bachelor_thesis/computations/C_L_elements_and_products.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Computing the Elements of the Local Clifford Group\n",
    "\n",
    "Known is that $H = \\frac{1}{\\sqrt{2}}\\left(\\begin{array}{cc} 1 & 1 \\\\ 1 & -1\\end{array}\\right) $ and $S = \\left(\\begin{array}{cc} 1 & 0 \\\\ 0 & i\\end{array}\\right)$ generate the local clifford group $C_L$. Also  it has been discussed before that $|C_L| = 24$.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy\n",
    "\n",
    "M = sympy.Matrix\n",
    "simplify = sympy.simplify\n",
    "sqrt = sympy.sqrt\n",
    "i = sympy.I\n",
    "\n",
    "from sympy.physics.quantum import Dagger\n",
    "\n",
    "sympy.init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "H = simplify(M([[1, 1], [1, -1]]) / sqrt(2))\n",
    "S = M([[1, 0], [0, i]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "C_L = [H, S]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As discussed before one can disregard an overall phase, so when checking whether the matrix is known one has to take this invariance into account.\n",
    "\n",
    "Also note that $C_L$ is a subgroup of $SU(2)$, so the inverse of an $a \\in C_L$ is $a^\\dagger$. Further $a$ has the structure $ a \\equiv \\left(\\begin{array}{cc}z_1 & z_2 \\\\ -z_2^* & z_1^* \\end{array}\\right)$ with the constraint $|z_1|^2 + |z_2|^2 = 1$.\n",
    "\n",
    "This yields $\\forall a,b \\in C_L$: $a = b$ disregarding a global phase $\\Leftrightarrow ba^\\dagger = \\exp(i\\phi)\\mathbb{1}$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "basis_vectors = [M([1, 0]), M([0, 1])]\n",
    "\n",
    "def getitem(m, i, j):\n",
    "    # Note that sympy uses an extremely weird way to store the matrices,\n",
    "    # in particular the internal representation is vastly different from what\n",
    "    # is printed. For instance the H matrix is stored as a Mul object\n",
    "    # (even after using simplify) instead of a matrix. \n",
    "    # Therefore m[i][j] will NOT work. This is a workaround.\n",
    "    return (Dagger(basis_vectors[i]) * m * basis_vectors[j])[0]\n",
    "\n",
    "def is_known(C_L, a):\n",
    "    for c in C_L:\n",
    "        test = c * Dagger(a)\n",
    "        if(simplify(getitem(test, 0, 1)) != 0):\n",
    "            continue\n",
    "        if(simplify(getitem(test, 0, 0) / getitem(test, 1, 1)) == 1):\n",
    "            return True\n",
    "    return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix([[1, 0], [0, 1]])\n",
      "got 3 matrices\n",
      "Matrix([[sqrt(2)/2, sqrt(2)/2], [sqrt(2)*I/2, -sqrt(2)*I/2]])\n",
      "got 4 matrices\n",
      "Matrix([[sqrt(2)/2, sqrt(2)*I/2], [sqrt(2)/2, -sqrt(2)*I/2]])\n",
      "got 5 matrices\n",
      "Matrix([[1, 0], [0, -1]])\n",
      "got 6 matrices\n",
      "Matrix([[sqrt(2)/2, sqrt(2)*I/2], [sqrt(2)*I/2, sqrt(2)/2]])\n",
      "got 7 matrices\n",
