gauss.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "4f090d84",
   "metadata": {},
   "source": [
    "# Representing Matrices Using Algebraic ZX-calculus\n",
    "\n",
    "Implements automatic ZX diagram synthesis using the work from [arxiv:2110.06898](https://arxiv.org/abs/2110.06898)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3aade8c3",
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "from discopy.quantum.zx import *\n",
    "from discopy import tensor, Tensor, Dim\n",
    "import numpy as np\n",
    "from itertools import chain\n",
    "import tensornetwork as tn\n",
    "from math import log2\n",
    "\n",
    "import sys\n",
    "import numpy\n",
    "numpy.set_printoptions(threshold=sys.maxsize)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b0ebb029",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Some helper functions on bits.\n",
    "\"\"\"\n",
    "\n",
    "def bitstring(x):\n",
    "    return [int(b) for b in \"{0:b}\".format(x)]\n",
    "\n",
    "def bitstring2(n, x):\n",
    "    arr = [int(b) for b in '0' * n + \"{0:b}\".format(x)]\n",
    "    return arr[-n:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d9707447",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Define the generators used in Algebraic ZX calculus.\n",
    "\"\"\"\n",
    "\n",
    "class Z(Spider):\n",
    "    \"\"\" Z spider. \"\"\"\n",
    "    def __init__(self, n_legs_in, n_legs_out, phase=0):\n",
    "        super().__init__(n_legs_in, n_legs_out, phase, name='Z')\n",
    "        self.color = \"green\"\n",
    "\n",
    "    @property\n",
    "    def array(self):\n",
    "        n, m = len(self.dom), len(self.cod)\n",
    "        array = np.zeros(1 << (n + m), dtype=complex)\n",
    "        array[0] = 1\n",
    "        array[-1] = np.exp(1j * self.phase)\n",
    "        return Tensor(Dim(2) ** n, Dim(2) ** m, array)\n",
    "\n",
    "    \n",
    "class ZBox(Spider):\n",
    "    \"\"\" Green box. \"\"\"\n",
    "    def __init__(self, n_legs_in, n_legs_out, phase=0):\n",
    "        super().__init__(n_legs_in, n_legs_out, phase, name='ZBox')\n",
    "        self.color = \"green\"\n",
    "        self.shape = 'rectangle'\n",
    "\n",
    "    @property\n",
    "    def array(self):\n",
    "        n, m = len(self.dom), len(self.cod)\n",
    "        array = np.zeros(1 << (n + m), dtype=complex)\n",
    "        array[0] = 1\n",
    "        array[-1] = self.phase\n",
    "        return Tensor(Dim(2) ** n, Dim(2) ** m, array)\n",
    "\n",
    "\n",
    "class X(Spider):\n",
    "    \"\"\" X spider. \"\"\"\n",
    "    def __init__(self, n_legs_in, n_legs_out, phase=0):\n",
    "        super().__init__(n_legs_in, n_legs_out, phase, name='X')\n",
    "        self.color = \"red\"\n",
    "\n",
    "    @property\n",
    "    def array(self):\n",
    "        assert self.phase in (0, 0.5)\n",
    "        n, m = len(self.dom), len(self.cod)\n",
    "        array = np.zeros(1 << (n + m), dtype=complex)\n",
    "        bit = 1 if self.phase == 0.5 else 0\n",
    "        for i in range(len(array)):\n",
    "            parity = (bitstring(i).count(1) + bit) % 2\n",
    "            array[i] = 1 - parity\n",
    "        return Tensor(Dim(2) ** n, Dim(2) ** m, array)\n",
    "       \n",
    "\n",
    "class AND(Spider):\n",
    "    \"\"\" AND spider. \"\"\"\n",
    "    def __init__(self, n_legs_in):\n",
    "        super().__init__(n_legs_in, 1, name='AND')\n",
    "        self.draw_as_spider = False\n",
    "        self.drawing_name = 'AND'\n",
    "\n",
    "    @property\n",
    "    def array(self):\n",
