Find R(2) .ipynb

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     "text": [
      "[[ 0.70710678  0.70710678]\n",
      " [ 0.70710678 -0.70710678]]\n",
      "[matrix([[0., 0., 1., 0.],\n",
      "        [0., 0., 0., 1.],\n",
      "        [1., 0., 0., 0.],\n",
      "        [0., 1., 0., 0.]]), matrix([[0., 1., 0., 0.],\n",
      "        [1., 0., 0., 0.],\n",
      "        [0., 0., 0., 1.],\n",
      "        [0., 0., 1., 0.]]), matrix([[ 1.,  0.,  0.,  0.],\n",
      "        [ 0.,  1.,  0.,  0.],\n",
      "        [ 0.,  0., -1., -0.],\n",
      "        [ 0.,  0., -0., -1.]]), matrix([[ 1.,  0.,  0.,  0.],\n",
      "        [ 0., -1.,  0., -0.],\n",
      "        [ 0.,  0.,  1.,  0.],\n",
      "        [ 0., -0.,  0., -1.]]), matrix([[ 0.5,  0.5,  0.5,  0.5],\n",
      "        [ 0.5,  0.5, -0.5, -0.5],\n",
      "        [ 0.5, -0.5,  0.5, -0.5],\n",
      "        [ 0.5, -0.5, -0.5,  0.5]]), matrix([[ 1.,  0.,  0.,  0.],\n",
      "        [ 0., -1.,  0.,  0.],\n",
      "        [ 0.,  0., -1.,  0.],\n",
      "        [ 0.,  0.,  0., -1.]]), matrix([[1, 0, 0, 0],\n",
      "        [0, 1, 0, 0],\n",
      "        [0, 0, 0, 1],\n",
      "        [0, 0, 1, 0]]), matrix([[1, 0, 0, 0],\n",
      "        [0, 0, 0, 1],\n",
      "        [0, 0, 1, 0],\n",
      "        [0, 1, 0, 0]])]\n",
      "made it through loop1\n",
      "['0', '1', '2', '3', '4', '5', '6', '7']\n",
      "9\n",
      "made it through loop2\n",
      "['01', '02', '03', '04', '05', '06', '07', '12', '13', '14', '15', '16', '17', '23', '24', '25', '26', '27', '34', '35', '36', '37', '45', '46', '47', '50', '51', '54', '56', '57', '60', '63', '67', '71', '72', '76']\n",
      "45\n",
      "made it through loop3\n",
      "['012', '013', '014', '015', '023', '024', '025', '026', '027', '034', '036', '037', '045', '046', '047', '051', '054', '056', '057', '063', '067', '072', '076', '123', '124', '126', '127', '134', '135', '136', '137', '145', '146', '147', '150', '154', '156', '157', '163', '167', '172', '176', '234', '235', '245', '246', '247', '250', '254', '256', '257', '260', '267', '271', '276', '345', '346', '347', '351', '354', '356', '357', '360', '367', '371', '376', '450', '451', '454', '456', '457', '460', '463', '467', '471', '472', '476', '501', '504', '506', '507', '514', '516', '517', '546', '547', '560', '563', '567', '571', '572', '576', '603', '605', '607', '637', '676', '712', '715', '716', '726']\n",
      "146\n",
      "made it through loop4\n",
      "['0123', '0124', '0134', '0145', '0154', '0234', '0245', '0246', '0247', '0254', '0256', '0257', '0267', '0276', '0346', '0347', '0367', '0376', '0451', '0454', '0456', '0457', '0460', '0467', '0471', '0476', '0514', '0516', '0517', '0546', '0547', '0560', '0563', '0567', '0571', '0572', '0576', '0637', '0676', '0726', '1234', '1246', '1247', '1267', '1276', '1345', '1346', '1347', '1354', '1356', '1357', '1367', '1376', '1450', '1454', '1456', '1457', '1460', '1467', '1471', '1476', '1504', '1506', '1507', '1546', '1547', '1567', '1576', '1637', '1676', '1726', '2345', '2354', '2450', '2454', '2456', '2457', '2463', '2467', '2472', '2476', '2504', '2546', '2547', '2567', '2576', '2607', '2676', '2716', '3451', '3454', '3456', '3457', '3463', '3467', '3472', '3476', '3514', '3546', '3547', '3567', '3576', '3607', '3676', '3716', '4501', '4504', '4506', '4507', '4514', '4516', '4517', '4546', '4547', '4560', '4563', '4567', '4571', '4572', '4576', '4603', '4605', '4607', '4637', '4676', '4712', '4715', '4716', '4726', '5014', '5046', '5047', '5067', '5076', '5146', '5147', '5167', '5176', '5460', '5463', '5467', '5471', '5472', '5476', '5607', '5637', '5676', '5716', '5726', '6037', '6054', '6057', '6076', '6376', '7126', '7154', '7156']\n",