      "Matrix([[sqrt(2)/2, -sqrt(2)/2], [sqrt(2)/2, sqrt(2)/2]])\n",
      "got 8 matrices\n",
      "Matrix([[1, 0], [0, -I]])\n",
      "got 9 matrices\n",
      "Matrix([[sqrt(2)/2, -sqrt(2)/2], [sqrt(2)*I/2, sqrt(2)*I/2]])\n",
      "got 10 matrices\n",
      "Matrix([[sqrt(2)/2, -sqrt(2)*I/2], [sqrt(2)/2, sqrt(2)*I/2]])\n",
      "got 11 matrices\n",
      "Matrix([[sqrt(2)/2, -sqrt(2)*I/2], [sqrt(2)*I/2, -sqrt(2)/2]])\n",
      "got 12 matrices\n",
      "After interation 0 there are 12 known matrices\n",
      "Matrix([[1/2 + I/2, 1/2 - I/2], [1/2 - I/2, 1/2 + I/2]])\n",
      "got 13 matrices\n",
      "Matrix([[sqrt(2)/2, sqrt(2)/2], [-sqrt(2)/2, sqrt(2)/2]])\n",
      "got 14 matrices\n",
      "Matrix([[0, 1], [1, 0]])\n",
      "got 15 matrices\n",
      "Matrix([[sqrt(2)/2, sqrt(2)/2], [-sqrt(2)*I/2, sqrt(2)*I/2]])\n",
      "got 16 matrices\n",
      "Matrix([[0, 1], [I, 0]])\n",
      "got 17 matrices\n",
      "Matrix([[1/2 - I/2, 1/2 + I/2], [-1/2 + I/2, 1/2 + I/2]])\n",
      "got 18 matrices\n",
      "Matrix([[0, I], [1, 0]])\n",
      "got 19 matrices\n",
      "Matrix([[sqrt(2)/2, sqrt(2)*I/2], [-sqrt(2)*I/2, -sqrt(2)/2]])\n",
      "got 20 matrices\n",
      "Matrix([[1/2 - I/2, -1/2 + I/2], [-1/2 + I/2, -1/2 + I/2]])\n",
      "got 21 matrices\n",
      "Matrix([[0, -1], [1, 0]])\n",
      "got 22 matrices\n",
      "Matrix([[sqrt(2)/2, -sqrt(2)/2], [-sqrt(2)*I/2, -sqrt(2)*I/2]])\n",
      "got 23 matrices\n",
      "Matrix([[1/2 - I/2, I*(-1 + I)/2], [-1/2 + I/2, I*(-1 + I)/2]])\n",
      "got 24 matrices\n",
      "After interation 1 there are 24 known matrices\n",
      "After interation 2 there are 24 known matrices\n",
      "After interation 3 there are 24 known matrices\n",
      "After interation 4 there are 24 known matrices\n"
     ]
    }
   ],
   "source": [
    "for i in range(5):\n",
    "    for m in (H, S):\n",
    "        for c in C_L:\n",
    "            c = simplify(c*m)\n",
    "            if(is_known(C_L, c)):\n",
    "                continue\n",
    "            print(c)\n",
    "            C_L.append(c)\n",
    "            print(\"got\", len(C_L), \"matrices\")\n",
    "    print(\"After interation\", i, \"there are\", len(C_L), \"known matrices\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/latex": [
       "$\\displaystyle \\left[ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}1 & 0\\\\0 & i\\end{matrix}\\right], \\  \\left[\\begin{matrix}1 & 0\\\\0 & 1\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2} i}{2} & - \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}1 & 0\\\\0 & -1\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2} i}{2} & \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}1 & 0\\\\0 & - i\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2} i}{2} & \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2} i}{2} & - \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{1}{2} + \\frac{i}{2} & \\frac{1}{2} - \\frac{i}{2}\\\\\\frac{1}{2} - \\frac{i}{2} & \\frac{1}{2} + \\frac{i}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\- \\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}0 & 1\\\\1 & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\- \\frac{\\sqrt{2} i}{2} & \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}0 & 1\\\\i & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{1}{2} - \\frac{i}{2} & \\frac{1}{2} + \\frac{i}{2}\\\\- \\frac{1}{2} + \\frac{i}{2} & \\frac{1}{2} + \\frac{i}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}0 & i\\\\1 & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\\\- \\frac{\\sqrt{2} i}{2} & - \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{1}{2} - \\frac{i}{2} & - \\frac{1}{2} + \\frac{i}{2}\\\\- \\frac{1}{2} + \\frac{i}{2} & - \\frac{1}{2} + \\frac{i}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}0 & -1\\\\1 & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\\\- \\frac{\\sqrt{2} i}{2} & - \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{1}{2} - \\frac{i}{2} & \\frac{i \\left(-1 + i\\right)}{2}\\\\- \\frac{1}{2} + \\frac{i}{2} & \\frac{i \\left(-1 + i\\right)}{2}\\end{matrix}\\right]\\right]$"
      ],
      "text/plain": [
       "⎡⎡√2   √2 ⎤                  ⎡ √2     √2  ⎤  ⎡√2   √2⋅ⅈ ⎤           ⎡ √2   √2⋅\n",
       "⎢⎢──   ── ⎥                  ⎢ ──     ──  ⎥  ⎢──   ──── ⎥           ⎢ ──   ───\n",
       "⎢⎢2    2  ⎥  ⎡1  0⎤  ⎡1  0⎤  ⎢ 2      2   ⎥  ⎢2     2   ⎥  ⎡1  0 ⎤  ⎢ 2     2 \n",
       "⎢⎢        ⎥, ⎢    ⎥, ⎢    ⎥, ⎢            ⎥, ⎢          ⎥, ⎢     ⎥, ⎢         \n",
       "⎢⎢√2  -√2 ⎥  ⎣0  ⅈ⎦  ⎣0  1⎦  ⎢√2⋅ⅈ  -√2⋅ⅈ ⎥  ⎢√2  -√2⋅ⅈ ⎥  ⎣0  -1⎦  ⎢√2⋅ⅈ   √2\n",
       "⎢⎢──  ────⎥                  ⎢────  ──────⎥  ⎢──  ──────⎥           ⎢────   ──\n",
       "⎣⎣2    2  ⎦                  ⎣ 2      2   ⎦  ⎣2     2   ⎦           ⎣ 2     2 \n",
       "\n",
       "ⅈ⎤  ⎡√2  -√2 ⎤           ⎡ √2   -√2 ⎤  ⎡√2  -√2⋅ⅈ ⎤  ⎡ √2   -√2⋅ⅈ ⎤  ⎡1   ⅈ  1\n",
       "─⎥  ⎢──  ────⎥           ⎢ ──   ────⎥  ⎢──  ──────⎥  ⎢ ──   ──────⎥  ⎢─ + ─  ─\n",
       " ⎥  ⎢2    2  ⎥  ⎡1  0 ⎤  ⎢ 2     2  ⎥  ⎢2     2   ⎥  ⎢ 2      2   ⎥  ⎢2   2  2\n",
       " ⎥, ⎢        ⎥, ⎢     ⎥, ⎢          ⎥, ⎢          ⎥, ⎢            ⎥, ⎢        \n",
       " ⎥  ⎢√2   √2 ⎥  ⎣0  -ⅈ⎦  ⎢√2⋅ⅈ  √2⋅ⅈ⎥  ⎢√2   √2⋅ⅈ ⎥  ⎢√2⋅ⅈ   -√2  ⎥  ⎢1   ⅈ  1\n",
       " ⎥  ⎢──   ── ⎥           ⎢────  ────⎥  ⎢──   ──── ⎥  ⎢────   ──── ⎥  ⎢─ - ─  ─\n",
       " ⎦  ⎣2    2  ⎦           ⎣ 2     2  ⎦  ⎣2     2   ⎦  ⎣ 2      2   ⎦  ⎣2   2  2\n",
       "\n",
       "   ⅈ⎤  ⎡ √2   √2⎤          ⎡  √2     √2 ⎤          ⎡ 1   ⅈ   1   ⅈ⎤          ⎡\n",
       " - ─⎥  ⎢ ──   ──⎥          ⎢  ──     ── ⎥          ⎢ ─ - ─   ─ + ─⎥          ⎢\n",
       "   2⎥  ⎢ 2    2 ⎥  ⎡0  1⎤  ⎢  2      2  ⎥  ⎡0  1⎤  ⎢ 2   2   2   2⎥  ⎡0  ⅈ⎤  ⎢\n",
       "    ⎥, ⎢        ⎥, ⎢    ⎥, ⎢            ⎥, ⎢    ⎥, ⎢              ⎥, ⎢    ⎥, ⎢\n",
       "   ⅈ⎥  ⎢-√2   √2⎥  ⎣1  0⎦  ⎢-√2⋅ⅈ   √2⋅ⅈ⎥  ⎣ⅈ  0⎦  ⎢  1   ⅈ  1   ⅈ⎥  ⎣1  0⎦  ⎢\n",