    "        n, m = len(self.dom), len(self.cod)\n",
    "        array = np.zeros(1 << (n + m), dtype=complex)\n",
    "        for i in range(0, (1 << (n + m)) - 2, 2):\n",
    "            array[i] = 1\n",
    "        array[-1] = 1\n",
    "        return Tensor(Dim(2) ** n, Dim(2) ** m, array)\n",
    "\n",
    "    def __repr__(self):\n",
    "        return f'{self.name}({self.dom})'\n",
    "\n",
    "\n",
    "class Tri(Spider):\n",
    "    \"\"\" Triangle gate. \"\"\"\n",
    "    def __init__(self):\n",
    "        super().__init__(1, 1, name='T')\n",
    "        self.color = 'yellow'\n",
    "        self.shape = 'triangle_up'\n",
    "\n",
    "    @property\n",
    "    def array(self):\n",
    "        return Tensor(Dim(2), Dim(2), [[1, 0], [1, 1]])\n",
    "\n",
    "    def __repr__(self):\n",
    "        return self.name\n",
    "\n",
    "T = Tri()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "bffef367",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Efficient evaluation of algebraic ZX diagrams\n",
    "using a functor + Google's tensornetwork library.\n",
    "\"\"\"\n",
    "\n",
    "def f_ob(ob):\n",
    "    return Dim(2) ** len(ob)\n",
    "\n",
    "def f_ar(box):\n",
    "    return tensor.Box(box.name, f_ob(box.dom), f_ob(box.cod), box.array)\n",
    "\n",
    "f = Functor(ob=f_ob, ar=f_ar, ar_factory=tensor.Diagram)\n",
    "\n",
    "def eval(diagram):\n",
    "    d = Functor(ob=f_ob, ar=f_ar, ar_factory=tensor.Diagram)(diagram)\n",
    "    t = d.eval(contractor=tn.contractors.auto)\n",
    "    dim = 1 << len(diagram.dom)\n",
    "    return t.array.astype(float).reshape(dim, dim).transpose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1e4ddd39",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "array([[1. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ],\n",
       "       [0. , 0.2, 0. , 0. , 0. , 0. , 0. , 0. ],\n",
       "       [0. , 0. , 1. , 0. , 0. , 0. , 0. , 0. ],\n",
       "       [0. , 0. , 0. , 1. , 0. , 0. , 0. , 0. ],\n",
       "       [0. , 0. , 0. , 0. , 1. , 0. , 0. , 0. ],\n",
       "       [0. , 0. , 0. , 0. , 0. , 1. , 0. , 0. ],\n",
       "       [0. , 0. , 0. , 0. , 0. , 0. , 1. , 0. ],\n",
       "       [0. , 0. , 0. , 0. , 0. , 0. , 0. , 1. ]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Verifying Theorem 3.1. (Row multiplication)\n",
    "\"\"\"\n",
    "\n",
    "def row_mul(n, i, a):\n",
    "    # TODO add boundary checks\n",
    "    bits = bitstring2(n, i)\n",
    "    diagram = Id().tensor(*[Z(1, 2) >> Id(1) @ X(1, 1, (1 ^ b) / 2) for b in bits])\n",
    "    perm = chain(range(0, 2 * n, 2), range(1, 2 * n, 2))\n",
    "    diagram = diagram.permute(*perm)\n",
    "    return diagram >> Id(n) @ (AND(n) >> ZBox(1, 0, a))\n",
    "\n",
    "diagram = row_mul(3, i=1, a=0.2)\n",
    "diagram.draw(figsize=(4, 6), nodesize=5)\n",
    "diagram.draw(figsize=(4, 6), nodesize=5, path='mul.pdf')\n",
    "\n",
    "eval(diagram)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5c294454",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 1., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 1., 0., 0., 0., 0., 0.],\n",
       "       [0., 2., 0., 1., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 1., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 1., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 0., 1., 0.],\n",
       "       [0., 0., 0., 0., 0., 0., 0., 1.]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Verifying Theorem 3.4. (Row addition)\n",
    "\"\"\"\n",
    "\n",
    "def row_add(n, i, j, a):\n",
    "    bits_i = bitstring2(n, i)\n",
    "    bits_j = bitstring2(n, j)\n",
