.n_i) - ], - 'NodeY': [ - [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] - for _ in range(self.n_i) - ], - 'CorrIJ': [ - [ - [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] - for _ in range(self.n_i) - ] - for _ in range(self.n_s) - ], - 'CorrIK': [ - [ - [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] - for _ in range(self.n_i) - ] - for _ in range(self.n_s) - ], - 'CorrJK': [ - [ - [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] - for _ in range(self.n_i) - ] - for _ in range(self.n_s) - ], - 'CorrJI': [ - [ - [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] - for _ in range(self.n_i) - ] - for _ in range(self.n_s) - ], - 'CorrKI': [ - [ - [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] - for _ in range(self.n_i) - ] - for _ in range(self.n_s) - ], - 'CorrKJ': [ - [ - [[-1 for _ in range(self.n_k)] for _ in range(self.n_j)] - for _ in range(self.n_i) - ] - for _ in range(self.n_s) - ], - } - - # in this file, the assigments are lines starting with 'v' like - # v -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 ... - # the vars starts from 1 and - means it's False; otherwise, it's True - # we scan through all these lines, and save the assignments to `sat` - with open(result_file, 'r') as f: - sat_output = f.readlines() - sat = {} - for line in sat_output: - if line.startswith('v'): - assignments = line[1:].strip().split(' ') - for assignment in assignments: - tmp = int(assignment) - if tmp < 0: - sat[str(-tmp)] = 0 - elif tmp > 0: - sat[str(tmp)] = 1 - - # in the dimacs generated by Z3, there are lines starting with 'c' like - # c 8804 CorrIJ(1,0,3,4) or c 60053 k!44404 - # which records the mapping from our variables to variables in dimacs - # the ones starting with k! are added in the translation, we don't care - with open(dimacs_file, 'r') as f: - dimacs = f.readlines() - for line in dimacs: - if line.startswith('c'): - _, index, name = line.strip().split(' ') - if name.startswith(( - 'NodeY', - 'ExistI', - 'ExistJ', - 'ExistK', - 'ColorI', - 'ColorJ', - 'CorrIJ', - 'CorrIK', - 'CorrJI', - 'CorrJK', - 'CorrKI', - 'CorrKJ', - )): - arr, tmp = name[:-1].split('(') - coords = [int(num) for num in tmp.split(',')] - if len(coords) == 3: - results[arr][coords[0]][coords[1]][coords[2]] = sat[index] - elif len(coords) == 4: - results[arr][coords[0]][coords[1]][coords[2]][coords[3]] = sat[ - index - ] - else: - raise ValueError('number of coord should be 3 or 4!') - - return results - - def check_external_solver( - self, - kissat_dir: str, - dimacs_file_name: Optional[str] = None, - sat_log_file_name: Optional[str] = None, - print_progress: bool = True, - ) -> bool: - """check whether there is a solution with an external solver, e.g., Kissat - - Args: - kissat_dir (str): directory containing an executable named kissat - dimacs_file_name (Optional[str], optional): Defaults to None. Then, the - dimacs file is in a tmp directory. If specified, the dimacs will be - saved to that path. - sat_log_file_name (Optional[str], optional): Defaults to None. Then, the - sat log file is in a tmp directory. If specified, the dimacs will be - saved to that path. - print_progress (bool, optional): whether print the SAT solving process - on screen. Defaults to True. - - Raises: - ValueError: kissat_dir is not a directory - ValueError: there is no executable kissat in kissat_dir - ValueError: the return code to kissat is neither SAT (10) nor UNSAT (20) - - Returns: - bool: True if SAT, False if UNSAT - """ - if not os.path.isdir(kissat_dir): - raise ValueError(f'{kissat_dir} is not a directory.') - if kissat_dir.endswith('/'): - solver_cmd = kissat_dir + 'kissat' - else: - solver_cmd = kissat_dir + '/kissat' - if not os.path.isfile(solver_cmd): - raise ValueError(f'There is no kissat in {kissat_dir}.') - - if_solved = False - with tempfile.TemporaryDirectory() as tmp_dir: - # open a tmp directory as workspace - - # dimacs and sat log are either in the tmp directory, or as user specified - tmp_dimacs_file_name = ( - dimacs_file_name if dimacs_file_name else tmp_dir + '/tmp.dimacs' - ) - tmp_sat_log_file_name = ( - sat_log_file_name if sat_log_file_name else tmp_dir + '/tmp.sat' - ) - - if self.write_cnf(tmp_dimacs_file_name): - # continue if the CNF is non-trivial. Otherwise, we conclude it's UNSAT - - with open(tmp_sat_log_file_name, 'w') as log: - # use tmp_sat_log_file_name to record stdout of kissat - - kissat_return_code = -100 - # -100 if the return code is not updated later on. - - with subprocess.Popen( - [solver_cmd, tmp_dimacs_file_name], - stdout=subprocess.PIPE, - bufsize=1, - universal_newlines=True, - ) as run_kissat: - for line in run_kissat.stdout: - log.write(line) - if print_progress: - sys.stdout.write(line) - get_return_code = run_kissat.communicate()[0] - kissat_return_code = run_kissat.returncode - - if kissat_return_code == 10: - # 10 means SAT in Kissat - if_solved = True - if print_progress: - print('kissat SAT') - - # we read the Kissat solution from the SAT log, then, plug those into - # the Z3 model and solved inside Z3 again. The reason is that Z3 did - # some simplification of the problem so not every variable appear in - # the DIMACS given to Kissat. We still need to know their value. - result = self.read_external_result( - tmp_dimacs_file_name, - tmp_sat_log_file_name, - ) - self.plugin_arrs(result, self.color_ij) - self.check_z3(print_progress) - - elif kissat_return_code == 20: - if print_progress: - print(f'{solver_cmd} UNSAT') - - elif kissat_return_code == -100: - print('Did not get Kissat return code.') - - else: - raise ValueError( - f'Kissat return code {kissat_return_code} is neither SAT nor' - ' UNSAT. Maybe you should add print_process=True to enable the' - ' Kissat printout message to see what is going on.' - ) - # closing the tmp directory, the files and itself are removed - - return if_solved diff --git a/glue/lattice_surgery/olssco/tools/verify_stabilizers.py b/glue/lattice_surgery/olssco/tools/verify_stabilizers.py deleted file mode 100644 index 87a0f15b9..000000000 --- a/glue/lattice_surgery/olssco/tools/verify_stabilizers.py +++ /dev/null @@ -1,40 +0,0 @@ -from typing import Sequence -import stim -import stimzx - - -def verify_stabilizers( - specified_paulistrings: Sequence[str], - result_networkx, - print_stabilizers: bool = False, -) -> bool: - result_stabilizers = [ - stab.output - for stab in stimzx.zx_graph_to_external_stabilizers(result_networkx) - ] - specified_stabilizers = [ - stim.PauliString(paulistring) for paulistring in specified_paulistrings - ] - if print_stabilizers: - print("specified:") - for s in specified_stabilizers: - print(s) - print("==================================================================") - print("resulting:") - for s in result_stabilizers: - print(s) - print("==================================================================") - - for s in result_stabilizers: - for ss in specified_stabilizers: - if not ss.commutes(s): - print( - f"result stabilizer {s} not commuting with specified stabilizer" - f" {ss}" - ) - if print_stabilizers: - print("specified and resulting stabilizers are not equivalent.") - return False - if print_stabilizers: - print("specified and resulting stabilizers are equivalent.") - return True diff --git a/glue/lattice_surgery/olssco/translators/__init__.py b/glue/lattice_surgery/olssco/translators/__init__.py deleted file mode 100644 index dbe918638..000000000 --- a/glue/lattice_surgery/olssco/translators/__init__.py +++ /dev/null @@ -1 +0,0 @@ -from olssco.translators.zx_grid_graph import ZXGridGraph diff --git a/glue/lattice_surgery/olssco/translators/gltf_generator.py b/glue/lattice_surgery/olssco/translators/gltf_generator.py