{ "nbformat": 2, "metadata": { "name": "qerror" }, "worksheets": [ { "cells": [ { "source": "

Quantum Error Correction

", "cell_type": "markdown" }, { "cell_type": "code", "language": "python", "outputs": [], "collapsed": true, "prompt_number": 1, "input": "%load_ext sympyprinting" }, { "cell_type": "code", "language": "python", "outputs": [], "collapsed": true, "prompt_number": 2, "input": "from sympy import sqrt, symbols, Rational\nfrom sympy import expand, Eq, Symbol, simplify, exp, sin\nfrom sympy.physics.quantum import *\nfrom sympy.physics.quantum.qubit import *\nfrom sympy.physics.quantum.gate import *\nfrom sympy.physics.quantum.grover import *\nfrom sympy.physics.quantum.qft import QFT, IQFT, Fourier\nfrom sympy.physics.quantum.circuitplot import circuit_plot" }, { "source": "

5 qubit code

", "cell_type": "markdown" }, { "cell_type": "code", "language": "python", "outputs": [ { "output_type": "pyout", "latex": "$$Z_{1} X_{2} X_{3} Z_{4}$$", "prompt_number": 3, "png": "iVBORw0KGgoAAAANSUhEUgAAAFsAAAAYCAYAAACV+oFbAAAABHNCSVQICAgIfAhkiAAAA2NJREFU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\nr7766quq/gHxxxJqg1cEfAAAAABJRU5ErkJggg==\n", "text": "Z \u22c5X \u22c5X \u22c5Z \n 1 2 3 4" } ], "collapsed": false, "prompt_number": 3, "input": "M0 = Z(1)*X(2)*X(3)*Z(4); M0\n" }, { "cell_type": "code", "language": "python", "outputs": [ { "output_type": "pyout", "latex": "$$Z_{2} X_{3} X_{4} Z_{0}$$", "prompt_number": 4, "png": "iVBORw0KGgoAAAANSUhEUgAAAFoAAAAYCAYAAAB6OOplAAAABHNCSVQICAgIfAhkiAAAA4lJREFU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\nAElFTkSuQmCC\n", "text": "Z \u22c5X \u22c5X \u22c5Z \n 2 3 4 0" } ], "collapsed": false, "prompt_number": 4, "input": "M1 = Z(2)*X(3)*X(4)*Z(0); M1\n" }, { "cell_type": "code", "language": "python", "outputs": [ { "output_type": "pyout", "latex": "$$Z_{3} X_{4} X_{0} Z_{1}$$", "prompt_number": 5, "png": "iVBORw0KGgoAAAANSUhEUgAAAFoAAAAYCAYAAAB6OOplAAAABHNCSVQICAgIfAhkiAAAA3RJREFU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\n", "text": "Z \u22c5X \u22c5X \u22c5Z \n 3 4 0 1" } ], "collapsed": false, "prompt_number": 5, "input": "M2 = Z(3)*X(4)*X(0)*Z(1); M2\n" }, { "cell_type": "code", "language": "python", "outputs": [ { "output_type": "pyout", "latex": "$$Z_{4} X_{0} X_{1} Z_{2}$$", "prompt_number": 6, "png": "iVBORw0KGgoAAAANSUhEUgAAAFoAAAAYCAYAAAB6OOplAAAABHNCSVQICAgIfAhkiAAAA2BJREFU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\nefy/8Q8KoQ22z/3wywAAAABJRU5ErkJggg==\n", "text": "Z \u22c5X \u22c5X \u22c5Z \n 4 0 1 2" } ], "collapsed": false, "prompt_number": 6, "input": "M3 = Z(4)*X(0)*X(1)*Z(2); M3\n" }, { "source": "These operators should mutually commute.", "cell_type": "markdown" }, { "cell_type": "code", "language": "python", "outputs": [ { "output_type": "pyout", "latex": "$$0$$", "prompt_number": 7, "png": "iVBORw0KGgoAAAANSUhEUgAAAAwAAAASCAYAAABvqT8MAAAABHNCSVQICAgIfAhkiAAAAN1JREFU\nKJHN0i1LRFEQxvGf7i6LrGE3adCoUbAZBT+GzWATi9Vm22D3Q9gtZqNo8WXNgi9BUHBdUMO9F8bD\nlG1OOcwz8z9zeM4wZcwU+RKGeMQbOjjGawa3MMJu0I5whtkM2MYYvaCt4Ac7GXCJ80R/wGmTNKPa\nWMN9AoywWQILKgPeE+ADA3QjsBiKGQD9CIzr8zsBOrHWALf4SpqpXJvgJQIT3NRvLWMeTyp7/3zI\nFZaL5hbWcZ2NPlCtwFzQNuqbtzJggDvsBe0EF7GpXL5VHOKzznvYx3M24Z/EL9XoKBNI+V0xAAAA\nAElFTkSuQmCC\n", "text": "0" } ], "collapsed": false, "prompt_number": 7, "input": "gate_simp(Commutator(M0,M1).doit())\n" }, { "source": "And square to the identity.", "cell_type": "markdown" }, { "cell_type": "code", "language": "python", "outputs": [ { "output_type": "display_data", "latex": "$$1$$", "png": "iVBORw0KGgoAAAANSUhEUgAAAAsAAAASCAYAAACNdSR1AAAABHNCSVQICAgIfAhkiAAAAGBJREFU\nKJHt0bENQGAQhuEnWp1CZQFbqExhOI1BtEbABgoj/AoKkcgfCZ23uUvuvcuXHC9QYI5JKWqMCNdh\ncupLdKiwPInRxi5H+eXX5eyo+d1ijh6T/XsBKwY0TxJ8zAZBcgy8TZqNTgAAAABJRU5ErkJggg==\n", "text": "1" }, { "output_type": "display_data", "latex": "$$1$$", "png": "iVBORw0KGgoAAAANSUhEUgAAAAsAAAASCAYAAACNdSR1AAAABHNCSVQICAgIfAhkiAAAAGBJREFU\nKJHt0bENQGAQhuEnWp1CZQFbqExhOI1BtEbABgoj/AoKkcgfCZ23uUvuvcuXHC9QYI5JKWqMCNdh\ncupLdKiwPInRxi5H+eXX5eyo+d1ijh6T/XsBKwY0TxJ8zAZBcgy8TZqNTgAAAABJRU5ErkJggg==\n", "text": "1" }, { "output_type": "display_data", "latex": "$$1$$", "png": "iVBORw0KGgoAAAANSUhEUgAAAAsAAAASCAYAAACNdSR1AAAABHNCSVQICAgIfAhkiAAAAGBJREFU\nKJHt0bENQGAQhuEnWp1CZQFbqExhOI1BtEbABgoj/AoKkcgfCZ23uUvuvcuXHC9QYI5JKWqMCNdh\ncupLdKiwPInRxi5H+eXX5eyo+d1ijh6T/XsBKwY0TxJ8zAZBcgy8TZqNTgAAAABJRU5ErkJggg==\n", "text": "1" }, { "output_type": "display_data", "latex": "$$1$$", "png": "iVBORw0KGgoAAAANSUhEUgAAAAsAAAASCAYAAACNdSR1AAAABHNCSVQICAgIfAhkiAAAAGBJREFU\nKJHt0bENQGAQhuEnWp1CZQFbqExhOI1BtEbABgoj/AoKkcgfCZ23uUvuvcuXHC9QYI5JKWqMCNdh\ncupLdKiwPInRxi5H+eXX5eyo+d1ijh6T/XsBKwY0TxJ8zAZBcgy8TZqNTgAAAABJRU5ErkJggg==\n", "text": "1" } ], "collapsed": false, "prompt_number": 8, "input": "for o in [M0,M1,M2,M3]:\n display(gate_simp(o*o))\n" }, { "source": "

Codewords

", "cell_type": "markdown" }, { "cell_type": "code", "language": "python", "outputs": [ { "output_type": "pyout", "latex": "$$\\frac{1}{4} \\left(1 + Z_{1} X_{2} X_{3} Z_{4}\\right) \\left(1 + Z_{2} X_{3} X_{4} Z_{0}\\right) \\left(1 + Z_{3} X_{4} X_{0} Z_{1}\\right) \\left(1 + Z_{4} X_{0} X_{1} Z_{2}\\right) {\\left|0\\right\\rangle }$$", "prompt_number": 9, "png": "iVBORw0KGgoAAAANSUhEUgAAAj4AAAAiCAYAAABfudNlAAAABHNCSVQICAgIfAhkiAAACrlJREFU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\nhBCC/wPS77xfXVkDTQAAAABJRU5ErkJggg==\n", "text": "\u239b1 + Z \u22c5X \u22c5X \u22c5Z \u239e\u22c5\u239b1 + Z \u22c5X \u22c5X \u22c5Z \u239e\u22c5\u239b1 + Z \u22c5X \u22c5X \u22c5Z \u239e\u22c5\u239b1 + Z \u22c5X \u22c5X \u22c5Z \u239e\u22c5\u27580\u27e9\n\u239d 1 2 3 4\u23a0 \u239d 2 3 4 0\u23a0 \u239d 3 4 0 1\u23a0 \u239d 4 0 1 2\u23a0 \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n 4" } ], "collapsed": false, "prompt_number": 9, "input": "zero = Rational(1,4)*(1+M0)*(1+M1)*(1+M2)*(1+M3)*IntQubit(0, 5); zero\n" }, { "cell_type": "code", "language": "python", "outputs": [ { "output_type": "pyout", "latex": "$${\\left|0\\right\\rangle } + {\\left|3\\right\\rangle } - {\\left|5\\right\\rangle } + {\\left|6\\right\\rangle } - {\\left|9\\right\\rangle } - {\\left|10\\right\\rangle } + {\\left|12\\right\\rangle } - {\\left|15\\right\\rangle } + {\\left|17\\right\\rangle } - {\\left|18\\right\\rangle } - {\\left|20\\right\\rangle } - {\\left|23\\right\\rangle } + {\\left|24\\right\\rangle } - {\\left|27\\right\\rangle } - {\\left|29\\right\\rangle } - {\\left|30\\right\\rangle }$$", "prompt_number": 