    "    diagram1 = Id().tensor(*[Z(1, 2) >> Id(1) @ X(1, 1, (1 - b) / 2) for b in bits_i])\n",
    "    perm = chain(range(0, 2 * n, 2), range(1, 2 * n, 2))\n",
    "    diagram1 = diagram1.permute(*perm)\n",
    "    \n",
    "    perm = []\n",
    "    app = []\n",
    "    off = 0\n",
    "    diagram2 = Id()\n",
    "    for x in range(n):\n",
    "        perm.append(x+off)\n",
    "        if bits_i[x] ^ bits_j[x]:\n",
    "            app.append(x + off + 1)\n",
    "            off += 1\n",
    "            diagram2 @= X(1, 2)\n",
    "        else:\n",
    "            diagram2 @= Id(1)\n",
    "    perm += app\n",
    "    diagram1 = diagram1 >> Id(n) @ (AND(n) >> T >> ZBox(1, len(app), a))\n",
    "    diagram2 = diagram2.permute(*perm)\n",
    "    return diagram1 >> diagram2.dagger()\n",
    "\n",
    "diagram = row_add(3, i=1, j=3, a=2)\n",
    "diagram.draw(figsize=(4, 7), nodesize=5)\n",
    "diagram.draw(figsize=(4, 7), nodesize=5, path='add.pdf')\n",
    "\n",
    "eval(diagram)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "45b2d525",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 0., 0., 1.],\n",
       "       [0., 0., 1., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 1., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 1., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 1., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 0., 1., 0.],\n",
       "       [0., 1., 0., 0., 0., 0., 0., 0.]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Verifying Theorem 3.7. (Row switching)\n",
    "\"\"\"\n",
    "\n",
    "def row_swap(n, i, j):\n",
    "    bits_i = bitstring2(n, i)\n",
    "    bits_j = bitstring2(n, j)\n",
    "    diagram1 = Id()\n",
    "\n",
    "    mis = []\n",
    "    for x, (b1, b2) in enumerate(zip(bits_i, bits_j)):\n",
    "        if b1 ^ b2:\n",
    "            mis.append(x)\n",
    "\n",
    "    assert mis\n",
    "    diagram0 = Id(n - mis[-1] - 1) @ Z(1, len(mis)) @ Id(mis[-1])\n",
    "    for x, pos in enumerate(mis):\n",
    "        diagram0 = diagram0.permute(mis[-1], *range(pos + x + 1, mis[-1]))\n",
    "    for x, (b1, b2) in enumerate(zip(bits_i, bits_j)):\n",
    "        if b1 ^ b2 and x != mis[-1]:\n",
    "            diagram1 @= Z(1, 2) @ Id(1) >> Id(1) @ X(2, 1, (1 ^ b1 ^ bits_i[mis[-1]]) / 2)\n",
    "        elif x == mis[-1]:\n",
    "            diagram1 @= Id(1) @ X(0, 1, 0.5)\n",
    "        else:\n",
    "            diagram1 @= Z(1, 2) >> Id(1) @ X(1, 1, (1 ^ b1) / 2)\n",
    "    perm = chain(range(0, 2 * n, 2), range(1, 2 * n, 2))\n",
    "    diagram1 = diagram1.permute(*perm)\n",
    "    \n",
    "    perm = []\n",
    "    app = []\n",
    "    off = 0\n",
    "    diagram2 = Id()\n",
    "    for x in range(n):\n",
    "        perm.append(x+off)\n",
    "        if bits_i[x] ^ bits_j[x]:\n",
    "            app.append(x + off + 1)\n",
    "            off += 1\n",
    "            diagram2 @= X(1, 2)\n",
    "        else:\n",
    "            diagram2 @= Id(1)\n",
    "    perm += app\n",
    "    diagram1 = diagram1 >> Id(n) @ (AND(n) >> Z(1, len(app)))\n",
    "    diagram2 = diagram2.permute(*perm)\n",
    "    return diagram0 >> diagram1 >> diagram2.dagger()\n",
    "\n",
    "diagram = row_swap(3, i=1, j=7)\n",
    "diagram.draw(figsize=(4, 7), nodesize=5)\n",
    "diagram.draw(figsize=(4, 7), nodesize=5, path='swap.pdf')\n",
    "\n",
    "\n",
    "eval(diagram)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a79b14a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Swapping row i with j is equal to swapping row j with i\n",
    "\"\"\"\n",
