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It simulates running given quantum program infinite number of times and averaging all the 0s and 1s we got in process. \n", 38 | "`Z_expectation_value` on the other hand gives us the expectation value of Z operator given a quantum state, so .\n", 39 | "\n", 40 | "Consider the following:\n", 41 | "We have a circuit which produces the following state: `|psi> = sqrt(0.3)|0> + sqrt(0.7)|1>`.\n", 42 | "If we measure it infinite number of times, we will get \"0\" 30% of times and \"1\" 70% of times. So the expected value of such circuit is 0.7.\n", 43 | "\n", 44 | "However, if we wan't to measure the expectation value of `Z` operator, we need to take into the account, that state |0> is associated with the eigenvalue 1 and state |1> with the eigenvalue -1. This means, that for each = 0.3 * 1 + 0.7 * (-1) = -0.4\n", 45 | "\n", 46 | "So each \"0\" we measure, we substitute it by \"1\" and each \"1\" we measure, we substitute it by \"-1\". And to get the expectation value, we simply average all the \"1\"s and \"-1\"s.\n", 47 | "\n", 48 | "It turns out that a simple transformation: X -> (-X+0.5)*2 maps the values from [0, 1] to [-1, 1]." 49 | ] 50 | }, 51 | { 52 | "cell_type": "code", 53 | "execution_count": 32, 54 | "metadata": {}, 55 | "outputs": [], 56 | "source": [ 57 | "# This calculates what's the expectation value of the quantum state produced by given program.\n", 58 | "def circuit_expectation_value(program):\n", 59 | " wf_sim = WavefunctionSimulator()\n", 60 | " result = 0 \n", 61 | " wavefunction = wf_sim.wavefunction(program)\n", 62 | " prob_dict = wavefunction.get_outcome_probs()\n", 63 | " for key, value in prob_dict.items():\n", 64 | " result += value * int(key)\n", 65 | " return result\n", 66 | "\n", 67 | "# This calculates what's the expectation value of the , where |psi> is given the state produced by given program.\n", 68 | "def Z_expectation_value(program):\n", 69 | " circuit_result = circuit_expectation_value(program)\n", 70 | " return (-circuit_result+0.5)*2" 71 | ] 72 | }, 73 | { 74 | "cell_type": "markdown", 75 | "metadata": {}, 76 | "source": [ 77 | "# VQE example" 78 | ] 79 | }, 80 | { 81 | "cell_type": "markdown", 82 | "metadata": {}, 83 | "source": [ 84 | "Our Hamiltonian is:\n", 85 | "\n", 86 | "H = 2\\*Z + X + I\n", 87 | "\n", 88 | "So the individual terms are:\n", 89 | "- H_1 = 2*Z\n", 90 | "- H_2 = X\n", 91 | "- H_3 = I" 92 | ] 93 | }, 94 | { 95 | "cell_type": "code", 96 | "execution_count": 21, 97 | "metadata": {}, 98 | "outputs": [], 99 | "source": [ 100 | "# Arbitrary value of theta\n", 101 | "theta = 1.5 * np.pi\n", 102 | "# Some ansatz\n", 103 | "ansatz = RY(theta, 0)\n", 104 | "# Circuit for measuring the first term\n", 105 | "# It consists only of Z, which is already in the computational basis\n", 106 | "circuit_1 = Program(ansatz)\n", 107 | "# Circuit for measuring the second term\n", 108 | "# It corresponds to X, so we need additional RY rotation. \n", 109 | "circuit_2 = Program([ansatz, RY(np.pi/2, 0)])" 110 | ] 111 | }, 112 | { 113 | "cell_type": "code", 114 | "execution_count": 22, 115 | "metadata": {}, 116 | "outputs": [ 117 | { 118 | "name": "stdout", 119 | "output_type": "stream", 120 | "text": [ 121 | "TERM 1: -4.440892098500626e-16\n", 122 | "TERM 2: 1.0\n", 123 | "TERM 3: 1\n" 124 | ] 125 | } 126 | ], 127 | "source": [ 128 | "#Here we account for the constants\n", 129 | "term_1_value = 2 * Z_expectation_value(circuit_1)\n", 130 | "print(\"TERM 1:\", term_1_value)\n", 131 | "term_2_value = Z_expectation_value(circuit_2)\n", 132 | "print(\"TERM 2:\", term_2_value)\n", 133 | "term_3_value = 1\n", 134 | "print(\"TERM 3:\", term_3_value)" 