       " + ─⎥  ⎢────  ──⎥          ⎢──────  ────⎥          ⎢- ─ + ─  ─ + ─⎥          ⎢\n",
       "   2⎦  ⎣ 2    2 ⎦          ⎣  2      2  ⎦          ⎣  2   2  2   2⎦          ⎣\n",
       "\n",
       "  √2    √2⋅ⅈ⎤  ⎡ 1   ⅈ     1   ⅈ⎤           ⎡  √2     -√2  ⎤  ⎡ 1   ⅈ   ⅈ⋅(-1 \n",
       "  ──    ────⎥  ⎢ ─ - ─   - ─ + ─⎥           ⎢  ──     ──── ⎥  ⎢ ─ - ─   ──────\n",
       "  2      2  ⎥  ⎢ 2   2     2   2⎥  ⎡0  -1⎤  ⎢  2       2   ⎥  ⎢ 2   2       2 \n",
       "            ⎥, ⎢                ⎥, ⎢     ⎥, ⎢              ⎥, ⎢               \n",
       "-√2⋅ⅈ   -√2 ⎥  ⎢  1   ⅈ    1   ⅈ⎥  ⎣1  0 ⎦  ⎢-√2⋅ⅈ   -√2⋅ⅈ ⎥  ⎢  1   ⅈ  ⅈ⋅(-1 \n",
       "──────  ────⎥  ⎢- ─ + ─  - ─ + ─⎥           ⎢──────  ──────⎥  ⎢- ─ + ─  ──────\n",
       "  2      2  ⎦  ⎣  2   2    2   2⎦           ⎣  2       2   ⎦  ⎣  2   2      2 \n",
       "\n",
       "+ ⅈ)⎤⎤\n",
       "────⎥⎥\n",
       "    ⎥⎥\n",
       "    ⎥⎥\n",
       "+ ⅈ)⎥⎥\n",
       "────⎥⎥\n",
       "    ⎦⎦"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C_L"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These are the 24 elements of $C_L$. Required to do further computations is the lookup table containing all the \n",
    "products between $C_L$ matrices:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from itertools import product\n",
    "\n",
    "product_table = []\n",
    "row = []\n",
    "\n",
    "for i,p in enumerate(product(C_L, C_L)):\n",
    "    if(i % 24 == 0):\n",
    "        product_table.append(row)\n",
    "        row = []\n",
    "    row.append(p[0] * p[1])\n",
    "product_table.append(row)\n",
    "\n",
    "product_table = product_table[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[ \\left[ 2, \\  4, \\  0, \\  12, \\  1, \\  7, \\  15, \\  5, \\  10, \\  19, \\  8, \\  22, \\  3, \\  14, \\  13, \\  6, \\  23, \\  18, \\  17, \\  9, \\  21, \\  20, \\  11, \\  16\\right], \\  \\left[ 3, \\  5, \\  1, \\  13, \\  6, \\  8, \\  17, \\  9, \\  2, \\  20, \\  11, \\  23, \\  10, \\  15, \\  16, \\  0, \\  21, \\  19, \\  14, \\  4, \\  22, \\  18, \\  7, \\  12\\right], \\  \\left[ 0, \\  1, \\  2, \\  3, \\  4, \\  5, \\  6, \\  7, \\  8, \\  9, \\  10, \\  11, \\  12, \\  13, \\  14, \\  15, \\  16, \\  17, \\  18, \\  19, \\  20, \\  21, \\  22, \\  23\\right], \\  \\left[ 1, \\  6, \\  3, \\  10, \\  5, \\  9, \\  0, \\  8, \\  11, \\  4, \\  2, \\  7, \\  13, \\  16, \\  15, \\  17, \\  12, \\  14, \\  19, \\  20, \\  18, \\  22, \\  23, \\  21\\right], \\  \\left[ 12, \\  7, \\  4, \\  14, \\  15, \\  10, \\  18, \\  19, \\  0, \\  21, \\  22, \\  16, \\  8, \\  6, \\  23, \\  2, \\  20, \\  9, \\  13, \\  1, \\  11, \\  17, \\  5, \\  3\\right], \\  \\left[ 13, \\  8, \\  5, \\  15, \\  17, \\  2, \\  19, \\  20, \\  1, \\  22, \\  23, \\  12, \\  11, \\  0, \\  21, \\  3, \\  18, \\  4, \\  16, \\  6, \\  7, \\  14, \\  9, \\  10\\right], \\  \\left[ 10, \\  9, \\  6, \\  16, \\  0, \\  11, \\  14, \\  4, \\  3, \\  18, \\  7, \\  21, \\  2, \\  17, \\  12, \\  1, \\  22, \\  20, \\  15, \\  5, \\  23, \\  19, \\  8, \\  13\\right], \\  \\left[ 14, \\  10, \\  7, \\  6, \\  18, \\  0, \\  9, \\  21, \\  4, \\  11, \\  16, \\  3, \\  22, \\  2, \\  20, \\  12, \\  17, \\  1, \\  23, \\  15, \\  5, \\  13, \\  19, \\  8\\right], \\  \\left[ 15, \\  2, \\  8, \\  0, \\  19, \\  1, \\  4, \\  22, \\  5, \\  7, \\  12, \\  10, \\  23, \\  3, \\  18, \\  13, \\  14, \\  6, \\  21, \\  17, \\  9, \\  16, \\  20, \\  11\\right], \\  \\left[ 16, \\  11, \\  9, \\  17, \\  14, \\  3, \\  20, \\  18, \\  6, \\  23, \\  21, \\  13, \\  7, \\  1, \\  22, \\  10, \\  19, \\  5, \\  12, \\  0, \\  8, \\  15, \\  4, \\  2\\right], \\  \\left[ 6, \\  0, \\  10, \\  2, \\  9, \\  4, \\  1, \\  11, \\  7, \\  5, \\  3, \\  8, \\  16, \\  12, \\  17, \\  14, \\  13, \\  15, \\  20, \\  18, \\  19, \\  23, \\  21, \\  22\\right], \\  \\left[ 17, \\  3, \\  11, \\  1, \\  20, \\  6, \\  5, \\  23, \\  9, \\  8, \\  13, \\  2, \\  21, \\  10, \\  19, \\  16, \\  15, \\  0, \\  22, \\  14, \\  4, \\  12, \\  18, \\  7\\right], \\  \\left[ 4, \\  15, \\  12, \\  8, \\  7, \\  19, \\  2, \\  10, \\  22, \\  1, \\  0, \\  5, \\  14, \\  23, \\  6, \\  18, \\  3, \\  13, \\  9, \\  21, \\  17, \\  11, \\  16, \\  20\\right], \\  \\left[ 5, \\  17, \\  13, \\  11, \\  8, \\  20, \\  3, \\  2, \\  23, \\  6, \\  1, \\  9, \\  15, \\  21, \\  0, \\  19, \\  10, \\  16, \\  4, \\  22, \\  14, \\  7, \\  12, \\  18\\right], \\  \\left[ 7, \\  18, \\  14, \\  22, \\  10, \\  21, \\  12, \\  0, \\  16, \\  15, \\  4, \\  19, \\  6, \\  20, \\  2, \\  9, \\  8, \\  23, \\  1, \\  11, \\  13, \\  5, \\  3, \\  17\\right], \\  \\left[ 8, \\  19, \\  15, \\  23, \\  2, \\  22, \\  13, \\  1, \\  12, \\  17, \\  5, \\  20, \\  0, \\  18, \\  3, \\  4, \\  11, \\  21, \\  6, \\  7, \\  16, \\  9, \\  10, \\  14\\right], \\  \\left[ 9, \\  14, \\  16, \\  7, \\  11, \\  18, \\  10, \\  3, \\  21, \\  0, \\  6, \\  4, \\  17, \\  22, \\  1, \\  20, \\  2, \\  12, \\  5, \\  23, \\  15, \\  8, \\  13, \\  19\\right], \\  \\left[ 11, \\  20, \\  17, \\  21, \\  3, \\  23, \\  16, \\  6, \\  13, \\  14, \\  9, \\  18, \\  1, \\  19, \\  10, \\  5, \\  7, \\  22, \\  0, \\  8, \\  12, \\  4, \\  2, \\  15\\right], \\  \\left[ 22, \\  21, \\  18, \\  20, \\  12, \\  16, \\  23, \\  15, \\  14, \\  13, \\  19, \\  17, \\  4, \\  9, \\  8, \\  7, \\  5, \\  11, \\  2, \\  10, \\  3, \\  1, \\  0, \\  6\\right], \\  \\left[ 23, \\  22, \\  19, \\  18, \\  13, \\  12, \\  21, \\  17, \\  15, \\  16, \\  20, \\  14, \\  5, \\  4, \\  11, \\  8, \\  9, \\  7, \\  3, \\  2, \\  10, \\  6, \\  1, \\  0\\right], \\  \\left[ 21, \\  23, \\  20, \\  19, \\  16, \\  13, \\  22, \\  14, \\  17, \\  12, \\  18, \\  15, \\  9, \\  5, \\  7, \\  11, \\  4, \\  8, \\  10, \\  3, \\  