      "303\n",
      "made it through loop5\n",
      "['01234', '01454', '02454', '02456', '02457', '02467', '02476', '02546', '02547', '02567', '02576', '02676', '03467', '03476', '03676', '04514', '04516', '04517', '04546', '04547', '04560', '04567', '04571', '04576', '04605', '04607', '04676', '04715', '04716', '05146', '05147', '05167', '05176', '05460', '05463', '05467', '05471', '05472', '05476', '05607', '05637', '05676', '05716', '05726', '06376', '12467', '12476', '12676', '13454', '13456', '13457', '13467', '13476', '13546', '13547', '13567', '13576', '13676', '14504', '14506', '14507', '14546', '14547', '14567', '14576', '14607', '14676', '14716', '15046', '15047', '15067', '15076', '15467', '15476', '15676', '16376', '23454', '24504', '24546', '24547', '24567', '24576', '24637', '24676', '24726', '25467', '25476', '25676', '26076', '34514', '34546', '34547', '34567', '34576', '34637', '34676', '34726', '35467', '35476', '35676', '36076', '45014', '45046', '45047', '45067', '45076', '45146', '45147', '45167', '45176', '45460', '45463', '45467', '45471', '45472', '45476', '45607', '45637', '45676', '45716', '45726', '46037', '46054', '46057', '46076', '46376', '47126', '47154', '47156', '50467', '50476', '50676', '51467', '51476', '51676', '54607', '54637', '54676', '54716', '54726', '56076', '56376', '60376', '60547', '60576', '71546']\n",
      "449\n",
      "made it through loop6\n",
      "['024546', '024547', '024567', '024576', '024676', '025467', '025476', '025676', '034676', '045146', '045147', '045167', '045176', '045463', '045467', '045472', '045476', '045607', '045676', '045716', '046054', '046057', '046076', '047154', '047156', '051467', '051476', '051676', '054607', '054637', '054676', '054716', '054726', '056076', '056376', '124676', '134546', '134547', '134567', '134576', '134676', '135467', '135476', '135676', '145046', '145047', '145067', '145076', '145467', '145476', '145676', '146076', '150467', '150476', '150676', '154676', '245467', '245476', '245676', '246376', '254676', '345467', '345476', '345676', '346376', '354676', '450467', '450476', '450676', '451467', '451476', '451676', '454607', '454637', '454676', '454716', '454726', '456076', '456376', '460376', '460547', '460576', '471546', '504676', '514676', '546076', '546376', '605476']\n",
      "537\n",
      "made it through loop7\n",
      "['0245467', '0245476', '0245676', '0254676', '0451467', '0451476', '0451676', '0454637', '0454676', '0454726', '0456076', '0460547', '0460576', '0471546', '0514676', '0546076', '0546376', '1345467', '1345476', '1345676', '1354676', '1450467', '1450476', '1450676', '1454676', '1504676', '2454676', '3454676', '4504676', '4514676', '4546076', '4546376', '4605476']\n",
      "570\n",
      "made it through loop8\n",
      "['02454676', '04514676', '04546376', '04605476', '13454676', '14504676']\n",
      "576\n",
      "made it through loop9\n",
      "[]\n",
      "576\n",
      "made it out\n"
     ]
    }
   ],
   "source": [
    "# Author: Joey Li\n",
    "# Date: 7/20/18\n",
    "# Generates all elements of the Realizable Group R(2), up to scalar multiple\n",