135 | ] 136 | }, 137 | { 138 | "cell_type": "code", 139 | "execution_count": 23, 140 | "metadata": {}, 141 | "outputs": [ 142 | { 143 | "name": "stdout", 144 | "output_type": "stream", 145 | "text": [ 146 | "Energy estimate: 1.9999999999999996\n" 147 | ] 148 | } 149 | ], 150 | "source": [ 151 | "energy_estimate = term_1_value + term_2_value + term_3_value\n", 152 | "print(\"Energy estimate:\", energy_estimate)" 153 | ] 154 | }, 155 | { 156 | "cell_type": "code", 157 | "execution_count": 24, 158 | "metadata": {}, 159 | "outputs": [], 160 | "source": [ 161 | "energy_estimates = []\n", 162 | "term_1_list = []\n", 163 | "term_2_list = []\n", 164 | "term_3_list = []\n", 165 | "\n", 166 | "theta_values = np.linspace(0, 2*np.pi, 100)\n", 167 | "\n", 168 | "for theta in theta_values:\n", 169 | " ansatz = Program([RY(theta, 0)])\n", 170 | " circuit_1 = ansatz\n", 171 | " circuit_2 = ansatz + Program(RY(np.pi/2, 0))\n", 172 | " term_1_value = 2 * Z_expectation_value(circuit_1)\n", 173 | " term_2_value = Z_expectation_value(circuit_2)\n", 174 | " term_3_value = 1\n", 175 | " energy_estimate = term_1_value + term_2_value + term_3_value\n", 176 | " term_1_list.append(term_1_value)\n", 177 | " term_2_list.append(term_2_value)\n", 178 | " term_3_list.append(term_3_value)\n", 179 | " energy_estimates.append(energy_estimate)\n", 180 | " " 181 | ] 182 | }, 183 | { 184 | "cell_type": "code", 185 | "execution_count": 25, 186 | "metadata": {}, 187 | "outputs": [], 188 | "source": [ 189 | "%matplotlib inline\n", 190 | "import matplotlib.pyplot as plt\n", 191 | "import matplotlib.ticker as tck" 192 | ] 193 | }, 194 | { 195 | "cell_type": "code", 196 | "execution_count": 26, 197 | "metadata": {}, 198 | "outputs": [], 199 | "source": [ 200 | "def plot_values(x, y, title=None):\n", 201 | " fig, ax = plt.subplots()\n", 202 | " ax.xaxis.set_major_formatter(tck.FuncFormatter(\n", 203 | " lambda val,pos: '{:.2f}$\\pi$'.format(val/np.pi) if val !=0 else '0'\n", 204 | " ))\n", 205 | " ax.xaxis.set_major_locator(tck.MultipleLocator(base=np.pi/4))\n", 206 | " ax.plot(x, y)\n", 207 | " if title is not None:\n", 208 | " ax.set_title(title)" 209 | ] 210 | }, 211 | { 212 | "cell_type": "code", 213 | "execution_count": 27, 214 | "metadata": {}, 215 | "outputs": [ 216 | { 217 | "data": { 218 | "image/png": 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\n", 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\n", 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\n", 255 | "text/plain": [ 256 | "
" 257 | ] 258 | }, 259 | "metadata": { 260 | "needs_background": "light" 261 | }, 262 | "output_type": "display_data" 263 | } 264 | ], 265 | "source": [ 266 | "plot_values(theta_values, term_1_list, \"Term 1\")\n", 267 | "plot_values(theta_values, term_2_list, \"Term 2\")\n", 268 | "plot_values(theta_values, term_3_list, \"Term 3\")\n", 269 | "plot_values(theta_values, energy_estimates, \"Energy estimate\")" 270 | ] 271 | }, 272 | { 273 | "cell_type": "code", 274 | "execution_count": null, 275 | "metadata": {}, 276 | "outputs": [], 277 | "source": [] 278 | } 279 | ], 280 | "metadata": { 281 | "kernelspec": { 282 | "display_name": "blog-stuff-venv", 283 | "language": "python", 284 | "name": "blog-stuff-venv" 285 | }, 286 | "language_info": { 287 | "codemirror_mode": { 288 | "name": "ipython", 289 | "version": 3 290 | }, 291 | "file_extension": ".py", 292 | "mimetype": "text/x-python", 293 | "name": "python", 294 | "nbconvert_exporter": "python", 295 | "pygments_lexer": "ipython3", 296 | "version": "3.6.8" 297 | } 298 | }, 299 | "nbformat": 4, 300 | "nbformat_minor": 2 301 | } 302 | --------------------------------------------------------------------------------