Implement decomposition for BitonicSort (#1089)

* decomposition for `GreaterThan`

* sorting: implement comparator

* implement bitonic sort

* add classical simulation tests, fix bugs

* more random tests and bug fixes

* fix mypy

* fix serialization bug

* add all perm 4! test

* more assertions

* use `bitsize` instead of `L`

* link issue in TODOs

* add to resolverdict

* add tests for `ParallelComparators`, more docstring

* more docstring

* more docstrings and tests for merge

* add BloqDocSpec for `BitonicMerge` and `ParallelComparators`

* add ancilla cost to docstring

* allow decomposing when `bitsize` is symbolic

* update docstrings, fix latex

* cleanup

* docstring: explain compare ancilla

dev_tools/autogenerate-bloqs-notebooks-v2.py

@@ -360,6 +360,8 @@
         module=qualtran.bloqs.arithmetic.sorting,
         bloq_specs=[
             qualtran.bloqs.arithmetic.sorting._COMPARATOR_DOC,
+            qualtran.bloqs.arithmetic.sorting._PARALLEL_COMPARATORS_DOC,
+            qualtran.bloqs.arithmetic.sorting._BITONIC_MERGE_DOC,
             qualtran.bloqs.arithmetic.sorting._BITONIC_SORT_DOC,
         ],
         directory=f'{SOURCE_DIR}/bloqs/arithmetic/',

qualtran/bloqs/arithmetic/comparison.py

@@ -45,9 +45,9 @@
     Register,
     Side,
     Signature,
+    Soquet,
     SoquetT,
 )
-from qualtran._infra.quantum_graph import Soquet
 from qualtran.bloqs.basic_gates import CNOT, TGate, XGate
 from qualtran.bloqs.mcmt.and_bloq import And, MultiAnd
 from qualtran.bloqs.mcmt.multi_control_multi_target_pauli import MultiControlX
@@ -671,8 +671,17 @@ def wire_symbol(self, reg: Optional[Register], idx: Tuple[int, ...] = tuple()) -
             return TextBox("⨁(a > b)")
         raise ValueError(f'Unknown register name {reg.name}')
 
+    def build_composite_bloq(
+        self, bb: 'BloqBuilder', a: 'Soquet', b: 'Soquet', target: 'Soquet'
+    ) -> Dict[str, 'SoquetT']:
+        a, b, target = bb.add(
+            LessThanEqual(self.a_bitsize, self.b_bitsize), x=a, y=b, target=target
+        )
+        target = bb.add(XGate(), q=target)
+        return {'a': a, 'b': b, 'target': target}
+
     def build_call_graph(self, ssa: 'SympySymbolAllocator') -> Set['BloqCountT']:
-        return {(LessThanEqual(self.a_bitsize, self.b_bitsize), 1)}
+        return {(LessThanEqual(self.a_bitsize, self.b_bitsize), 1), (XGate(), 1)}
 
 
 @bloq_example

qualtran/bloqs/arithmetic/comparison_test.py

@@ -230,7 +230,9 @@ def test_greater_than_manual():
     qlt_testing.assert_wire_symbols_match_expected(
         GreaterThanConstant(bitsize, 17), ['In(x)', '⨁(x > 17)']
     )
-    assert cbloq.t_complexity() == t_complexity(LessThanEqual(bitsize, bitsize))
+    assert cbloq.t_complexity() == (
+        t_complexity(LessThanEqual(bitsize, bitsize)) + TComplexity(clifford=1)
+    )
 
 
 @pytest.mark.parametrize('bitsize', [1, 2, 5])