    "\n",
    "import numpy as np\n",
    "from numpy import matrix\n",
    "import math\n",
    "import pickle\n",
    "\n",
    "h = matrix([[1/math.sqrt(2),1/math.sqrt(2)],[1/math.sqrt(2),-1/math.sqrt(2)]])\n",
    "print(h)\n",
    "\n",
    "# 0\n",
    "x1 = np.kron(matrix([[0,1],[1,0]]), np.identity(2))\n",
    "\n",
    "#1\n",
    "x2 = np.kron(np.identity(2), matrix([[0,1],[1,0]]))\n",
    "\n",
    "#2\n",
    "z1 = np.kron(matrix([[1,0],[0,-1]]), np.identity(2))\n",
    "\n",
    "#3\n",
    "z2 = np.kron(np.identity(2), matrix([[1,0],[0,-1]]))\n",
    "\n",
    "\n",
    "h1 = np.kron(h, np.identity(2))\n",
    "\n",
    "#4\n",
    "swaph = matrix([[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]])*np.kron(h,h)\n",
    "\n",
    "\n",
    "h2 = np.kron(np.identity(2),h)\n",
    "\n",
    "#5\n",
    "cz = z1*z2 * matrix([[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,-1]])\n",
    "\n",
    "#6\n",
    "cnot12 = matrix([[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]])\n",
    "\n",
    "#7\n",
    "cnot21 = matrix([[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]])\n",
    "\n",
    "gens = [x1, x2, z1, z2, swaph, cz, cnot12, cnot21]\n",
    "\n",
    "print(gens)\n",
    "\n",
    "r2group = {}\n",
    "r2group[\"\"] = np.identity(4)\n",
    "\n",
    "interestingStrings = [\"\"]\n",
    "\n",
    "matrices = []\n",
    "\n",
    "# converts a matrix to a simpler vector\n",
    "def convertToVec(mat):\n",
    "    vec = mat.flatten()\n",
    "    return np.round(vec, 1)\n",
    "    \n",
    "\n",
    "# iterate over all possible lengths\n",
    "for length in range(1,10):\n",
    "    \n",
    "    # initialize new interesting string group\n",
    "    newInteresting = []\n",
    "        \n",
    "    # iterate over previously interesting strings\n",
    "    for string in interestingStrings:\n",
    "        # check new strings for interesting quality\n",
    "        for nextLetter in range(len(gens)):\n",
    "            if len(string)>0 and string[-1] == nextLetter:\n",
    "                continue\n",
    "            interesting = True\n",
    "                \n",
    "            # build new string\n",
    "            newString = string+str(nextLetter)\n",
    "            \n",
    "            # find corresponding matrix\n",
    "            newGate = np.around(r2group[string]*gens[nextLetter], decimals = 12)\n",
    "            \n",
    "            # check if seen before\n",
    "            for gate in r2group.values():\n",
    "                if np.array_equal(convertToVec(gate), convertToVec(newGate)) or np.array_equal(-1*convertToVec(gate), convertToVec(newGate)):\n",
    "                    interesting = False\n",
    "                    break\n",
    "            \n",
    "            if interesting:\n",
    "                #if not, add it\n",
    "                r2group[newString] = newGate\n",
    "                newInteresting.append(newString)\n",
    "                    \n",
    "    interestingStrings = newInteresting\n",
    "    print(\"made it through loop\"+ str(length))\n",
    "    \n",
    "    print(interestingStrings)\n",
    "                \n",
    "\n",
    "    print(len(r2group))\n",
    "\n",
    "f = open(\"r2group.pkl\",\"wb\")\n",
    "pickle.dump(r2group,f)\n",
    "f.close()\n",
    "print(\"made it out\")\n",
    "    \n"
   ]
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