deleted file mode 100644 index a40ff227d..000000000 --- a/glue/lattice_surgery/olssco/translators/gltf_generator.py +++ /dev/null @@ -1,1582 +0,0 @@ -"""A one-line summary of the module or program, terminated by a period. - -Leave one blank line. The rest of this docstring should contain an -overall description of the module or program. Optionally, it may also -contain a brief description of exported classes and functions and/or usage -examples. - -Typical usage example: - - foo = ClassFoo() - bar = foo.FunctionBar() -""" - -import json -from typing import Any, Mapping, Optional, Sequence - -SQ2 = 0.707106769085 -BASE_GLTF = { - "asset": {"generator": "LaSIR CodeGen", "version": "2.0"}, - "scene": 0, - "scenes": [{"name": "Scene", "nodes": [0]}], - "nodes": [{"name": "try", "children": []}], -} - - -def float_to_little_endian_hex(f): - from struct import pack - - # Pack the float into a binary string using the little-endian format - binary_data = pack(" -1: - rectangles = [rect for rect in rectangles if rm_dir not in rect["name"]] - else: - rectangles = [rect for rect in rectangles if "Corr" not in rect["name"]] - return rectangles - - -def cube_gen( - SEP, - loc, - exists, - colors, - stabilizer, - corr, - noColor, - rm_dir: str = ":+J", -): - squares = [] - for face in ["-K", "+K"]: - if exists[face] == 0: - squares.append({ - "name": f"spider{loc}:{face}", - "mesh": 2, - "translation": [ - SEP * loc[0], - (1 if face == "+K" else 0) + SEP * loc[2], - -SEP * loc[1], - ], - }) - for dir in ["+I", "-I", "+J", "-J"]: - if exists[dir]: - if dir == "+I" or dir == "-I": - if colors[dir] == 1: - squares[-1]["mesh"] = 0 - else: - squares[-1]["mesh"] = 1 - else: - if colors[dir] == 0: - squares[-1]["mesh"] = 0 - else: - squares[-1]["mesh"] = 1 - break - for face in ["-I", "+I"]: - if exists[face] == 0: - squares.append({ - "name": f"spider{loc}:{face}", - "mesh": 2, - "translation": [ - (1 if face == "+I" else 0) + SEP * loc[0], - SEP * loc[2], - -SEP * loc[1], - ], - "rotation": [0, 0, SQ2, SQ2], - }) - for dir in ["+J", "-J", "+K", "-K"]: - if exists[dir]: - if dir == "+J" or dir == "-J": - if colors[dir] == 1: - squares[-1]["mesh"] = 0 - else: - squares[-1]["mesh"] = 1 - elif not noColor: - if colors[dir] == 1: - squares[-1]["mesh"] = 1 - elif colors[dir] == 0: - squares[-1]["mesh"] = 0 - for face in ["-J", "+J"]: - if exists[face] == 0: - squares.append({ - "name": f"spider{loc}:{face}", - "mesh": 2, - "translation": [ - 1 + SEP * loc[0], - SEP * loc[2], - (-1 if face == "+J" else 0) - SEP * loc[1], - ], - "rotation": [0.5, 0.5, 0.5, 0.5], - }) - for dir in ["+I", "-I", "+K", "-K"]: - if exists[dir]: - if dir == "+I" or dir == "-I": - if colors[dir] == 0: - squares[-1]["mesh"] = 0 - else: - squares[-1]["mesh"] = 1 - elif not noColor: - if colors[dir] == 1: - squares[-1]["mesh"] = 0 - elif colors[dir] == 0: - squares[-1]["mesh"] = 1 - - degree = sum([v for (k, v) in exists.items()]) - normal = {"I": 0, "J": 0, "K": 0} - if exists["-I"] == 0 and exists["+I"] == 0: - normal["I"] = 1 - if exists["-J"] == 0 and exists["+J"] == 0: - normal["J"] = 1 - if exists["-K"] == 0 and exists["+K"] == 0: - normal["K"] = 1 - if degree > 1: - if ( - exists["-I"] - and exists["+I"] - and exists["-J"] == 0 - and exists["+J"] == 0 - and exists["-K"] == 0 - and exists["+K"] == 0 - ): - if corr["-I"][0]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 9, - "translation": [ - SEP * loc[0], - 0.5 + SEP * loc[2], - -SEP * loc[1], - ], - }) - if corr["-I"][1]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 9, - "translation": [ - 1 + SEP * loc[0], - SEP * loc[2], - -0.5 - SEP * loc[1], - ], - "rotation": [0.5, 0.5, 0.5, 0.5], - }) - elif ( - exists["-I"] == 0 - and exists["+I"] == 0 - and exists["-J"] - and exists["+J"] - and exists["-K"] == 0 - and exists["+K"] == 0 - ): - if corr["-J"][0]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 9, - "translation": [ - 0.5 + SEP * loc[0], - SEP * loc[2], - -SEP * loc[1], - ], - "rotation": [0, 0, SQ2, SQ2], - }) - if corr["-J"][1]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 9, - "translation": [ - SEP * loc[0], - 0.5 + SEP * loc[2], - -SEP * loc[1], - ], - }) - elif ( - exists["-I"] == 0 - and exists["+I"] == 0 - and exists["-J"] == 0 - and exists["+J"] == 0 - and exists["-K"] - and exists["+K"] - ): - if corr["-K"][0]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 9, - "translation": [ - 1 + SEP * loc[0], - SEP * loc[2], - -0.5 - SEP * loc[1], - ], - "rotation": [0.5, 0.5, 0.5, 0.5], - }) - if corr["-K"][1]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 9, - "translation": [ - 0.5 + SEP * loc[0], - SEP * loc[2], - -SEP * loc[1], - ], - "rotation": [0, 0, SQ2, SQ2], - }) - else: - if normal["I"]: - if corr["-J"][0] or corr["+J"][0] or corr["-K"][1] or corr["+K"][1]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 9, - "translation": [ - 0.5 + SEP * loc[0], - SEP * loc[2], - -SEP * loc[1], - ], - "rotation": [0, 0, SQ2, SQ2], - }) - - if corr["-J"][1] and corr["+J"][1] and corr["-K"][0] and corr["+K"][0]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 11, - "translation": [ - SEP * loc[0], - SEP * loc[2], - -1 - SEP * loc[1], - ], - "rotation": [0, -SQ2, 0, SQ2], - }) - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 11, - "translation": [ - SEP * loc[0], - 0.5 + SEP * loc[2], - -0.5 - SEP * loc[1], - ], - "rotation": [0, -SQ2, 0, SQ2], - }) - elif corr["-J"][1] and corr["+J"][1]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 9, - "translation": [ - SEP * loc[0], - 0.5 + SEP * loc[2], - -SEP * loc[1], - ], - }) - elif corr["-K"][0] and corr["+K"][0]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 9, - "translation": [ - 1 + SEP * loc[0], - SEP * loc[2], - -0.5 - SEP * loc[1], - ], - "rotation": [0.5, 0.5, 0.5, 0.5], - }) - elif corr["-J"][1] and corr["-K"][0]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 11, - "translation": [ - 1 + SEP * loc[0], - SEP * loc[2], - -SEP * loc[1], - ], - "rotation": [0, SQ2, 0, SQ2], - }) - elif corr["+J"][1] and corr["+K"][0]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 11, - "translation": [ - 1 + SEP * loc[0], - 0.5 + SEP * loc[2], - -0.5 - SEP * loc[1], - ], - "rotation": [0, SQ2, 0, SQ2], - }) - elif corr["+J"][1] and corr["-K"][0]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 11, - "translation": [ - SEP * loc[0], - SEP * loc[2], - -1 - SEP * loc[1], - ], - "rotation": [0, -SQ2, 0, SQ2], - }) - elif corr["-J"][1] and corr["+K"][0]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 11, - "translation": [ - SEP * loc[0], - 0.5 + SEP * loc[2], - -0.5 - SEP * loc[1], - ], - "rotation": [0, -SQ2, 0, SQ2], - }) - elif normal["J"]: - if corr["-K"][0] or corr["+K"][0] or corr["-I"][1] or corr["+I"][1]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 9, - "translation": [ - 1 + SEP * loc[0], - SEP * loc[2], - -0.5 - SEP * loc[1], - ], - "rotation": [0.5, 0.5, 0.5, 0.5], - }) - - if corr["-K"][1] and corr["+K"][1] and corr["-I"][0] and corr["+I"][0]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 11, - "translation": [ - 0.5 + SEP * loc[0], - 0.5 + SEP * loc[2], - -SEP * loc[1], - ], - "rotation": [0, 0, SQ2, SQ2], - }) - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 11, - "translation": [ - 1 + SEP * loc[0], - SEP * loc[2], - -SEP * loc[1], - ], - "rotation": [0, 0, SQ2, SQ2], - }) - elif corr["-K"][1] and corr["+K"][1]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 9, - "translation": [ - 0.5 + SEP * loc[0], - SEP * loc[2], - -SEP * loc[1], - ], - "rotation": [0, 0, SQ2, SQ2], - }) - elif corr["-I"][0] and corr["+I"][0]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 