2, \\  0, \\  6, \\  1\\right], \\  \\left[ 20, \\  16, \\  21, \\  9, \\  23, \\  14, \\  11, \\  13, \\  18, \\  3, \\  17, \\  6, \\  19, \\  7, \\  5, \\  22, \\  1, \\  10, \\  8, \\  12, \\  0, \\  2, \\  15, \\  4\\right], \\  \\left[ 18, \\  12, \\  22, \\  4, \\  21, \\  15, \\  7, \\  16, \\  19, \\  10, \\  14, \\  0, \\  20, \\  8, \\  9, \\  23, \\  6, \\  2, \\  11, \\  13, \\  1, \\  3, \\  17, \\  5\\right], \\  \\left[ 19, \\  13, \\  23, \\  5, \\  22, \\  17, \\  8, \\  12, \\  20, \\  2, \\  15, \\  1, \\  18, \\  11, \\  4, \\  21, \\  0, \\  3, \\  7, \\  16, \\  6, \\  10, \\  14, \\  9\\right]\\right]$"
      ],
      "text/plain": [
       "[[2, 4, 0, 12, 1, 7, 15, 5, 10, 19, 8, 22, 3, 14, 13, 6, 23, 18, 17, 9, 21, 20\n",
       ", 11, 16], [3, 5, 1, 13, 6, 8, 17, 9, 2, 20, 11, 23, 10, 15, 16, 0, 21, 19, 14\n",
       ", 4, 22, 18, 7, 12], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16\n",
       ", 17, 18, 19, 20, 21, 22, 23], [1, 6, 3, 10, 5, 9, 0, 8, 11, 4, 2, 7, 13, 16, \n",
       "15, 17, 12, 14, 19, 20, 18, 22, 23, 21], [12, 7, 4, 14, 15, 10, 18, 19, 0, 21,\n",
       " 22, 16, 8, 6, 23, 2, 20, 9, 13, 1, 11, 17, 5, 3], [13, 8, 5, 15, 17, 2, 19, 2\n",
       "0, 1, 22, 23, 12, 11, 0, 21, 3, 18, 4, 16, 6, 7, 14, 9, 10], [10, 9, 6, 16, 0,\n",
       " 11, 14, 4, 3, 18, 7, 21, 2, 17, 12, 1, 22, 20, 15, 5, 23, 19, 8, 13], [14, 10\n",
       ", 7, 6, 18, 0, 9, 21, 4, 11, 16, 3, 22, 2, 20, 12, 17, 1, 23, 15, 5, 13, 19, 8\n",
       "], [15, 2, 8, 0, 19, 1, 4, 22, 5, 7, 12, 10, 23, 3, 18, 13, 14, 6, 21, 17, 9, \n",
       "16, 20, 11], [16, 11, 9, 17, 14, 3, 20, 18, 6, 23, 21, 13, 7, 1, 22, 10, 19, 5\n",
       ", 12, 0, 8, 15, 4, 2], [6, 0, 10, 2, 9, 4, 1, 11, 7, 5, 3, 8, 16, 12, 17, 14, \n",
       "13, 15, 20, 18, 19, 23, 21, 22], [17, 3, 11, 1, 20, 6, 5, 23, 9, 8, 13, 2, 21,\n",
       " 10, 19, 16, 15, 0, 22, 14, 4, 12, 18, 7], [4, 15, 12, 8, 7, 19, 2, 10, 22, 1,\n",
       " 0, 5, 14, 23, 6, 18, 3, 13, 9, 21, 17, 11, 16, 20], [5, 17, 13, 11, 8, 20, 3,\n",
       " 2, 23, 6, 1, 9, 15, 21, 0, 19, 10, 16, 4, 22, 14, 7, 12, 18], [7, 18, 14, 22,\n",
       " 10, 21, 12, 0, 16, 15, 4, 19, 6, 20, 2, 9, 8, 23, 1, 11, 13, 5, 3, 17], [8, 1\n",
       "9, 15, 23, 2, 22, 13, 1, 12, 17, 5, 20, 0, 18, 3, 4, 11, 21, 6, 7, 16, 9, 10, \n",
       "14], [9, 14, 16, 7, 11, 18, 10, 3, 21, 0, 6, 4, 17, 22, 1, 20, 2, 12, 5, 23, 1\n",
       "5, 8, 13, 19], [11, 20, 17, 21, 3, 23, 16, 6, 13, 14, 9, 18, 1, 19, 10, 5, 7, \n",
       "22, 0, 8, 12, 4, 2, 15], [22, 21, 18, 20, 12, 16, 23, 15, 14, 13, 19, 17, 4, 9\n",
       ", 8, 7, 5, 11, 2, 10, 3, 1, 0, 6], [23, 22, 19, 18, 13, 12, 21, 17, 15, 16, 20\n",
       ", 14, 5, 4, 11, 8, 9, 7, 3, 2, 10, 6, 1, 0], [21, 23, 20, 19, 16, 13, 22, 14, \n",
       "17, 12, 18, 15, 9, 5, 7, 11, 4, 8, 10, 3, 2, 0, 6, 1], [20, 16, 21, 9, 23, 14,\n",
       " 11, 13, 18, 3, 17, 6, 19, 7, 5, 22, 1, 10, 8, 12, 0, 2, 15, 4], [18, 12, 22, \n",