    "row_swap(3, 3, 7) == row_swap(3, 7, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b026a442",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "array([[0., 1.],\n",
       "       [1., 0.]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Swapping 0 with 1 for 1 qubit gives you the NOT gate\n",
    "\"\"\"\n",
    "\n",
    "diagram = row_swap(1, 1, 0)\n",
    "diagram.draw(figsize=(4, 5), nodesize=3)\n",
    "\n",
    "eval(diagram)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "86d4f284",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Gaussian Elimination\n",
    "\"\"\"\n",
    "\n",
    "def gauss(mat):\n",
    "    # TODO for non-invertible\n",
    "    n, m = len(mat), len(mat[0])\n",
    "    if n != m:\n",
    "        raise NotImplementedError\n",
    "    log_n = int(log2(n))\n",
    "    diagram = Id(log_n)\n",
    "    for i in range(n):\n",
    "        j = i\n",
    "        while j < n and mat[j][i] == 0:\n",
    "            j += 1\n",
    "        if j == n:\n",
    "            raise Exception('Not invertible')\n",
    "        # row swap\n",
    "        if i != j:\n",
    "            mat[i], mat[j] = mat[j], mat[i]\n",
    "            diagram <<= row_swap(log_n, i, j)\n",
    "        # row scale\n",
    "        s = mat[i][i]\n",
    "        for j in range(i, n):\n",
    "            mat[i][j] /= s\n",
    "        diagram <<= row_mul(log_n, i, s)\n",
    "        for j in range(i + 1, n):\n",
    "            if mat[j][i] != 0:\n",
    "                s = mat[j][i]\n",
    "                for k in range(i, n):\n",
    "                    mat[j][k] -= s * mat[i][k]\n",
    "                diagram <<= row_add(log_n, i, j, s)\n",
    "    # back sub\n",
    "    for i in range(1, n)[::-1]:\n",
    "        j = i - 1\n",
    "        while j >= 0:\n",
    "            if mat[j][i] != 0:\n",
    "                s = mat[j][i]\n",
    "                for k in range(n):\n",
    "                    mat[j][k] -= s * mat[i][k]\n",
    "                diagram <<= row_add(log_n, i, j, s)\n",
    "            j -= 1\n",
    "    return mat, diagram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "5484d0db",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result:\n",
      "[[0. 2.]\n",
      " [3. 1.]]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "2 x 2 example\n",
    "\"\"\"\n",
    "m, d = gauss([[0, 2], [3, 1]])\n",
    "print('result:')\n",
    "print(eval(d))\n",
    "d.draw(figsize=(4, 6), nodesize=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5b3477d9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result:\n",
      "[[1. 2.]\n",
      " [3. 4.]]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "2 x 2 example\n",
    "\"\"\"\n",
    "\n",
    "m, d = gauss([[1, 2], [3, 4]])\n",
    "print('result:')\n",
    "print(eval(d))\n",
    "d.draw(figsize=(4, 6), nodesize=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "de318e68",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result:\n",
      "[[1. 2. 3. 4.]\n",
      " [2. 2. 4. 4.]\n",
      " [3. 7. 2. 0.]\n",
      " [9. 9. 9. 9.]]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1080x1440 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "4 x 4 example\n",
    "\"\"\"\n",
    "\n",
    "m, d = gauss([[1, 2, 3, 4], [2, 2, 4, 4], [3, 7, 2, 0], [9, 9, 9, 9]])\n",
    "print('result:')\n",
    "print(eval(d))\n",
    "d.draw(figsize=(15, 20), draw_box_labels=False, nodesize=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3487c1c3",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.8.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}