10, "png": "iVBORw0KGgoAAAANSUhEUgAAAqcAAAAVCAYAAAB7eEdTAAAABHNCSVQICAgIfAhkiAAACzRJREFU\neJztnXuwVVUdxz8gIAoBRiaa0C1Se2ijZBgKoynTOIJKj1HTtFtpLwetFClSSAcxMMsae1GTVEZT\nUqmZQlqTphmpjZi9RpQbTvRwkCAukwjaH7+1Ouusu/Y+a5979t6/Q+szc2bfs/a6+35/v/P77bXP\nel1IJBKJRCKRSCT2AD5et4AWaNKnSUsITfo0aYmlGzX7dKMN3ag5RDfakTRXQzdqDtGNdiTN5ZOp\nd5jz89nAPcBfgXHAdUA/8AwwElgOPOnU7wdeCvyzw2JDuNoA9gYuN39/HDAR+CrwzQr0+VqWAkcC\nK4E7gRmmTh9wSclaYvRZTgbONxr6gXXATSXrC2mZBpwFDAX+A2wCPg88X4MWy1Qk3mcEzmnPBUue\nDYeYcyOB/YC1wJXA006dMm1oR3O35BXk27EJ+CMSOzuB55xzLwAXoC/mAc4DDgf2BcYAP6Vxv4Dq\nNMfELtSbp+1qrrMdC9GuHSFWAD8Afmzea/O9prws4mcN7WdM3EIHc7IX6DE/3w0s8849htyoLOOB\nj7a2qSP00tAGEvDTnPenIwH1SaesLH2+luvN33ZfNyMfRNlaQvTSrA8ksO5DAh9gDrAVOMi8r8pX\nbwL+AbzGKfsuzd+eqtJi/9YZSOI8lvF72nOhlQ0vB34NvNK8HwM8CPzZnHOvU5YNvRTTDN2RV63s\nOICBNriv7zjX0RTzlwLnOu+HIQ+mVedpbOxCvXnaS3ua62zHQvTSnh0+b0bseIdTpsn3mvKyiJ+1\ntJ8xcQuDzMmhgbJjgJOAG52y7wGTkadly2bkYSd0jVYcAoxu4/cAXgHMBuY6ZauRbxEf6JC+otwE\nrEK+JcwCzjR6OqFlML4CmAB8BjgH2GLKRgHbgL06oK8INwMPIN9YLbcAV9FIxKq0nAx8BXg18qAe\nQnsuxNiwGLiCxrfVbcD7gEOBhU49TX63aM6rGDteC8wD9gGGI/k2xLxfDVxo6mny/RDgvcC3nbJd\nwHzgg05ZFZpjY7eKPI0lVnMV7dhgYjzWDp8RGec1+V5TXhbxs4b2MzZuO5qTvciT8SpgY+D8GuBR\nr+xY4JS8i2awGJheoL7VBjAW+Vax1Dm/F/BsB/XFagHp4Tky4vfq8BU0D63kUbavDkO+XS3z6hxu\nyt9foRafhwj3ImnPBZcsG54EngBe4pVvQYbIXcrwOxTXDPrzyiXLjguR+Pa5DjjRK9MS85OQfHy7\nV34g0pC4jUjZmmNjt4o8zaOX4pqraMcGE+NF7hsuC4B3MbDnFPT4XlNexmrW0n7Gxu2gczL0tPoG\n4PFA+XrgCKQb1vIrc+Eq2Yp8UPOdsinIN7ZVXt069GVRh5YRwKnIMEErytZnhyKe9co3mOMJFWqJ\nRXsuxPA4cDDwIq98B3JDdO8BWm3IQ7PmLzLwAfAEc/y5V67Fjo3IPLYbkJ4PSy/wLRpz26B8zbGx\nqylPYzVrb8eK3Dcsr0JG5R7JuKYW32vKy1jNWtrP2LgddE6GAuwAYHugvN8cJ3jlG2k9B6VMRgNL\nkC7vqwPnq9A3HRk6X4J0Y5+VUa9qX70OGbZ4GulyXwLcClyLBJNPmfrsDctPwgPNcWKFWmLptlwI\ncQri4w1O2XhkvvGDND9sgC4btOZVuwxHFi+E7lOgx46LkUUKdyMLHeYjw3nzAnXL1Bwbu5rytGi+\nWTS0Yy7t2PEJ4JoW19Xo+zrzMlaz1vYzK24HnZP+w+lYZN5FPwOxZeO88tuROQhVMwn4FLKK9F/I\nPKndgXpl69uNdKtfigxpXAx8AXhrDVp87LDoacik6wXI5OVJwE8C9cvU1wf8Hpnv5nKcOY73yuuK\nK0s35UIeu5HFLy4fMsclgfpabNCcV+0yF+lN8D8PixY7ViHze59HhgvnI1ODdgXqlqk5Jna15WnR\nfNPSjvkUteOdiMbQA4mLJt9b6szLWM196Go/8+K2IznpP5w+h9yQQt8whpujf2424QedstmIOOdY\nZB7DU8AbA/XK1jcPGSawbEO2VFiBbLlQpRafMeZot46yLAdmAm/z6petbw4yBGCHCychPTIwcIFG\nXXFl6aZcKMJEZCumzwJ3Bc5rsUFzXrXDMOAjiP4stNhxEDLndBYylL8fcBvw4