       "4, 21, 15, 7, 16, 19, 10, 14, 0, 20, 8, 9, 23, 6, 2, 11, 13, 1, 3, 17, 5], [19\n",
       ", 13, 23, 5, 22, 17, 8, 12, 20, 2, 15, 1, 18, 11, 4, 21, 0, 3, 7, 16, 6, 10, 1\n",
       "4, 9]]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def get_matrix_index(C_L, a):\n",
    "    for i,c in enumerate(C_L):\n",
    "        test = c * Dagger(a)\n",
    "        if(simplify(getitem(test, 0, 1)) != 0):\n",
    "            continue\n",
    "        if(simplify(getitem(test, 0, 0) / getitem(test, 1, 1)) == 1):\n",
    "            return i\n",
    "    return None\n",
    "\n",
    "product_table_indices = [[get_matrix_index(C_L, m) for m in row] for row in product_table]\n",
    "product_table_indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 24$"
      ],
      "text/plain": [
       "24"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(product_table_indices)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Also necessary to convert a graph state into a naive state are the numpy array versions of $C_L$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([[ 0.70710678+0.j,  0.70710678+0.j],\n",
       "        [ 0.70710678+0.j, -0.70710678+0.j]]), array([[1.+0.j, 0.+0.j],\n",
       "        [0.+0.j, 0.+1.j]]), array([[1.+0.j, 0.+0.j],\n",
       "        [0.+0.j, 1.+0.j]]), array([[0.70710678+0.j        , 0.70710678+0.j        ],\n",
       "        [0.        +0.70710678j, 0.        -0.70710678j]]), array([[0.70710678+0.j        , 0.        +0.70710678j],\n",
       "        [0.70710678+0.j        , 0.        -0.70710678j]]), array([[ 1.+0.j,  0.+0.j],\n",
       "        [ 0.+0.j, -1.+0.j]]), array([[0.70710678+0.j        , 0.        +0.70710678j],\n",
       "        [0.        +0.70710678j, 0.70710678+0.j        ]]), array([[ 0.70710678+0.j, -0.70710678+0.j],\n",
       "        [ 0.70710678+0.j,  0.70710678+0.j]]), array([[1.+0.j, 0.+0.j],\n",
       "        [0.+0.j, 0.-1.j]]), array([[ 0.70710678+0.j        , -0.70710678+0.j        ],\n",
       "        [ 0.        +0.70710678j,  0.        +0.70710678j]]), array([[0.70710678+0.j        , 0.        -0.70710678j],\n",
       "        [0.70710678+0.j        , 0.        +0.70710678j]]), array([[ 0.70710678+0.j        ,  0.        -0.70710678j],\n",
       "        [ 0.        +0.70710678j, -0.70710678+0.j        ]]), array([[0.5+0.5j, 0.5-0.5j],\n",
       "        [0.5-0.5j, 0.5+0.5j]]), array([[ 0.70710678+0.j,  0.70710678+0.j],\n",
       "        [-0.70710678+0.j,  0.70710678+0.j]]), array([[0.+0.j, 1.+0.j],\n",
       "        [1.+0.j, 0.+0.j]]), array([[0.70710678+0.j        , 0.70710678+0.j        ],\n",
       "        [0.        -0.70710678j, 0.        +0.70710678j]]), array([[0.+0.j, 1.+0.j],\n",
       "        [0.+1.j, 0.+0.j]]), array([[ 0.5-0.5j,  0.5+0.5j],\n",
       "        [-0.5+0.5j,  0.5+0.5j]]), array([[0.+0.j, 0.+1.j],\n",
       "        [1.+0.j, 0.+0.j]]), array([[ 0.70710678+0.j        ,  0.        +0.70710678j],\n",