9, - "translation": [ - SEP * loc[0], - 0.5 + SEP * loc[2], - -SEP * loc[1], - ], - }) - elif corr["-K"][1] and corr["-I"][0]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 11, - "translation": [SEP * loc[0], SEP * loc[2], -SEP * loc[1]], - }) - elif corr["+K"][1] and corr["+I"][0]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 11, - "translation": [ - 0.5 + SEP * loc[0], - 0.5 + SEP * loc[2], - -SEP * loc[1], - ], - }) - elif corr["+K"][1] and corr["-I"][0]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 11, - "translation": [ - 0.5 + SEP * loc[0], - 0.5 + SEP * loc[2], - -SEP * loc[1], - ], - "rotation": [0, 0, SQ2, SQ2], - }) - elif corr["-K"][1] and corr["+I"][0]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 11, - "translation": [ - 1 + SEP * loc[0], - SEP * loc[2], - -SEP * loc[1], - ], - "rotation": [0, 0, SQ2, SQ2], - }) - else: - if corr["-I"][0] or corr["+I"][0] or corr["-J"][1] or corr["+J"][1]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 9, - "translation": [ - SEP * loc[0], - 0.5 + SEP * loc[2], - -SEP * loc[1], - ], - }) - - if corr["-I"][1] and corr["+I"][1] and corr["-J"][0] and corr["+J"][0]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 11, - "translation": [ - 0.5 + SEP * loc[0], - SEP * loc[2], - -0.5 - SEP * loc[1], - ], - "rotation": [SQ2, 0, 0, SQ2], - }) - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 11, - "translation": [ - SEP * loc[0], - SEP * loc[2], - -1 - SEP * loc[1], - ], - "rotation": [SQ2, 0, 0, SQ2], - }) - elif corr["-I"][1] and corr["+I"][1]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 9, - "translation": [ - 1 + SEP * loc[0], - SEP * loc[2], - -0.5 - SEP * loc[1], - ], - "rotation": [0.5, 0.5, 0.5, 0.5], - }) - elif corr["-J"][0] and corr["+J"][0]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 9, - "translation": [ - 0.5 + SEP * loc[0], - SEP * loc[2], - -SEP * loc[1], - ], - "rotation": [0, 0, SQ2, SQ2], - }) - elif corr["-I"][1] and corr["-J"][0]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 11, - "translation": [ - SEP * loc[0], - 1 + SEP * loc[2], - -SEP * loc[1], - ], - "rotation": [-SQ2, 0, 0, SQ2], - }) - elif corr["+I"][1] and corr["+J"][0]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 11, - "translation": [ - 0.5 + SEP * loc[0], - 1 + SEP * loc[2], - -0.5 - SEP * loc[1], - ], - "rotation": [-SQ2, 0, 0, SQ2], - }) - elif corr["+I"][1] and corr["-J"][0]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 11, - "translation": [ - 0.5 + SEP * loc[0], - SEP * loc[2], - -0.5 - SEP * loc[1], - ], - "rotation": [SQ2, 0, 0, SQ2], - }) - elif corr["-I"][1] and corr["+J"][0]: - squares.append({ - "name": f"spider{loc}:Corr", - "mesh": 11, - "translation": [ - SEP * loc[0], - SEP * loc[2], - -1 - SEP * loc[1], - ], - "rotation": [SQ2, 0, 0, SQ2], - }) - - if stabilizer > -1: - squares = [sqar for sqar in squares if rm_dir not in sqar["name"]] - else: - squares = [sqar for sqar in squares if "Corr" not in sqar["name"]] - return squares - - -def special_gen( - SEP, - loc, - exists, - type, - stabilizer, - rm_dir: str = ":+J", -): - if type == "Y": - square_mesh = 3 - half_dist_mesh = 12 - elif type == "T": - square_mesh = 13 - half_dist_mesh = 14 - else: - square_mesh = -1 - half_dist_mesh = -1 - - shapes = [] - if exists["+K"]: - # need connect to top - shapes.append({ - "name": f"spider{loc}:top:-K", - "mesh": square_mesh, - "translation": [ - SEP * loc[0], - 0.55 + SEP * loc[2], - -SEP * loc[1], - ], - }) - shapes.append({ - "name": f"spider{loc}:top:-I", - "mesh": half_dist_mesh, - "rotation": [0, 0, SQ2, SQ2], - "translation": [SEP * loc[0], 0.55 + SEP * loc[2], -SEP * loc[1]], - }) - shapes.append({ - "name": f"spider{loc}:top:+I", - "mesh": half_dist_mesh, - "rotation": [0, 0, SQ2, SQ2], - "translation": [1 + SEP * loc[0], 0.55 + SEP * loc[2], -SEP * loc[1]], - }) - shapes.append({ - "name": f"spider{loc}:top:-J", - "mesh": half_dist_mesh, - "rotation": [0.5, 0.5, 0.5, 0.5], - "translation": [1 + SEP * loc[0], 0.55 + SEP * loc[2], -SEP * loc[1]], - }) - shapes.append({ - "name": f"spider{loc}:top:+J", - "mesh": half_dist_mesh, - "rotation": [0.5, 0.5, 0.5, 0.5], - "translation": [ - 1 + SEP * loc[0], - 0.55 + SEP * loc[2], - -SEP * loc[1] - 1, - ], - }) - - if exists["-K"]: - # need connect to bottom - shapes.append({ - "name": f"spider{loc}:bottom:+K", - "mesh": square_mesh, - "translation": [ - SEP * loc[0], - 0.45 + SEP * loc[2], - -SEP * loc[1], - ], - }) - shapes.append({ - "name": f"spider{loc}:bottom:-I", - "mesh": half_dist_mesh, - "rotation": [0, 0, SQ2, SQ2], - "translation": [SEP * loc[0], SEP * loc[2], -SEP * loc[1]], - }) - shapes.append({ - "name": f"spider{loc}:bottom:+I", - "mesh": half_dist_mesh, - "rotation": [0, 0, SQ2, SQ2], - "translation": [1 + SEP * loc[0], SEP * loc[2], -SEP * loc[1]], - }) - shapes.append({ - "name": f"spider{loc}:bottom:-J", - "mesh": half_dist_mesh, - "rotation": [0.5, 0.5, 0.5, 0.5], - "translation": [1 + SEP * loc[0], SEP * loc[2], -SEP * loc[1]], - }) - shapes.append({ - "name": f"spider{loc}:bottom:+J", - "mesh": half_dist_mesh, - "rotation": [0.5, 0.5, 0.5, 0.5], - "translation": [ - 1 + SEP * loc[0], - SEP * loc[2], - -SEP * loc[1] - 1, - ], - }) - - if stabilizer > -1: - shapes = [shp for shp in shapes if rm_dir not in shp["name"]] - return shapes - - -def gltf_generator( - lasir: Mapping[str, Any], - output_file: Optional[str] = "", - stabilizer: Optional[int] = -1, - tube_len: Optional[float] = 2.0, - no_color_z: Optional[bool] = False, -) -> Mapping[str, Any]: - gltf_file, s, tubelen, noColor = ( - output_file, - stabilizer, - tube_len, - no_color_z, - ) - rm_dir = ":+J" - - gltf = base_gen(BASE_GLTF, tubelen) - - gltf["nodes"] = [ - {"name": "smaple"}, - ] - i_bound = lasir["n_i"] - j_bound = lasir["n_j"] - k_bound = lasir["n_k"] - NodeY = lasir["NodeY"] - ExistI = lasir["ExistI"] - ColorI = lasir["ColorI"] - ExistJ = lasir["ExistJ"] - ColorJ = lasir["ColorJ"] - ExistK = lasir["ExistK"] - CorrIJ = lasir["CorrIJ"] - CorrIK = lasir["CorrIK"] - CorrJI = lasir["CorrJI"] - CorrJK = lasir["CorrJK"] - CorrKI = lasir["CorrKI"] - CorrKJ = lasir["CorrKJ"] - if "ColorKP" not in lasir: - ColorKP = [ - [[-1 for _ in range(k_bound)] for _ in range(j_bound)] - for _ in range(i_bound) - ] - else: - ColorKP = lasir["ColorKP"] - if "ColorKM" not in lasir: - ColorKM = [ - [[-1 for _ in range(k_bound)] for _ in range(j_bound)] - for _ in range(i_bound) - ] - else: - ColorKM = lasir["ColorKM"] - port_cubes = lasir["port_cubes"] - t_injections = ( - lasir["optional"]["t_injections"] - if "t_injections" in lasir["optional"] - else [] - ) - - if s >= len(CorrIJ) or s < -1: - raise ValueError(f"No such stabilizer {s}.") - for i in range(i_bound): - for j in range(j_bound): - for k in range(k_bound): - if ExistI[i][j][k]: - gltf["nodes"] += tube_gen( - tubelen + 1.0, - (i, j, k), - "I", - ColorI[i][j][k], - s, - (CorrIJ[s][i][j][k], CorrIK[s][i][j][k]), - noColor, - rm_dir, - ) - if ExistJ[i][j][k]: - gltf["nodes"] += tube_gen( - tubelen + 1.0, - (i, j, k), - "J", - ColorJ[i][j][k], - s, - (CorrJK[s][i][j][k], CorrJI[s][i][j][k]), - noColor, - rm_dir, - ) - if ExistK[i][j][k]: - gltf["nodes"] += tube_gen( - tubelen + 1.0, - (i, j, k), - "K", - 7 * ColorKM[i][j][k] + ColorKP[i][j][k], - s, - (CorrKI[s][i][j][k], CorrKJ[s][i][j][k]), - noColor, - rm_dir, - ) - - for i in range(i_bound): - for j in range(j_bound): - for k in range(k_bound): - exists = {"-I": 0, "+I": 0, "-K": 0, "+K": 0, "-J": 0, "+J": 0} - colors = {} - corr = { - "-I": (0, 0), - "+I": (0, 0), - "-J": (0, 0), - "+J": (0, 0), - "-K": (0, 0), - "+K": (0, 0), - } - if i > 0 and ExistI[i - 1][j][k]: - exists["-I"] = 1 - colors["-I"] = ColorI[i - 1][j][k] - corr["-I"] = (CorrIJ[s][i - 1][j][k], CorrIK[s][i - 1][j][k]) - if ExistI[i][j][k]: - exists["+I"] = 1 - colors["+I"] = ColorI[i][j][k] - corr["+I"] = (CorrIJ[s][i][j][k], CorrIK[s][i][j][k]) - if j > 0 and ExistJ[i][j - 1][k]: - exists["-J"] = 1 - colors["-J"] = ColorJ[i][j - 1][k] - corr["-J"] = (CorrJK[s][i][j - 1][k], CorrJI[s][i][j - 1][k]) - if ExistJ[i][j][k]: - exists["+J"] = 1 - colors["+J"] = ColorJ[i][j][k] - corr["+J"] = (CorrJK[s][i][j][k], CorrJI[s][i][j][k]) - if k > 0 and ExistK[i][j][k - 1]: - exists["-K"] = 1 - colors["-K"] = ColorKP[i][j][k - 1] - corr["-K"] = (CorrKI[s][i][j][k - 1], CorrKJ[s][i][j][k - 1]) - if ExistK[i][j][k]: - exists["+K"] = 1 - colors["+K"] = ColorKM[i][j][k] - corr["+K"] = (CorrKI[s][i][j][k], CorrKJ[s][i][j][k]) - if sum([v for (k, v) in exists.items()]) > 0: - if [i, j, k] not in port_cubes: - if NodeY[i][j][k]: - gltf["nodes"] += special_gen( - tubelen + 1.0, - (i, j, k), - exists, - "Y", - s, - rm_dir, - ) - else: - gltf["nodes"] += cube_gen( - tubelen + 1.0, - (i, j, k), - exists, - colors, - s, - corr, - noColor, - rm_dir, - ) - elif [i, j, k] in t_injections: - gltf["nodes"] += special_gen( - tubelen + 1.0, - (i, j, k), - exists, - "T", - s, - rm_dir, - ) - - gltf["nodes"][0]["children"] = list(range(1, len(gltf["nodes"]))) - with open(gltf_file, "w") as f: - json.dump(gltf, f) - - return gltf diff --git a/glue/lattice_surgery/olssco/translators/networkx_generator.py b/glue/lattice_surgery/olssco/translators/networkx_generator.py deleted file mode 100644 index 0481bd9e0..000000000 --- a/glue/lattice_surgery/olssco/translators/networkx_generator.py +++ /dev/null @@ -1,250 +0,0 @@ -import argparse -import json -from networkx import Graph -import stimzx - - -class ZXNode: - - def __init__(self, coord3, n_j): - self.type = 'N' - i, j, k = coord3 - self.yTailP = False - self.yTailM = False - self.node_id = -1 - - self.y = -(n_j + 1) * i + j - self.x = k * (n_j + 2) + j - - def getCoord2(self): - return (self.x, self.y) - - def computeType(self, exists, colors): - deg = sum([v for (k, v) in exists.items()]) - if deg == 0: - self.type = 'N' - return - elif deg == 1: - raise ValueError('There should not be deg-1 Z or X spiders.') - elif deg == 2: - self.type = 'I' - elif deg >= 5: - raise ValueError('deg > 4: 3D corner exists') - else: - if exists['-I'] == 0 and exists['+I'] == 0: - if exists['-J']: - if colors['-J'] == 0: - self.type = 'X' - else: - self.type = 'Z' - else: # must exist +J - if colors['+J'] == 0: - self.type = 'X' - else: - self.type = 'Z' - - if exists['-J'] == 0 and exists['+J'] == 0: - if exists['-I']: - if colors['-I'] == 0: - self.type = 'Z' - else: - self.type = 'X' - else: # must exist +I - if colors['+I'] == 0: - self.type = 'Z' - else: - self.type = 'X' - - if exists['-K'] == 0 and exists['+K'] == 0: - if exists['-I']: - if colors['-I'] == 0: - self.type = 'X' - else: - self.type = 'Z' - else: # must exist +I - if colors['+I'] == 0: - self.type = 'X' - else: - self.type = 'Z' - - def emit(self): - zigxag = { - 'Z': '@', - 'X': 'O', - 'S': 's', - 'W': 'w', - 'I': 'O', - 'Pi': 'in', - 'Po': 'out', - } - # return str(self.x) + ',' + str(self.y) + ',' + str(zigxag[self.type]) - return str(-self.y) + ',' + str(self.x) + ',' + str(zigxag[self.type]) - - -class ZXEdge: - - def __init__(self, ifH, nodea: ZXNode, nodeb: ZXNode): - self.type = '-' - if ifH: - self.type = 'h' - self.nodea = nodea - self.nodeb = nodeb - - def emit(self): - # return ( - # str(self.xa) - # + ',' - # + str(self.ya) - # + ',' - # + str(self.xb) - # + ',' - # + str(self.yb) - # + ',' - # + self.type - # ) - - return ( - str(-self.ya) - + ',' - + str(self.xa) - + ',' - + str(-self.yb) - + ',' - + str(self.xb) - + ',' - + self.type - ) - - -def networkx_generator(lasir: dict): - n_i = lasir['n_i'] - n_j = lasir['n_j'] - n_k = lasir['n_k'] - NodeY = lasir['NodeY'] - ExistI = lasir['ExistI'] - ColorI = lasir['ColorI'] - ExistJ = lasir['ExistJ'] - ColorJ = lasir['ColorJ'] - ExistK = lasir['ExistK'] - ColorKP = lasir['ColorKP'] - ColorKM = lasir['ColorKM'] - port_cubes = lasir['port_cubes'] - - nodes = [ - [[ZXNode((i, j, k), n_j) for k in range(n_k + 1)] for j in range(n_j + 1)] - for i in range(n_i + 1) - ] - - # Y spiders - for i in range(n_i): - for j in range(n_j): - for k in range(n_k): - if NodeY[i][j][k]: - if k - 1 >= 0 and ExistK[i][j][k - 1] and (not NodeY[i][j][k - 1]): - nodes[i][j][k - 1].yTailP = True - if k + 1 < n_k and ExistK[i][j][k] and (not NodeY[i][j][k + 1]): - nodes[i][j][k + 1].yTailM = True - - # Z/X Spiders - for i in range(n_i): - for j in range(n_j): - for k in range(n_k): - if (i, j, k) not in port_cubes and NodeY[i][j][k] == 0: - exists = {'-I': 0, '+I': 0, '-K': 0, '+K': 0, '-J': 0, '+J': 0} - colors = {} - if i > 0 and ExistI[i - 1][j][k]: - exists['-I'] = 1 - colors['-I'] = ColorI[i - 1][j][k] - if ExistI[i][j][k]: - exists['+I'] = 1 - colors['+I'] = ColorI[i][j][k] - if j > 0 and ExistJ[i][j - 1][k]: - exists['-J'] = 1 - colors['-J'] = ColorJ[i][j - 1][k] - if ExistJ[i][j][k]: - exists['+J'] = 1 - colors['+J'] = ColorJ[i][j][k] - if k > 0 and ExistK[i][j][k - 1]: - exists['-K'] = 1 - colors['-K'] = ColorKP[i][j][k - 1] - if ExistK[i][j][k]: - exists['+K'] = 1 - colors['+K'] = ColorKM[i][j][k] - nodes[i][j][k].computeType(exists, colors) - - for i, j, k in port_cubes: - nodes[i][j][k].type = 'Po' - - # edges - edges = [] - # anc_nodes = [] - valid_types = ['Z', 'X', 'S', 'W', 'I', 'Pi', 'Po'] - for i in range(n_i): - for j in range(n_j): - for k in range(n_k): - if ( - ExistI[i][j][k] == 1 - and nodes[i][j][k].type in valid_types - and nodes[i + 1][j][k].type in valid_types - ): - edges.append(ZXEdge(0, nodes[i][j][k], nodes[i + 1][j][k])) - - if ( - ExistJ[i][j][k] == 1 - and nodes[i][j][k].type in valid_types - and nodes[i][j + 1][k].type in valid_types - ): - # anc_nodes.append( (nodes[i][j][k].x+1, nodes[i][j][k].y) ) - # edges.append(ZXEdge(0, nodes[i][j][k].getCoord2(), anc_nodes[-1])) - # edges.append(ZXEdge(0, anc_nodes[-1], nodes[i][j+1][k].getCoord2())) - edges.append(ZXEdge(0, nodes[i][j][k], nodes[i][j + 1][k])) - - if ( - ExistK[i][j][k] == 1 - and nodes[i][j][k].type in valid_types - and nodes[i][j][k + 1].type in valid_types - ): - edges.append( - ZXEdge( - abs(ColorKM[i][j][k] - ColorKP[i][j][k]), - nodes[i][j][k], - nodes[i][j][k + 1], - ) - ) - - zx_graph = Graph() - type_to_str = {'X': 'X', 'Z': 'Z', 'Pi': 'in', 'Po': 'out', 'I': 'X'} - cnt = 0 - for i, j, k in port_cubes: - node = nodes[i][j][k] - zx_graph.add_node(cnt, value=stimzx.ZxType(type_to_str[node.type])) - node.node_id = cnt - cnt += 1 - - for i in range(n_i + 1): - for j in range(n_j + 1): - for k in range(n_k + 1): - node = nodes[i][j][k] - if node.type not in ['N', 'Po', 'Pi']: - zx_graph.add_node(cnt, value=stimzx.ZxType(type_to_str[node.type])) - node.node_id = cnt - cnt += 1 - if node.yTailM: - zx_graph.add_node(cnt, value=stimzx.ZxType('Z', 1)) - zx_graph.add_edge(node.node_id, cnt) - cnt += 1 - if node.yTailP: - zx_graph.add_node(cnt, value=stimzx.ZxType('Z', 3)) - zx_graph.add_edge(node.node_id, cnt) - cnt += 1 - - for edge in edges: - if edge.type != 'h': - zx_graph.add_edge(edge.nodea.node_id, edge.nodeb.node_id) - else: - zx_graph.add_node(cnt, value=stimzx.ZxType('H')) - zx_graph.add_edge(cnt, edge.nodea.node_id) - zx_graph.add_edge(cnt, edge.nodeb.node_id) - cnt += 1 - - return zx_graph diff --git a/glue/lattice_surgery/olssco/translators/textfig_generator.py b/glue/lattice_surgery/olssco/translators/textfig_generator.py deleted file mode 100644 index a2e7b8ac9..000000000 --- a/glue/lattice_surgery/olssco/translators/textfig_generator.py +++ /dev/null @@ -1,184 +0,0 @@ -"""A one-line summary of the module or program, terminated by a period. - -Leave one blank line. The rest of this docstring should contain an -overall description of the module or program. Optionally, it may also -contain a brief description of exported classes and functions and/or usage -examples. - -Typical usage example: - - foo = ClassFoo() - bar = foo.FunctionBar() -""" - -import argparse -import json -from typing import Any, Mapping, Sequence - -from olssco.translators import ZXGridGraph - - -class TextLayer: - pad_i = 1 - pad_j = 1 - sep_i = 4 - sep_j = 4 - - def __init__(self, zx_graph: ZXGridGraph, k: int, if_middle: bool) -> None: - self.n_i, self.n_j, self.n_k = ( - zx_graph.n_i, - zx_graph.n_j, - zx_graph.n_k, - ) - self.chars = [ - [ - " " - for _ in range( - 2 * TextLayer.pad_i + (self.n_i - 1) * TextLayer.sep_i + 1 - ) - ] - + ["\n"] - for _ in range( - 2 * TextLayer.pad_j + (self.n_j - 1) * TextLayer.sep_j + 1 - ) - ] - if if_middle: - self.compute_middle(zx_graph, k) - else: - self.compute_normal(zx_graph, k) - - def set_char(self, j: int, i: int, character): - self.chars[j][i] = character - - def compute_middle(self, zx_graph: ZXGridGraph, k: int): - for i in range(self.n_i): - for j in range(self.n_j): - self.set_char( - TextLayer.pad_j + j * TextLayer.sep_j, - TextLayer.pad_i + i * TextLayer.sep_i, - ".", - ) - spider = zx_graph.spiders[i][j][k] - color_sum = -1 - if k == self.n_k - 1: - try: - for port in zx_graph.lasir["ports"]: - if (port["i"], port["j"], port["k"]) == (i, j, k): - color_sum = port["c"] + spider.colors["+K"] - break - except ValueError: - print(f"KPipe({i},{j},{k}) connecting outside but not port.") - else: - upper_spider = zx_graph.spiders[i][j][k + 1] - if spider.exists["+K"] == 1 and upper_spider.exists["-K"] == 1: - color_sum = spider.colors["+K"] + upper_spider.colors["-K"] - if spider.exists["+K"] == 0 and upper_spider.exists["-K"] == 1: - try: - for port in zx_graph.lasir["ports"]: - if (port["i"], port["j"], port["k"]) == (i, j, k): - color_sum = port["c"] + upper_spider.colors["-K"] - break - except ValueError: - print(f"KPipe({i},{j},{k})- should be a port.") - if spider.exists["+K"] == 1 and upper_spider.exists["-K"] == 0: - try: - for port in zx_graph.lasir["ports"]: - if (port["i"], port["j"], port["k"]) == (i, j, k + 1): - color_sum = port["c"] + spider.colors["+K"] - break - except ValueError: - print(f"KPipe({i},{j},{k + 1})- should be a port") - - if color_sum != -1: - self.set_char( - TextLayer.pad_j + j * TextLayer.sep_j - 1, - TextLayer.pad_i + i * TextLayer.sep_i + 1, - "/", - ) - self.set_char( - TextLayer.pad_j + j * TextLayer.sep_j + 1, - TextLayer.pad_i + i * TextLayer.sep_i - 1, - "/", - ) - if color_sum == 1: - self.set_char( - TextLayer.pad_j + j * TextLayer.sep_j, - TextLayer.pad_i + i * TextLayer.sep_i, - "H", - ) - else: - self.set_char( - TextLayer.pad_j + j * TextLayer.sep_j, - TextLayer.pad_i + i * TextLayer.sep_i, - "X", - ) - - def compute_normal(self, zx_graph: ZXGridGraph, k: int): - for i in range(self.n_i): - for j in range(self.n_j): - spider = zx_graph.spiders[i][j][k] - - if spider.type == "N": - self.set_char( - TextLayer.pad_j + j * TextLayer.sep_j, - TextLayer.pad_i + i * TextLayer.sep_i, - ".", - ) - continue - else: - self.set_char( - TextLayer.pad_j + j * TextLayer.sep_j, - TextLayer.pad_i + i * TextLayer.sep_i, - spider.type, - ) - - # I pipes - if spider.exists["+I"]: - for offset in range(1, TextLayer.sep_i): - self.set_char( - TextLayer.pad_j + j * TextLayer.sep_j, - TextLayer.pad_i + i * TextLayer.sep_i + offset, - "-", - ) - - # J pipes - if spider.exists["+J"]: - for offset in range(1, TextLayer.sep_i): - self.set_char( - TextLayer.pad_j + j * TextLayer.sep_j + offset, - TextLayer.pad_i + i * TextLayer.sep_i, - "|", - ) - - # K pipes - if spider.exists["+K"]: - self.set_char( - TextLayer.pad_j + j * TextLayer.sep_j - 1, - TextLayer.pad_i + i * TextLayer.sep_i + 1, - "/", - ) - if spider.exists["-K"]: - self.set_char( - TextLayer.pad_j + j * TextLayer.sep_j + 1, - TextLayer.pad_i + i * TextLayer.sep_i - 1, - "/", - ) - - def get_text(self): - text = "" - for j in range(2 * TextLayer.pad_j + (self.n_j - 1) * TextLayer.sep_j): - for i in range(2 * TextLayer.pad_i + (self.n_i - 1) * TextLayer.sep_i): - text += self.chars[j][i] - text += "\n" - return text - - -def textfig_generator(lasir: dict): - text = "" - zx_graph = ZXGridGraph(lasir) - for k in range(lasir["n_k"] - 1, -1, -1): - text += TextLayer(zx_graph, k, True).get_text() - text += "\n======================================\n" - text += TextLayer(zx_graph, k, False).get_text() - text += "\n======================================\n" - return text diff --git a/glue/lattice_surgery/olssco/translators/zigxag_generator.py b/glue/lattice_surgery/olssco/translators/zigxag_generator.py deleted file mode 100644 index 12085f4c0..000000000 --- a/glue/lattice_surgery/olssco/translators/zigxag_generator.py +++ /dev/null @@ -1,301 +0,0 @@ -"""A one-line summary of the module or program, terminated by a period. - -Leave one blank line. The rest of this docstring should contain an -overall description of the module or program. Optionally, it may also -contain a brief description of exported classes and functions and/or usage -examples. - -Typical usage example: - - foo = ClassFoo() - bar = foo.FunctionBar() -""" - -from typing import Sequence - - -class ZXNode: - - def __init__(self, coord3, n_j): - self.type = 'N' - i, j, k = coord3 - self.yTailP = False - self.yTailM = False - - self.y = -(n_j + 1) * i + j - self.x = k * (n_j + 2) + j - - def getCoord2(self): - return (self.x, self.y) - - def computeType(self, exists, colors): - deg = sum([v for (k, v) in exists.items()]) - if deg == 0: - self.type = 'N' - return - elif deg == 1: - raise ValueError('There should not be deg-1 Z or X spiders.') - elif deg == 2: - self.type = 'I' - elif deg >= 5: - raise ValueError('deg > 4: 3D corner exists') - else: - if exists['-I'] == 0 and exists['+I'] == 0: - if exists['-J']: - if colors['-J'] == 0: - self.type = 'X' - else: - self.type = 'Z' - else: # must exist +J - if colors['+J'] == 0: - self.type = 'X' - else: - self.type = 'Z' - - if exists['-J'] == 0 and exists['+J'] == 0: - if exists['-I']: - if colors['-I'] == 0: - self.type = 'Z' - else: - self.type = 'X' - else: # must exist +I - if colors['+I'] == 0: - self.type = 'Z' - else: - self.type = 'X' - - if exists['-K'] == 0 and exists['+K'] == 0: - if exists['-I']: - if colors['-I'] == 0: - self.type = 'X' - else: - self.type = 'Z' - else: # must exist +I - if colors['+I'] == 0: - self.type = 'X' - else: - self.type = 'Z' - - def emit(self): - zigxag = { - 'Z': '@', - 'X': 'O', - 'S': 's', - 'W': 'w', - 'I': 'O', - 'Pi': 'in', - 'Po': 'out', - } - # return str(self.x) + ',' + str(self.y) + ',' + str(zigxag[self.type]) - return str(-self.y) + ',' + str(-self.x) + ',' + str(zigxag[self.type]) - - -class ZXEdge: - - def __init__(self, ifH, coord2a, coord2b): - self.xa, self.ya = coord2a - self.xb, self.yb = coord2b - self.type = '-' - if ifH: - self.type = 'h' - - def emit(self): - # return ( - # str(self.xa) - # + ',' - # + str(self.ya) - # + ',' - # + str(self.xb) - # + ',' - # + str(self.yb) - # + ',' - # + self.type - # ) - - return ( - str(-self.ya) - + ',' - + str(-self.xa) - + ',' - + str(-self.yb) - + ',' - + str(-self.xb) - + ',' - + self.type - ) - - -def zigxag_generator(lasir: dict, io_spec: Sequence[str] = None): - n_i = lasir['n_i'] - n_j = lasir['n_j'] - n_k = lasir['n_k'] - NodeY = lasir['NodeY'] - ExistI = lasir['ExistI'] - ColorI = lasir['ColorI'] - ExistJ = lasir['ExistJ'] - ColorJ = lasir['ColorJ'] - ExistK = lasir['ExistK'] - ColorKP = lasir['ColorKP'] - ColorKM = lasir['ColorKM'] - port_cubes = lasir['port_cubes'] - - nodes = [ - [[ZXNode((i, j, k), n_j) for k in range(n_k + 1)] for j in range(n_j + 1)] - for i in range(n_i + 1) - ] - - # ports - for [i, j, k] in port_cubes: - nodes[i][j][k].type = 'Po' - if io_spec: - if len(io_spec) != len(port_cubes): - raise ValueError('io_spec should be of same length as port_cubes') - for w, [i, j, k] in enumerate(port_cubes): - nodes[i][j][k].type = io_spec[w] - - # Y spiders - for i in range(n_i): - for j in range(n_j): - for k in range(n_k): - if NodeY[i][j][k]: - if k - 1 >= 0 and ExistK[i][j][k - 1] and (not NodeY[i][j][k - 1]): - nodes[i][j][k - 1].yTailP = True - if k + 1 < n_k and ExistK[i][j][k] and (not NodeY[i][j][k + 1]): - nodes[i][j][k + 1].yTailM = True - - # Z/X Spiders - for i in range(n_i): - for j in range(n_j): - for k in range(n_k): - if (i, j, k) not in port_cubes and NodeY[i][j][k] == 0: - exists = {'-I': 0, '+I': 0, '-K': 0, '+K': 0, '-J': 0, '+J': 0} - colors = {} - if i > 0 and ExistI[i - 1][j][k]: - exists['-I'] = 1 - colors['-I'] = ColorI[i - 1][j][k] - if ExistI[i][j][k]: - exists['+I'] = 1 - colors['+I'] = ColorI[i][j][k] - if j > 0 and ExistJ[i][j - 1][k]: - exists['-J'] = 1 - colors['-J'] = ColorJ[i][j - 1][k] - if ExistJ[i][j][k]: - exists['+J'] = 1 - colors['+J'] = ColorJ[i][j][k] - if k > 0 and ExistK[i][j][k - 1]: - exists['-K'] = 1 - colors['-K'] = ColorKP[i][j][k - 1] - if ExistK[i][j][k]: - exists['+K'] = 1 - colors['+K'] = ColorKM[i][j][k] - nodes[i][j][k].computeType(exists, colors) - - # edges - edges = [] - # anc_nodes = [] - valid_types = ['Z', 'X', 'S', 'W', 'I', 'Pi', 'Po'] - for i in range(n_i): - for j in range(n_j): - for k in range(n_k): - if ( - ExistI[i][j][k] == 1 - and nodes[i][j][k].type in valid_types - and nodes[i + 1][j][k].type in valid_types - ): - edges.append( - ZXEdge( - 0, nodes[i][j][k].getCoord2(), nodes[i + 1][j][k].getCoord2() - ) - ) - - if ( - ExistJ[i][j][k] == 1 - and nodes[i][j][k].type in valid_types - and nodes[i][j + 1][k].type in valid_types - ): - # anc_nodes.append( (nodes[i][j][k].x+1, nodes[i][j][k].y) ) - # edges.append(ZXEdge(0, nodes[i][j][k].getCoord2(), anc_nodes[-1])) - # edges.append(ZXEdge(0, anc_nodes[-1], nodes[i][j+1][k].getCoord2())) - edges.append( - ZXEdge( - 0, nodes[i][j][k].getCoord2(), nodes[i][j + 1][k].getCoord2() - ) - ) - - if ( - ExistK[i][j][k] == 1 - and nodes[i][j][k].type in valid_types - and nodes[i][j][k + 1].type in valid_types - ): - edges.append( - ZXEdge( - abs(ColorKM[i][j][k] - ColorKP[i][j][k]), - nodes[i][j][k].getCoord2(), - nodes[i][j][k + 1].getCoord2(), - ) - ) - - nodes_str = '' - first = True - for i in range(n_i + 1): - for j in range(n_j + 1): - for k in range(n_k + 1): - if nodes[i][j][k].type in valid_types: - if not first: - nodes_str += ';' - nodes_str += nodes[i][j][k].emit() - first = False - - # for (x,y) in anc_nodes: - # zigxag_str += ';' + str(x) + ',' + str(y) + '+' - - edges_str = '' - for i, edge in enumerate(edges): - if i > 0: - edges_str += ';' - edges_str += edge.emit() - - for i in range(n_i): - for j in range(n_j): - for k in range(n_k): - if nodes[i][j][k].yTailP: - nodes_str += ( - ';' - + str(nodes[i][j][k].x + n_j - j) - + ',' - + str(nodes[i][j][k].y) - + ',s' - ) - edges_str += ( - ';' - + str(nodes[i][j][k].x + n_j - j) - + ',' - + str(nodes[i][j][k].y) - + ',' - + str(nodes[i][j][k].x) - + ',' - + str(nodes[i][j][k].y) - + ',-' - ) - if nodes[i][j][k].yTailM: - nodes_str += ( - ';' - + str(nodes[i][j][k].x - j - 1) - + ',' - + str(nodes[i][j][k].y) - + ',s' - ) - edges_str += ( - ';' - + str(nodes[i][j][k].x - j - 1) - + ',' - + str(nodes[i][j][k].y) - + ',' - + str(nodes[i][j][k].x) - + ',' - + str(nodes[i][j][k].y) - + ',-' - ) - - zigxag_str = 'https://algassert.com/zigxag#' + nodes_str + ':' + edges_str - return zigxag_str diff --git a/glue/lattice_surgery/olssco/translators/zx_grid_graph.py b/glue/lattice_surgery/olssco/translators/zx_grid_graph.py deleted file mode 100644 index bd2349970..000000000 --- a/glue/lattice_surgery/olssco/translators/zx_grid_graph.py +++ /dev/null @@ -1,157 +0,0 @@ -"""A one-line summary of the module or program, terminated by a period. - -Leave one blank line. The rest of this docstring should contain an -overall description of the module or program. Optionally, it may also -contain a brief description of exported classes and functions and/or usage -examples. - -Typical usage example: - - foo = ClassFoo() - bar = foo.FunctionBar() -""" - - -from typing import Any, Mapping, Sequence - - -class ZXEdge: - - def __init__(self, if_h: bool, spider0, spider1): - self.spider0, self.spider1 = spider0, spider1 - self.type = "h" if if_h else "-" - - -class ZXSpider: - - def __init__(self, coord3): - self.type = "N" - self.i, self.j, self.k = coord3 - self.y_tail_plus = False - self.y_tail_minus = False - self.exists = {"-I": 0, "+I": 0, "-K": 0, "+K": 0, "-J": 0, "+J": 0} - self.colors = {"-I": -1, "+I": -1, "-K": -1, "+K": -1, "-J": -1, "+J": -1} - - def compute_type(self, exists: dict, colors: dict): - self.exists, self.colors = exists, colors - deg = sum([v for (k, v) in exists.items()]) - if deg == 0: - self.type = "N" - return - elif deg == 1: - raise ValueError("There should not be deg-1 Z or X spiders.") - elif deg == 2: - self.type = "X" - elif deg >= 5: - raise ValueError("deg > 4: 3D corner exists") - else: - if exists["-I"] == 0 and exists["+I"] == 0: - if exists["-J"]: - if colors["-J"] == 0: - self.type = "X" - else: - self.type = "Z" - else: # must exist +J - if colors["+J"] == 0: - self.type = "X" - else: - self.type = "Z" - - if exists["-J"] == 0 and exists["+J"] == 0: - if exists["-I"]: - if colors["-I"] == 0: - self.type = "Z" - else: - self.type = "X" - else: # must exist +I - if colors["+I"] == 0: - self.type = "Z" - else: - self.type = "X" - - if exists["-K"] == 0 and exists["+K"] == 0: - if exists["-I"]: - if colors["-I"] == 0: - self.type = "X" - else: - self.type = "Z" - else: # must exist +I - if colors["+I"] == 0: - self.type = "X" - else: - self.type = "Z" - - -class ZXGridGraph: - - def __init__(self, lasir: dict) -> None: - self.lasir = lasir - self.n_i, self.n_j, self.n_k = ( - lasir["n_i"], - lasir["n_j"], - lasir["n_k"], - ) - self.spiders = [ - [ - [ZXSpider((i, j, k)) for k in range(self.n_k + 1)] - for j in range(self.n_j + 1) - ] - for i in range(self.n_i + 1) - ] - self.edges = [] - self.append_y_tails() - self.compute_spiders_type() - - def append_y_tails(self): - for i in range(self.n_i): - for j in range(self.n_j): - for k in range(self.n_k): - if self.lasir["NodeY"][i][j][k]: - if ( - k - 1 >= 0 - and self.lasir["ExistK"][i][j][k - 1] - and (not self.lasir["NodeY"][i][j][k - 1]) - ): - self.spiders[i][j][k - 1].y_tail_plus = True - if ( - k + 1 < self.n_k - and self.lasir["ExistK"][i][j][k] - and (not self.lasir["NodeY"][i][j][k + 1]) - ): - self.spiders[i][j][k + 1].y_tail_minus = True - - def compute_spiders_type(self): - for i in range(self.n_i): - for j in range(self.n_j): - for k in range(self.n_k): - if ((i, j, k) not in self.lasir["port_cubes"]) and ( - self.lasir["NodeY"][i][j][k] == 0 - ): - exists = {"-I": 0, "+I": 0, "-K": 0, "+K": 0, "-J": 0, "+J": 0} - colors = { - "-I": -1, - "+I": -1, - "-K": -1, - "+K": -1, - "-J": -1, - "+J": -1, - } - if i > 0 and self.lasir["ExistI"][i - 1][j][k]: - exists["-I"] = 1 - colors["-I"] = self.lasir["ColorI"][i - 1][j][k] - if self.lasir["ExistI"][i][j][k]: - exists["+I"] = 1 - colors["+I"] = self.lasir["ColorI"][i][j][k] - if j > 0 and self.lasir["ExistJ"][i][j - 1][k]: - exists["-J"] = 1 - colors["-J"] = self.lasir["ColorJ"][i][j - 1][k] - if self.lasir["ExistJ"][i][j][k]: - exists["+J"] = 1 - colors["+J"] = self.lasir["ColorJ"][i][j][k] - if k > 0 and self.lasir["ExistK"][i][j][k - 1]: - exists["-K"] = 1 - colors["-K"] = self.lasir["ColorKP"][i][j][k - 1] - if self.lasir["ExistK"][i][j][k]: - exists["+K"] = 1 - colors["+K"] = self.lasir["ColorKM"][i][j][k] - self.spiders[i][j][k].compute_type(exists, colors) diff --git a/glue/lattice_surgery/paper/graph_state_olssco.py b/glue/lattice_surgery/paper/graph_state_olssco.py deleted file mode 100644 index e6d053e85..000000000 --- a/glue/lattice_surgery/paper/graph_state_olssco.py +++ /dev/null @@ -1,111 +0,0 @@ -import json -import multiprocessing -import sys -from olssco import OptimalLatticeSurgerySubroutineCompiler - - -def graph_state_olssco( - edges, seed, layout, wdir, starting_depth, if_print: bool = True -): - n_q = 8 - # dimensions depending on the qubit layout - if layout == "1row": - data = { - "max_i": n_q, - "max_j": 2, - } - elif layout == "2rows": - data = { - "max_i": n_q // 2, - "max_j": 3, - } - else: - raise ValueError("layout not supported! ") - - # should not be too low, avoids being trivially proved UNSAT by Z3 - depth = starting_depth - - checked_depth = {} - while True: - data["max_k"] = depth - - # get the outgoing ports - if layout == "1row": - data["ports"] = [ - { - "location": [i, 0, depth], - "direction": "-K", - "z_basis_direction": "I", - } - for i in range(n_q) - ] - elif layout == "2rows": - data["ports"] = [ - { - "location": [i, 0, depth], - "direction": "-K", - "z_basis_direction": "I", - } - for i in range(n_q // 2) - ] + [ - { - "location": [i - (n_q // 2), 2, depth], - "direction": "-K", - "z_basis_direction": "I", - } - for i in range(n_q // 2, n_q) - ] - - # stabilizers are X on qubit and Z on all its neighbors - data["stabilizers"] = [] - for i in range(n_q): - stab = "." * i + "X" + "." * (n_q - i - 1) - for edge in edges: - if edge[0] == i: - stab = stab[: edge[1]] + "Z" + stab[edge[1] + 1 :] - if edge[1] == i: - stab = stab[: edge[0]] + "Z" + stab[edge[0] + 1 :] - data["stabilizers"].append(stab) - - olssco = OptimalLatticeSurgerySubroutineCompiler(data, color_ij=True) - - if olssco.check_external_solver( - f"{wdir}graph_n{n_q}_s{seed}", print_progress=if_print - ): - checked_depth[str(depth)] = "SAT" - with open(f"{wdir}graph_n{n_q}_s{seed}.json", "w") as f: - json.dump(data, f) - if str(depth - 1) in checked_depth: - break - else: - depth -= 1 - else: - checked_depth[str(depth)] = "UNSAT" - if str(depth + 1) in checked_depth: - break - else: - depth += 1 - - with open(f"{wdir}graph_n{n_q}_s{seed}.json", "r") as f: - opt_data = json.load(f) - - with open(wdir + "olsco_stats", "a") as f: - f.write(f"{n_q}, {seed}, {opt_data['max_k']}\n") - - -if __name__ == "__main__": - n_core = int(sys.argv[1]) - layout = sys.argv[2] - wdir = sys.argv[3] - starting_depth = int(sys.argv[4]) - - def f(s): - # read the edges from the graph library - with open("graphs8.json", "r") as f: - graphs = json.load(f) - edges = graphs["8"][s] - return graph_state_olssco(edges, s, "1row", wdir, 3, if_print=False) - - pool = multiprocessing.Pool(n_core) - - outputs = pool.map(f, range(101), chunksize=1) diff --git a/glue/lattice_surgery/paper/graphs8.json b/glue/lattice_surgery/paper/graphs8.json deleted file mode 100644 index 838af862e..000000000 --- a/glue/lattice_surgery/paper/graphs8.json +++ /dev/null @@ -1,106 +0,0 @@ -{ - "8":[ - [[0,7],[1,7],[2,7],[3,7],[4,7],[5,7],[6,7]], - [[0,7],[5,6],[1,7],[2,7],[3,7],[4,7],[6,7]], - [[0,7],[4,6],[1,7],[5,6],[2,7],[3,7],[6,7]], - [[0,7],[5,6],[1,7],[4,6],[2,7],[3,7],[5,7]], - [[0,6],[1,7],[2,7],[4,6],[3,7],[5,6],[6,7]], - [[0,7],[5,6],[1,7],[3,6],[2,7],[4,6],[5,7]], - [[0,7],[3,5],[4,6],[1,7],[2,7],[5,7],[6,7]], - [[0,7],[5,6],[1,7],[3,5],[4,6],[2,7],[6,7]], - [[0,7],[3,5],[4,6],[1,7],[5,6],[2,7],[4,7]], - [[0,7],[2,5],[3,6],[1,7],[4,6],[5,7],[6,7]], - [[0,7],[3,5],[4,6],[1,7],[2,6],[4,7],[5,7]], - [[0,7],[1,5],[2,6],[3,6],[5,7],[4,5],[6,7]], - [[0,6],[2,7],[4,5],[1,6],[5,7],[3,7],[4,6]], - [[0,7],[3,4],[5,6],[1,6],[4,7],[2,6],[5,7]], - [[0,7],[1,6],[4,5],[2,6],[3,5],[4,7],[6,7]], - [[0,6],[3,5],[4,7],[1,6],[2,4],[5,7],[6,7]], - [[0,7],[3,4],[5,6],[1,7],[2,6],[4,5],[3,7]], - [[0,7],[3,5],[4,6],[1,5],[2,6],[3,7],[4,7]], - [[0,7],[1,4],[2,5],[3,6],[4,7],[5,7],[6,7]], - [[1,6],[2,4],[5,7],[0,7],[3,5],[4,6],[6,7]], - [[0,7],[1,6],[2,4],[3,5],[3,7],[5,6],[4,7]], - [[0,6],[1,4],[2,5],[3,7],[3,6],[4,7],[5,7]], - [[2,3],[4,6],[5,7],[0,7],[1,6],[2,4],[3,5]], - [[0,7],[4,6],[1,7],[5,6],[2,7],[3,6],[4,7],[5,7]], - [[1,7],[4,6],[2,7],[5,6],[0,6],[4,7],[3,6],[5,7]], - [[0,7],[5,6],[1,7],[3,5],[4,6],[2,7],[5,7],[6,7]], - [[0,7],[3,5],[4,6],[1,7],[5,6],[2,7],[3,7],[4,7]], - [[2,7],[5,6],[0,5],[1,6],[3,7],[4,6],[5,7],[6,7]], - [[0,7],[2,5],[3,6],[1,7],[4,6],[3,7],[5,6],[4,7]], - [[0,7],[3,5],[4,6],[1,7],[5,6],[2,6],[3,7],[4,7]], - [[0,7],[2,3],[4,6],[3,7],[5,6],[1,6],[4,7],[5,7]], - [[0,5],[2,7],[3,6],[1,5],[3,7],[4,6],[4,7],[5,6]], - [[4,7],[5,6],[0,4],[3,6],[5,7],[1,4],[2,5],[6,7]], - [[0,7],[3,4],[5,6],[1,7],[2,6],[4,5],[5,7],[6,7]], - [[0,7],[3,4],[5,6],[1,7],[2,6],[4,5],[3,7],[6,7]], - [[0,7],[2,5],[3,6],[1,7],[4,5],[2,7],[4,6],[3,7]], - [[1,5],[3,7],[4,6],[0,7],[2,6],[3,5],[4,7],[5,6]], - [[0,7],[2,6],[4,5],[1,5],[2,7],[3,6],[3,7],[4,6]], - [[0,6],[2,3],[5,7],[3,6],[4,7],[1,7],[2,4],[5,6]], - [[0,7],[2,6],[3,5],[1,7],[2,4],[3,6],[4,5],[6,7]], - [[0,7],[1,4],[5,6],[2,5],[3,6],[4,7],[5,7],[6,7]], - [[0,4],[3,6],[5,7],[4,5],[6,7],[1,7],[2,5],[4,6]], - [[0,7],[1,2],[3,5],[4,6],[2,7],[5,6],[3,7],[4,7]], - [[0,5],[1,6],[3,7],[2,3],[4,7],[5,6],[4,6],[5,7]], - [[0,5],[3,6],[4,7],[2,7],[3,4],[5,6],[1,6],[5,7]], - [[0,6],[2,4],[5,7],[2,6],[3,5],[4,7],[1,7],[3,6]], - [[1,3],[4,7],[5,6],[2,4],[3,6],[5,7],[0,5],[6,7]], - [[0,7],[1,5],[2,4],[3,6],[2,7],[4,6],[3,7],[5,6]], - [[2,4],[3,7],[5,6],[1,6],[3,4],[5,7],[0,5],[6,7]], - [[1,6],[2,4],[5,7],[0,7],[2,3],[4,6],[3,5],[6,7]], - [[0,7],[1,5],[2,3],[4,6],[2,7],[3,4],[5,6],[6,7]], - [[0,4],[1,7],[2,5],[3,6],[1,4],[2,7],[5,6],[3,7]], - [[0,7],[1,5],[2,6],[3,4],[1,7],[3,5],[4,6],[2,7]], - [[1,7],[2,4],[3,5],[0,1],[2,7],[4,6],[3,7],[5,6]], - [[0,1],[2,7],[3,5],[4,6],[0,2],[1,6],[3,4],[5,7]], - [[0,6],[2,3],[4,7],[2,6],[5,7],[3,7],[4,6],[1,7],[5,6]], - [[0,7],[2,6],[4,5],[1,5],[2,7],[3,6],[3,7],[4,6],[5,7]], - [[1,6],[2,5],[4,7],[1,5],[2,7],[3,6],[0,5],[3,7],[4,6]], - [[1,6],[3,5],[4,7],[2,7],[3,6],[4,5],[0,5],[3,7],[4,6]], - [[0,7],[2,3],[5,6],[1,7],[3,5],[4,6],[2,4],[5,7],[6,7]], - [[0,7],[3,4],[5,6],[2,6],[3,5],[4,7],[1,5],[3,7],[4,6]], - [[0,6],[3,5],[4,7],[4,6],[5,7],[1,7],[2,4],[5,6],[6,7]], - [[0,6],[2,4],[5,7],[1,7],[3,5],[4,6],[2,5],[3,4],[6,7]], - [[0,7],[1,6],[2,4],[3,5],[1,7],[4,6],[2,7],[5,6],[3,7]], - [[1,6],[2,7],[4,5],[0,7],[3,5],[4,6],[2,3],[4,7],[5,6]], - [[1,6],[2,7],[4,5],[0,7],[3,5],[4,6],[2,4],[3,7],[5,6]], - [[1,7],[2,4],[5,6],[2,3],[4,6],[5,7],[0,6],[3,5],[4,7]], - [[1,5],[2,7],[4,6],[1,7],[2,3],[5,6],[0,5],[3,4],[6,7]], - 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-} \ No newline at end of file diff --git a/glue/lattice_surgery/paper/rand_graph_baseline_opt.py b/glue/lattice_surgery/paper/rand_graph_baseline_opt.py deleted file mode 100644 index 333263c7c..000000000 --- a/glue/lattice_surgery/paper/rand_graph_baseline_opt.py +++ /dev/null @@ -1,103 +0,0 @@ -import json -import random -import sys - - -def split_map_i(i, lorr, n_col): - if i == 0: - return 0 - elif i == n_col - 1: - return 2 * n_col - 3 - else: - if lorr == "L": - return 2 * i - elif lorr == "R": - return 2 * i - 1 - else: - raise ValueError() - - -def split_map_back_i(i, n_col): - if i == 0: - return 0 - elif i == n_col - 1: - return i // 2 - else: - return (i + 1) // 2 - - -def