UDdKjWHYld7nrbK\nNy3tWCvy7BiLrND/UcR1NPke9OVlnmZN7Wde3HYkJ/2H0x0070HlMsoc/+aV95A/QboKvo40XquR\nRHHpoVx9oQ9gE/JgOKViLT6bzdGfA/SUOc7yynsoV996ZH/Fo4DPIb1gXzPn/DlAZWtpRbfmQh7D\nkW1SVtLYK9SnBx02aM6rdjgVGcpanVOnh/rt2AeZA3Y1ovXdyCr/jcg81GO8+j1UozkrdjXnaUy+\nudTZjuXRyo7LyR4S9+lBl+815WUrzVrbTz9uO5KTwxjIozT2w3SxW1L83SmbhtzIslgGvCVQPgEZ\nNgp1+y4A7si55t7Ifl/30zzMtA4JtJnICvU8fbNp3s6gFbcSnkszC5mTdTrwsKcRZDuIB1posZTh\nK7tabotXbq/lzlMJ6euUn1z6kHmElkPN8Xc1aGmF9lwoypeRVdofyzhfdr7Eoj2v2mE2cgMPDY2D\nHt+fZnS4jd0a4Gjgt8g9dq0pr1JzXuwONk/L8nGe5k60Y5ayYzzPjqnI3pt/ibiOFt/7f79oXtap\nuY9628/YuO1k2/m/rQIWMXCpP0jvm7/66ira209rMFtcfIPwhq93mXJ30US7+mK1XIYk/nFenZVG\ni7tZbh2+GoHMAVrk1Zls9F3bAX2xWrK4ANkjbXKNWrK21dGeCy552zKBbNS81Cs7D9nfz1KG36G4\nZu155dPK9yALHrJ6E0BPzC9HhutCLEYWjliq0twqdqvI0zx6Ka65inasEzHeyo4rkfmCtzivexEb\nfmPeH23qavG9i5a8LKLZper2MzZuB52TIQPWIZvUTnLK9gdeT/MT+4uRHrmsFXBlsdn8XXd7pCHI\nfIddNLrnq9B3L/Ih3O+VT0G+SdrNcuvy1U7kXz8e5ZUfZo4/M8eq9K1g4DyaM5FvaE9UrCUG7bkQ\nyxmI7vle+fHIDQV02aA9r4oyDFmJui3jvCY7fkH2vzSdSWNeWFWaY2JXW57GaNbUjmURY8cipFdu\njvOye3EuM+8fQpfvLVryMlbzCupvP2PjdtA5GRrWvwPpYr0EWSEL8B5kjsAKp97ZSE9G1dyI7JNl\nu7GHAhchWyzMRVaOQTX61iLfbmYAvzRlJyEOdzfzrctXIJ/hw8jK/UeQQLoI6QGxgVSVvm00uvWH\nIDF2MPBpp07VvhqOxM5I83L/A5H2XLDk2TANGS66k+b/jT6C5n8Fqsnv3ZBXljw7LPsj8f7vjGto\n8v1tyCblC2isFh6B/Nea9TT2gaxCc2zsasrTWM2a2rEQsXaEGOMdQZfvLRrysohmDe1nbNwOOifd\nh9MdSE/bTmQV9xLEWVsRBxxP8wawo5G5JlVgtQH8ATgfGXoahezz1Y/MT7u9An2ulheQlX4LkW7v\noUgAnUjzkFldvgJZRDIbCaB9zbk1NA/PVeErkEnzC5Hg7EGGU6ZTTVz5WqYiKyJ7gJeZsg3mdRlw\nH/pzIcaG7yMPdecErnW983OZNhTV3A15FWOH5RngT2TP8dMU89uRDb2vAH5ofn80cA9wLo2enCo0\nx8Zu3Xnajua627EQ7djhcgTwJRoLFm9AHkjmosv3Fg15WUSzhvazj7i4rTsn26boXJj/Z5Kv9mzS\n51sPye+JPZ0U44mupYzFDzFsR57EE61JvtqzSZ9vPSS/J/Z0UownEolEIpFIJBKJRCKRSCQSiUQi\nkUgkEolEIpFIJDrNfwGfohC3+6QZuAAAAABJRU5ErkJggg==\n", "text": "\u27580\u27e9 + \u27583\u27e9 - \u27585\u27e9 + \u27586\u27e9 - \u27589\u27e9 - \u275810\u27e9 + \u275812\u27e9 - \u275815\u27e9 + \u275817\u27e9 - \u275818\u27e9 - \u275820\u27e9 - \u275823\u27e9 +\n \u275824\u27e9 - \u275827\u27e9 - \u275829\u27e9 - \u275830\u27e9" } ], "collapsed": false, "prompt_number": 10, "input": "qapply(4*zero)\n" }, { "cell_type": "code", "language": "python", "outputs": [ { "output_type": "pyout", "latex": "$$\\frac{1}{4} \\left(1 + Z_{1} X_{2} X_{3} Z_{4}\\right) \\left(1 + Z_{2} X_{3} X_{4} Z_{0}\\right) \\left(1 + Z_{3} X_{4} X_{0} Z_{1}\\right) \\left(1 + Z_{4} X_{0} X_{1} Z_{2}\\right) {\\left|31\\right\\rangle }$$", "prompt_number": 11, "png": 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"text": "\u239b1 + Z \u22c5X \u22c5X \u22c5Z \u239e\u22c5\u239b1 + Z \u22c5X \u22c5X \u22c5Z \u239e\u22c5\u239b1 + Z \u22c5X \u22c5X \u22c5Z \u239e\u22c5\u239b1 + Z \u22c5X \u22c5X \u22c5Z \u239e\u22c5\u275831\u27e9\n\u239d 1 2 3 4\u23a0 \u239d 2 3 4 0\u23a0 \u239d 3 4 0 1\u23a0 \u239d 4 0 1 2\u23a0 \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n 4" } ], "collapsed": false, "prompt_number": 11, "input": "one = Rational(1,4)*(1+M0)*(1+M1)*(1+M2)*(1+M3)*IntQubit(2**5-1, 5); one\n" }, { "cell_type": "code", "language": "python", "outputs": [ { "output_type": "pyout", "latex": "$$- {\\left|1\\right\\rangle } - {\\left|2\\right\\rangle } - {\\left|4\\right\\rangle } + {\\left|7\\right\\rangle } - {\\left|8\\right\\rangle } - {\\left|11\\right\\rangle } - {\\left|13\\right\\rangle } + {\\left|14\\right\\rangle } - {\\left|16\\right\\rangle } + {\\left|19\\right\\rangle } - {\\left|21\\right\\rangle } - {\\left|22\\right\\rangle } + {\\left|25\\right\\rangle } - {\\left|26\\right\\rangle } + {\\left|28\\right\\rangle } + {\\left|31\\right\\rangle }$$", "prompt_number": 12, "png": "iVBORw0KGgoAAAANSUhEUgAAArsAAAAVCAYAAABG6iY1AAAABHNCSVQICAgIfAhkiAAACpxJREFU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\n", "text": "-\u27581\u27e9 - \u27582\u27e9 - \u27584\u27e9 + \u27587\u27e9 - \u27588\u27e9 - \u275811\u27e9 - \u275813\u27e9 + \u275814\u27e9 - \u275816\u27e9 + \u275819\u27e9 - \u275821\u27e9 - \u275822\u27e9 \n+ \u275825\u27e9 - \u275826\u27e9 + \u275828\u27e9 + \u275831\u27e9" } ], "collapsed": false, "prompt_number": 12, "input": "qapply(4*one)\n" }, { "source": "

The encoding circuit

