{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# One Qubit Gates - Rotation" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "ExecuteTime": { "end_time": "2019-08-22T14:44:26.162937Z", "start_time": "2019-08-22T14:44:25.781597Z" } }, "outputs": [], "source": [ "from qiskit import *\n", "from math import pi\n", "from qiskit.visualization import plot_bloch_multivector" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### General Unitary Gate" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$U_3(\\theta, \\phi, \\lambda) = \\begin{bmatrix} \\cos(\\theta/2) & -e^{i\\lambda}\\sin(\\theta/2) \\\\\n", " e^{i\\phi}\\sin(\\theta/2) & e^{i\\lambda+i\\phi}\\cos(\\theta/2)\n", " \\end{bmatrix}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\begin{aligned}\n", "U_3(\\tfrac{\\pi}{2}, \\phi, \\lambda) = U_2 = \\tfrac{1}{\\sqrt{2}}\\begin{bmatrix} 1 & -e^{i\\lambda} \\\\\n", " e^{i\\phi} & e^{i\\lambda+i\\phi}\n", " \\end{bmatrix}\n", "& \\quad &\n", "U_3(0, 0, \\lambda) = U_1 = \\begin{bmatrix} 1 & 0 \\\\\n", " 0 & e^{i\\lambda}\\\\\n", " \\end{bmatrix}\n", "\\end{aligned}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### U3 gate" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "<Figure size 233.576x84.28 with 1 Axes>" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(1)\n", "qc.u3(pi/4,pi/4,pi/4,0)\n", "qc.draw(output='mpl')" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 288x288 with 1 Axes>" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's see the result\n", "backend = Aer.get_backend('statevector_simulator')\n", "out = execute(qc,backend).result().get_statevector()\n", "plot_bloch_multivector(out)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### U2 Gate" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "<Figure size 233.576x84.28 with 1 Axes>" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(1)\n", "qc.u2(pi/4,pi/4,0)\n", "qc.draw(output='mpl')" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 288x288 with 1 Axes>" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's see the result\n", "backend = Aer.get_backend('statevector_simulator')\n", "out = execute(qc,backend).result().get_statevector()\n", "plot_bloch_multivector(out)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### U1 Gate" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "<Figure size 233.576x84.28 with 1 Axes>" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(1)\n", "qc.x(0)\n", "qc.u1(pi/4,0)\n", "qc.draw(output='mpl')" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0. +0.j 0.70710678+0.70710678j]\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 288x288 with 1 Axes>" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's see the result\n", "backend = Aer.get_backend('statevector_simulator')\n", "out = execute(qc,backend).result().get_statevector()\n", "print(out)\n", "plot_bloch_multivector(out)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Standard Rotations\n", "\n", "The standard rotation gates are those that define rotations around the Paulis $P=\\{X,Y,Z\\}$. They are defined as \n", "\n", "$$ R_P(\\theta) = \\exp(-i \\theta P/2) = \\cos(\\theta/2)I -i \\sin(\\theta/2)P$$\n", "\n", "##### Rotation around X-axis\n", "\n", "$$\n", "R_x(\\theta) = \n", "\\begin{pmatrix}\n", "\\cos(\\theta/2) & -i\\sin(\\theta/2)\\\\\n", "-i\\sin(\\theta/2) & \\cos(\\theta/2)\n", "\\end{pmatrix} = u3(\\theta, -\\pi/2,\\pi/2)\n", "$$" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "ExecuteTime": { "end_time": "2019-08-22T14:44:28.826344Z", "start_time": "2019-08-22T14:44:28.820278Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "<Figure size 173.376x84.28 with 1 Axes>" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(1)\n", "qc.rx(pi/2,0)\n", "qc.draw(output='mpl')" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "ExecuteTime": { "end_time": "2019-08-22T14:44:28.841420Z", "start_time": "2019-08-22T14:44:28.828459Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 288x288 with 1 Axes>" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's see the result\n", "backend = Aer.get_backend('statevector_simulator')\n", "out = execute(qc,backend).result().get_statevector()\n", "plot_bloch_multivector(out)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Rotation around Y-axis\n", "\n", "$$\n", "R_y(\\theta) =\n", "\\begin{pmatrix}\n", "\\cos(\\theta/2) & - \\sin(\\theta/2)\\\\\n", "\\sin(\\theta/2) & \\cos(\\theta/2).\n", "\\end{pmatrix} =u3(\\theta,0,0)\n", "$$" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "ExecuteTime": { "end_time": "2019-08-22T14:44:28.853141Z", "start_time": "2019-08-22T14:44:28.843281Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "<Figure size 173.376x84.28 with 1 Axes>" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(1)\n", "qc.ry(pi/2,0)\n", "qc.draw(output='mpl')" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "ExecuteTime": { "end_time": "2019-08-22T14:44:28.874195Z", "start_time": "2019-08-22T14:44:28.857971Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0.70710678+0.j 0.70710678+0.j]\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 288x288 with 1 Axes>" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's see the result\n", "backend = Aer.get_backend('statevector_simulator')\n", "out = execute(qc,backend).result().get_statevector()\n", "print(out)\n", "plot_bloch_multivector(out)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Rotation around Z-axis\n", "\n", "$$\n", "R_z(\\phi) = \n", "\\begin{pmatrix}\n", "e^{-i \\phi/2} & 0 \\\\\n", "0 & e^{i \\phi/2}\n", "\\end{pmatrix}\\equiv u1(\\phi)\n", "$$\n", "\n", "Note here we have used an equivalent as is different to u1 by global phase $e^{-i \\phi/2}$." ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "ExecuteTime": { "end_time": "2019-08-22T14:44:28.891314Z", "start_time": "2019-08-22T14:44:28.880141Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "<Figure size 173.376x84.28 with 1 Axes>" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(1)\n", "qc.rz(pi/2,0)\n", "qc.draw(output='mpl')" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "ExecuteTime": { "end_time": "2019-08-22T14:44:28.906087Z", "start_time": "2019-08-22T14:44:28.893516Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1.+0.j 0.+0.j]\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 288x288 with 1 Axes>" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's see the result\n", "backend = Aer.get_backend('statevector_simulator')\n", "out = execute(qc,backend).result().get_statevector()\n", "print(out)\n", "plot_bloch_multivector(out)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note this is different due only to a global phase" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "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": "3.7.3" }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 1 }