split_map_edge(edge, n_col): - if len(edge) != 2: - raise ValueError() - left = min(edge) - right = max(edge) - return (split_map_i(left, "L", n_col), split_map_i(right, "R", n_col)) - - -def depth_baseline(edges, n_col, layout): - # sort according to the smaller col involved (beginning of interval) - edges.sort(key=lambda x: x[0]) - - original_edges = edges - split_edges = [split_map_edge(edge, n_col) for edge in edges] - edges = split_edges - n_col = 2 * (n_col - 1) - - # calculate number of layers - n_layer = 0 - for c in range(n_col): - cnt = 0 - for edge in edges: - if c >= edge[0] and c <= edge[1]: - cnt += 1 - n_layer = max(n_layer, cnt) - - layer = [-1 for _ in edges] - for i, edge in enumerate(edges): - used = [] - for j in range(i): - if edges[j][1] >= edge[0]: - used.append(layer[j]) - for l in range(n_layer): - if l not in used: - layer[i] = l - break - - # for l in range(n_layer): - # info = f"layer {l}:" - # for i, edge in enumerate(edges): - # if layer[i] == l: - # info += f" {edge}" - # print(info) - - # for l in range(n_layer): - # info = f"layer {l}:" - # for i, edge in enumerate(original_edges): - # if layer[i] == l: - # info += f" {edge}" - # print(info) - - return 2 * n_layer - - -if __name__ == "__main__": - n_q = int(sys.argv[1]) - layout = sys.argv[2] - wdir = sys.argv[3] - graph_lib = sys.argv[4] - - # read the edges from the graph library - with open(graph_lib, "r") as f: - graphs = json.load(f) - if str(n_q) not in graphs: # all n_q should be even - raise ValueError("n_q not found in graph library!") - with open(wdir + "baseline_stats", "w") as f: - f.write("n_q, ratio, s, n_layer\n") - - for r in range(1, 5): - for s in range(len(graphs[str(n_q)][r])): - edges = graphs[str(n_q)][r][s] - with open(wdir + "baseline_stats", "a") as f: - f.write( - f"{n_q}, {(r+1)/10}, {s}, {2*depth_baseline(edges, n_q, layout)}\n" - ) diff --git a/glue/lattice_surgery/paper/rand_graph_olsco_hier.py b/glue/lattice_surgery/paper/rand_graph_olsco_hier.py deleted file mode 100644 index efa74a489..000000000 --- a/glue/lattice_surgery/paper/rand_graph_olsco_hier.py +++ /dev/null @@ -1,193 +0,0 @@ -import json -import math -import subprocess -import sys -from olsco_compiler import OLSCo -from rand_graph.rand_graph_baseline_opt import depth_baseline - - -def solve_sub( - edges, ratioX10_1, seed, layout, wdir, starting_depth, if_print, note, n_q=8 -): - # dimensions depending on the qubit layout - if layout == "1row": - data = { - "max_i": n_q, - "max_j": 2, - } - elif layout == "2rows": - data = { - "max_i": n_q // 2, - "max_j": 3, - } - else: - raise ValueError("layout not supported! ") - - # should not be too low, avoids being trivially proved UNSAT by Z3 - depth = starting_depth - - checked_depth = {} - while True: - data["max_k"] = depth - - # get the outgoing ports - if layout == "1row": - data["ports"] = [ - { - "location": [i, 0, 0], - "direction": "+K", - "z_basis_direction": "I", - } - for i in range(n_q) - ] + [ - { - "location": [i, 0, depth], - "direction": "-K", - "z_basis_direction": "I", - } - for i in range(n_q) - ] - elif layout == "2rows": - data["ports"] = [ - { - "location": [i, 0, depth], - "direction": "-K", - "z_basis_direction": "I", - } - for i in range(n_q // 2) - ] + [ - { - "location": [i - (n_q // 2), 2, depth], - "direction": "-K", - "z_basis_direction": "I", - } - for i in range(n_q // 2, n_q) - ] - - # stabilizers are X on qubit and Z on all its neighbors - data["stabilizers"] = [ - ("." * i + "Z" + "." * (n_q - i - 1)) * 2 for i in range(n_q) - ] - for i in range(n_q): - stab = ("." * i + "X" + "." * (n_q - i - 1)) * 2 - for edge in edges: - if edge[0] == i: - stab = stab[: n_q + edge[1]] + "Z" + stab[n_q + edge[1] + 1 :] - if edge[1] == i: - stab = stab[: n_q + edge[0]] + "Z" + stab[n_q + edge[0] + 1 :] - data["stabilizers"].append(stab) - - olsco = OLSCo(data, cnf=True, color_ij=True) - olsco.write_cnf(f"{wdir}graph_n{n_q}_r{ratioX10_1}_s{seed}{note}.dimacs") - - subprocess.run( - f"kissat {wdir}graph_n{n_q}_r{ratioX10_1}_s{seed}{note}.dimacs" - + ( - f" | tee {wdir}graph_n{n_q}_r{ratioX10_1}_s{seed}{note}.sat" - if if_print - else f" > {wdir}graph_n{n_q}_r{ratioX10_1}_s{seed}{note}.sat" - ), - capture_output=False, - check=False, - shell=True, - ) - - with open(f"{wdir}graph_n{n_q}_r{ratioX10_1}_s{seed}{note}.sat", "r") as f: - sat_output = f.readlines() - - if "exit 10" in sat_output[-1]: # found SAT - checked_depth[str(depth)] = "SAT" - with open( - f"{wdir}graph_n{n_q}_r{ratioX10_1}_s{seed}{note}.json", "w" - ) as f: - json.dump(data, f) - if str(depth - 1) in checked_depth or depth <= 2: - break - else: - depth -= 1 - else: - checked_depth[str(depth)] = "UNSAT" - if str(depth + 1) in checked_depth: - break - else: - depth += 1 - - with open(f"{wdir}graph_n{n_q}_r{ratioX10_1}_s{seed}{note}.json", "r") as f: - opt_data = json.load(f) - - return opt_data["max_k"] - - -if __name__ == "__main__": - n_q = int(sys.argv[1]) - ratioX10_1 = int(sys.argv[2]) - seed = int(sys.argv[3]) - layout = sys.argv[4] - wdir = sys.argv[5] - graph_lib = sys.argv[6] - starting_depth = int(sys.argv[7]) - if_print = int(sys.argv[8]) - - max_q = 8 - - # read the edges from the graph library - with open(graph_lib, "r") as f: - graphs = json.load(f) - if str(n_q) not in graphs: # all n_q should be even - raise ValueError("n_q not found in graph library!") - if ratioX10_1 not in range(10): - raise ValueError("invalid ratio x 10 - 1!") - ratio = (1 + ratioX10_1) / 10 - if seed not in range(10): - raise ValueError("invalid random seed!") - edges = graphs[str(n_q)][ratioX10_1][seed] - - total_cycle = 0 - n_stretch = int(math.log(n_q // max_q, 2)) + 1 - for t in range(n_stretch): - for l in range(2**t): - n_partition = n_q // (max_q * (2**t)) - max_cycle = 0 - for p in range(n_partition): - if not edges: - continue - subset = [] - others = [] - i_start = max_q * (2**t) * p + l - i_end = i_start + (2**t) * max_q - for edge in edges: - if (edge[0] in range(i_start, i_end, 2**t)) and ( - edge[1] in range(i_start, i_end, 2**t) - ): - subset.append([ - (edge[0] - i_start) // (2**t), - (edge[1] - i_start) // (2**t), - ]) - else: - others.append(edge) - edges = others - - max_cycle = max( - max_cycle, - solve_sub( - subset, - ratioX10_1, - seed, - layout, - wdir, - starting_depth, - if_print, - f"_t{t}_l{l}_p{p}", - n_q=max_q, - ), - ) - - total_cycle += max_cycle - - if edges: - total_cycle += depth_baseline(edges, n_q, layout) - - by_gate_d = depth_baseline(graphs[str(n_q)][ratioX10_1][seed], n_q, layout) - # print(f"baseline:{by_gate_d} vs partially-compiled:{total_cycle-1}") - with open(wdir + "hybrid_stats", "a") as f: - f.write(f"{n_q}, {ratio}, {seed}, {total_cycle}\n") diff --git a/glue/lattice_surgery/setup.py b/glue/lattice_surgery/setup.py index 447af34b2..008b51bb0 100644 --- a/glue/lattice_surgery/setup.py +++ b/glue/lattice_surgery/setup.py @@ -1,19 +1,19 @@ from setuptools import find_packages, setup with open('README.md', encoding='UTF-8') as f: - long_description = f.read() + long_description = f.read() __version__ = '0.1.0' setup( - name='olssco', + name='LaSsynth', version=__version__, - author='Daniel Bochen Tan', - author_email='tbcdebug@outlook.com', - url='https://github.com/quantumlib/stim/', + author='', + author_email='', + url='', license='Apache 2', packages=find_packages(), - description='A Compiler for Lattice Surgery Subroutines', + description='Lattice Surgery Subroutine Synthesizer', long_description=long_description, long_description_content_type='text/markdown', python_requires='>=3.6.0', @@ -22,6 +22,7 @@ 'z3-solver==4.12.1.0', 'stim', 'networkx', + 'ipykernel', ], tests_require=['pytest', 'python3-distutils'], )