", "cell_type": "markdown" }, { "cell_type": "code", "language": "python", "outputs": [], "collapsed": true, "prompt_number": 13, "input": "encoding_circuit = H(3)*H(4)*CNOT(2,0)*CNOT(3,0)*CNOT(4,0)*H(1)*H(4)*\\\n CNOT(2,1)*CNOT(4,1)*H(2)*CNOT(3,2)*CNOT(4,2)*H(3)*\\\n H(4)*CNOT(4, 3)*Z(4)*H(4)*Z(4)\n" }, { "cell_type": "code", "language": "python", "outputs": [ { "output_type": "pyout", "prompt_number": 14, "text": "<sympy.physics.quantum.circuitplot.CircuitPlot object at 0x38a6950>" }, { "output_type": "display_data", "png": 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GvLy8escjIpIbp0WIalFaWoqQkBDY2dlh2bJl6Nq164OyP1+aLS4uRnR0NFauXImvv/4a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\nX2lpKaZNm4YuXbr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} ], "collapsed": false, "prompt_number": 14, "input": "circuit_plot(encoding_circuit, nqubits=5, scale=0.5)" }, { "cell_type": "code", "language": "python", "outputs": [ { "output_type": "pyout", "latex": "$$\\left(\\begin{smallmatrix}1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0\\\\0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1\\\\0 & 1 & 0 & -1 & 0 & 1 & 0 & -1 & -1 & 0 & 1 & 0 & -1 & 0 & 1 & 0 & -1 & 0 & 1 & 0 & -1 & 0 & 1 & 0 & 0 & -1 & 0 & 1 & 0 & -1 & 0 & 1\\\\1 & 0 & -1 & 0 & 1 & 0 & -1 & 0 & 0 & -1 & 0 & 1 & 0 & -1 & 0 & 1 & 0 & -1 & 0 & 1 & 0 & -1 & 0 & 1 & -1 & 0 & 1 & 0 & -1 & 0 & 1 & 0\\\\0 & -1 & 0 & -1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & 1 & 0 & 1 & 0 & 0 & -1 & 0 & -1 & 0 & 1 & 0 & 1\\\\-1 & 0 & -1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & 1 & 0 & 1 & -1 & 0 & -1 & 0 & 1 & 0 & 1 & 0\\\\1 & 0 & -1 & 0 & -1 & 0 & 1 & 0 & 0 & -1 & 0 & 1 & 0 & 1 & 0 & -1 & 0 & 1 & 0 & -1 & 0 & -1 & 0 & 1 & 1 & 0 & -1 & 0 & -1 & 0 & 1 & 0\\\\0 & 1 & 0 & -1 & 0 & -1 & 0 & 1 & -1 & 0 & 1 & 0 & 1 & 0 & -1 & 0 & 1 & 0 & -1 & 0 & -1 & 0 & 1 & 0 & 0 & 1 & 0 & -1 & 0 & -1 & 0 & 1\\\\0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1\\\\-1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0\\\\-1 & 0 & 1 & 0 & -1 & 0 & 1 & 0 & 0 & 1 & 0 & -1 & 0 & 1 & 0 & -1 & 0 & -1 & 0 & 1 & 0 & -1 & 0 & 1 & -1 & 0 & 1 & 0 & -1 & 0 & 1 & 0\\\\0 & -1 & 0 & 1 & 0 & -1 & 0 & 1 & 1 & 0 & -1 & 0 & 1 & 0 & -1 & 0 & -1 & 0 & 1 & 0 & -1 & 0 & 1 & 0 & 0 & -1 & 0 & 1 & 0 & -1 & 0 & 1\\\\1 & 0 & 1 & 0 & -1 & 0 & -1 & 0 & 0 & -1 & 0 & -1 & 0 & 1 & 0 & 1 & 0 & -1 & 0 & -1 & 0 & 1 & 