       "        [ 0.        -0.70710678j, -0.70710678+0.j        ]]), array([[ 0.5-0.5j, -0.5+0.5j],\n",
       "        [-0.5+0.5j, -0.5+0.5j]]), array([[ 0.+0.j, -1.+0.j],\n",
       "        [ 1.+0.j,  0.+0.j]]), array([[ 0.70710678+0.j        , -0.70710678+0.j        ],\n",
       "        [ 0.        -0.70710678j,  0.        -0.70710678j]]), array([[ 0.5-0.5j, -0.5-0.5j],\n",
       "        [-0.5+0.5j, -0.5-0.5j]])]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[np.array(c.tolist()).astype(np.cdouble) for c in C_L]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEYAAAAzCAYAAAAqwX72AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAC50lEQVRoBe2bi00jMRCGs4gCEHQQOuBRwYUOgA6AEhAVIOiAuwpOdx0EKkDQAXQAooPw/+CRlsVje3czUmxsydmsH+OZb8deO6M0k8lkA/lbWiwWb98KCyxomsZrP019Ql508g3ATH5Cht3zju1kMV/DB9MBIDStfPZZXP4nbP5iOyz+sF3AlE+gp4XrKe0xD69cuxdct5GvQPo5pe8qtIH+O9DjH/Iu9E5aO6NgIPQBAi8h8D+NdIvVA650wZWF4/T8A5VfkfeQp8jJKTiVIPwUkjYECqU64oR0w/tVTdQT+QiZa8bfvnoGwUDYEfKjR+g9ymbuqXiq8y+KgZnBRLpiN8k8ZX2RSQWT6A2bRVKBUSoY1InR4h1tBuJF6q6x3TjH7yEwKfZspTTKsU3odS1e4bNLvIn7GpPkpvIdhPfxSr6FfC+L3jqqYPi6g3IU6FNMysz2MRwfY+/2tmhJHWJT6RbjTD1jicewvsgUA8NtNHeN3cQn+eieareuiPsgGBj+G1a+YkodirVu7h/j/kTKSryqa0zLWHrHBYDIlNrH/S9AW8oi1xpn6V+hMz2e66F4Pc941Pse+l+HBoyCcdPlPCRkVeugO480g1JwKg2SWEinCkZ5kBVMBaMQUIqrx1QwCgGluHpMBaMQUIqrx1QwCgGlOHokkH44Y+zge6+glfS1vEIvk2BgEAwG5QFscNDKEghlQz+zYGBwjeEBkgcx5EFBK0swgGIaDAyCsTRsCbJNg4E5g5kBru8He/5WzMT6wSlLMG7tixktv0vH2nnrswQDS8Ro8Y62ceJFfHEMTrmCSTF4VDAwVzDiFT5A4k2jgoFZguE2whHxTRcpGxUMzBKMg2IaDMwZjGkwMFswmE6mwcDgWYkuiz3D4KCVc3nLi1kwMAqGZyVLy8bIdouwSTAw26k0BmhK3wpGoVTBVDAKAaW4eowCRt5K0+5RvrXtVrqWUdy1G1bJkaL+kQswun9km78DNA5P/ouKOwEAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & -1\\\\1 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡0  -1⎤\n",
       "⎢     ⎥\n",
       "⎣1  0 ⎦"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = M([[0, 1], [1, 0]])\n",
    "Z = M([[1, 0], [0, -1]])\n",
    "XZ = X*Z\n",
    "XZ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABIAAAAOCAYAAAAi2ky3AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABD0lEQVQoFZWTgW3CMBBFCWKAiBFggwIbMEJZod0AZoANYAVGIBtUZQMYoXSD8F6KUYIdQk/68vnf+Z99tntlWfawEdje8M14AG/GUjAGTiAPcfxKZB8IR2wNdOaBx8/BHljQYsYbQgbvRG3hBf4S5vURfgkaQn2IuQuyLLNi3QomObzH7jSFXHCm4m9L9mOBZNoAgUUy8tdQm31siTdodxQZx/FWPNIqCrYQSSFyvYAdu9m0rIvoSIjdeL0FIp9R9hOiIYTIh7n/FXHNXQiRd+bjugjcSJjYZZUQyTZ3hshjcxX/6RIxPrhVtLkFvv0JNsTxv73U8Ixk/407StkRoUkIUKj6TsynwId6Br6zrytJ1JPO4orZMQAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle 21$"
      ],
      "text/plain": [
       "21"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_matrix_index(C_L, XZ)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 20$"
      ],
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_matrix_index(C_L, H * Z * X)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
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