0 & 1 & -1 & 0 & -1 & 0 & 1 & 0 & 1 & 0\\\\0 & 1 & 0 & 1 & 0 & -1 & 0 & -1 & -1 & 0 & -1 & 0 & 1 & 0 & 1 & 0 & -1 & 0 & -1 & 0 & 1 & 0 & 1 & 0 & 0 & -1 & 0 & -1 & 0 & 1 & 0 & 1\\\\0 & -1 & 0 & 1 & 0 & 1 & 0 & -1 & 1 & 0 & -1 & 0 & -1 & 0 & 1 & 0 & 1 & 0 & -1 & 0 & -1 & 0 & 1 & 0 & 0 & 1 & 0 & -1 & 0 & -1 & 0 & 1\\\\-1 & 0 & 1 & 0 & 1 & 0 & -1 & 0 & 0 & 1 & 0 & -1 & 0 & -1 & 0 & 1 & 0 & 1 & 0 & -1 & 0 & -1 & 0 & 1 & 1 & 0 & -1 & 0 & -1 & 0 & 1 & 0\\\\0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1\\\\1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0\\\\-1 & 0 & 1 & 0 & -1 & 0 & 1 & 0 & 0 & -1 & 0 & 1 & 0 & -1 & 0 & 1 & 0 & 1 & 0 & -1 & 0 & 1 & 0 & -1 & -1 & 0 & 1 & 0 & -1 & 0 & 1 & 0\\\\0 & -1 & 0 & 1 & 0 & -1 & 0 & 1 & -1 & 0 & 1 & 0 & -1 & 0 & 1 & 0 & 1 & 0 & -1 & 0 & 1 & 0 & -1 & 0 & 0 & -1 & 0 & 1 & 0 & -1 & 0 & 1\\\\-1 & 0 & -1 & 0 & 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0 & -1 & 0 & 1 & 0 & -1 & 0 & 1 & 1 & 0 & -1 & 0 & 1 & 0 & -1 & 0\\\\0 & -1 & 0 & -1 & 0 & 1 & 0 & 1 & -1 & 0 & -1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & -1 & 0 & -1 & 0 & 0 & -1 & 0 & -1 & 0 & 1 & 0 & 1\\\\-1 & 0 & -1 & 0 & 1 & 0 & 1 & 0 & 0 & -1 & 0 & -1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & -1 & 0 & -1 & -1 & 0 & -1 & 0 & 1 & 0 & 1 & 0\\\\-1 & 0 & 1 & 0 & 1 & 0 & -1 & 0 & 0 & -1 & 0 & 1 & 0 & 1 & 0 & -1 & 0 & 1 & 0 & -1 & 0 & -1 & 0 & 1 & -1 & 0 & 1 & 0 & 1 & 0 & -1 & 0\\\\0 & -1 & 0 & 1 & 0 & 1 & 0 & -1 & -1 & 0 & 1 & 0 & 1 & 0 & -1 & 0 & 1 & 0 & -1 & 0 & -1 & 0 & 1 & 0 & 0 & -1 & 0 & 1 & 0 & 1 & 0 & -1\\end{smallmatrix}\\right)$$", "prompt_number": 15, "text": "\u23a11 0 1 0 1 0 1 0 0 -1 0 -1 0 -1 0 -1 0 -1 0 -\n\u23a2 \n\u23a20 1 0 1 0 1 0 1 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0\n\u23a2 \n\u23a20 1 0 -1 0 1 0 -1 -1 0 1 0 -1 0 1 0 -1 0 1 0\n\u23a2 \n\u23a21 0 -1 0 1 0 -1 0 0 -1 0 1 0 -1 0 1 0 -1 0 1\n\u23a2 \n\u23a20 -1 0 -1 0 1 0 1 1 0 1 0 -1 0 -1 0 -1 0 -1 0\n\u23a2 \n\u23a2-1 0 -1 0 1 0 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\u23a5\n \u23a5\n -1 0 1 0 0 -1 0 1 0 1 0 -1\u23a6" } ], "collapsed": false, "prompt_number": 15, "input": "represent(4*encoding_circuit, nqubits=5)" } ] } ] }