{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Optimization of a State-to-State Transfer in a Two-Level-System" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2019-07-14T20:35:02.377487Z", "start_time": "2019-07-14T20:35:00.999460Z" }, "attributes": { "classes": [], "id": "", "n": "1" }, "execution": { "iopub.execute_input": "2021-01-13T19:19:44.665929Z", "iopub.status.busy": "2021-01-13T19:19:44.664641Z", "iopub.status.idle": "2021-01-13T19:19:46.393975Z", "shell.execute_reply": "2021-01-13T19:19:46.394993Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Python implementation: CPython\n", "Python version : 3.7.6\n", "IPython version : 7.19.0\n", "\n", "krotov : 1.2.1\n", "qutip : 4.5.0\n", "numpy : 1.17.2\n", "scipy : 1.3.1\n", "matplotlib: 3.3.3\n", "\n" ] } ], "source": [ "# NBVAL_IGNORE_OUTPUT\n", "%load_ext watermark\n", "import qutip\n", "import numpy as np\n", "import scipy\n", "import matplotlib\n", "import matplotlib.pylab as plt\n", "import krotov\n", "%watermark -v --iversions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\newcommand{tr}[0]{\\operatorname{tr}}\n", "\\newcommand{diag}[0]{\\operatorname{diag}}\n", "\\newcommand{abs}[0]{\\operatorname{abs}}\n", "\\newcommand{pop}[0]{\\operatorname{pop}}\n", "\\newcommand{aux}[0]{\\text{aux}}\n", "\\newcommand{opt}[0]{\\text{opt}}\n", "\\newcommand{tgt}[0]{\\text{tgt}}\n", "\\newcommand{init}[0]{\\text{init}}\n", "\\newcommand{lab}[0]{\\text{lab}}\n", "\\newcommand{rwa}[0]{\\text{rwa}}\n", "\\newcommand{bra}[1]{\\langle#1\\vert}\n", "\\newcommand{ket}[1]{\\vert#1\\rangle}\n", "\\newcommand{Bra}[1]{\\left\\langle#1\\right\\vert}\n", "\\newcommand{Ket}[1]{\\left\\vert#1\\right\\rangle}\n", "\\newcommand{Braket}[2]{\\left\\langle #1\\vphantom{#2}\\mid{#2}\\vphantom{#1}\\right\\rangle}\n", "\\newcommand{op}[1]{\\hat{#1}}\n", "\\newcommand{Op}[1]{\\hat{#1}}\n", "\\newcommand{dd}[0]{\\,\\text{d}}\n", "\\newcommand{Liouville}[0]{\\mathcal{L}}\n", "\\newcommand{DynMap}[0]{\\mathcal{E}}\n", "\\newcommand{identity}[0]{\\mathbf{1}}\n", "\\newcommand{Norm}[1]{\\lVert#1\\rVert}\n", "\\newcommand{Abs}[1]{\\left\\vert#1\\right\\vert}\n", "\\newcommand{avg}[1]{\\langle#1\\rangle}\n", "\\newcommand{Avg}[1]{\\left\\langle#1\\right\\rangle}\n", "\\newcommand{AbsSq}[1]{\\left\\vert#1\\right\\vert^2}\n", "\\newcommand{Re}[0]{\\operatorname{Re}}\n", "\\newcommand{Im}[0]{\\operatorname{Im}}$\n", "\n", "This first example illustrates the basic use of the `krotov` package by solving\n", "a simple canonical optimization problem: the transfer of population in a two\n", "level system." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Two-level-Hamiltonian" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We consider the Hamiltonian $\\op{H}_{0} = - \\frac{\\omega}{2} \\op{\\sigma}_{z}$, representing\n", "a simple qubit with energy level splitting $\\omega$ in the basis\n", "$\\{\\ket{0},\\ket{1}\\}$. The control field $\\epsilon(t)$ is assumed to couple via\n", "the Hamiltonian $\\op{H}_{1}(t) = \\epsilon(t) \\op{\\sigma}_{x}$ to the qubit,\n", "i.e., the control field effectively drives transitions between both qubit\n", "states." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2019-07-14T20:35:02.386131Z", "start_time": "2019-07-14T20:35:02.380331Z" }, "execution": { "iopub.execute_input": "2021-01-13T19:19:46.410246Z", "iopub.status.busy": "2021-01-13T19:19:46.408668Z", "iopub.status.idle": "2021-01-13T19:19:46.413830Z", "shell.execute_reply": "2021-01-13T19:19:46.415108Z" } }, "outputs": [], "source": [ "def hamiltonian(omega=1.0, ampl0=0.2):\n", " \"\"\"Two-level-system Hamiltonian\n", "\n", " Args:\n", " omega (float): energy separation of the qubit levels\n", " ampl0 (float): constant amplitude of the driving field\n", " \"\"\"\n", " H0 = -0.5 * omega * qutip.operators.sigmaz()\n", " H1 = qutip.operators.sigmax()\n", "\n", " def guess_control(t, args):\n", " return ampl0 * krotov.shapes.flattop(\n", " t, t_start=0, t_stop=5, t_rise=0.3, func=\"blackman\"\n", " )\n", "\n", " return [H0, [H1, guess_control]]\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2019-07-14T20:35:02.396725Z", "start_time": "2019-07-14T20:35:02.389898Z" }, "execution": { "iopub.execute_input": "2021-01-13T19:19:46.427358Z", "iopub.status.busy": "2021-01-13T19:19:46.425505Z", "iopub.status.idle": "2021-01-13T19:19:46.430133Z", "shell.execute_reply": "2021-01-13T19:19:46.430876Z" } }, "outputs": [], "source": [ "H = hamiltonian()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The control field here switches on from zero at $t=0$ to it's maximum amplitude\n", "0.2 within the time period 0.3 (the switch-on shape is half a [Blackman pulse](https://en.wikipedia.org/wiki/Window_function#Blackman_window)).\n", "It switches off again in the time period 0.3 before the\n", "final time $T=5$). We use a time grid with 500 time steps between 0 and $T$:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2019-07-14T20:35:02.403354Z", "start_time": "2019-07-14T20:35:02.399999Z" }, "execution": { "iopub.execute_input": "2021-01-13T19:19:46.442452Z", "iopub.status.busy": "2021-01-13T19:19:46.441005Z", "iopub.status.idle": "2021-01-13T19:19:46.445245Z", "shell.execute_reply": "2021-01-13T19:19:46.446218Z" }, "lines_to_next_cell": 2 }, "outputs": [], "source": [ "tlist = np.linspace(0, 5, 500)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2019-07-14T20:35:02.410815Z", "start_time": "2019-07-14T20:35:02.405695Z" }, "attributes": { "classes": [], "id": "", "n": "10" }, "execution": { "iopub.execute_input": "2021-01-13T19:19:46.460637Z", "iopub.status.busy": "2021-01-13T19:19:46.459158Z", "iopub.status.idle": "2021-01-13T19:19:46.466454Z", "shell.execute_reply": "2021-01-13T19:19:46.468083Z" } }, "outputs": [], "source": [ "def plot_pulse(pulse, tlist):\n", " fig, ax = plt.subplots()\n", " if callable(pulse):\n", " pulse = np.array([pulse(t, args=None) for t in tlist])\n", " ax.plot(tlist, pulse)\n", " ax.set_xlabel('time')\n", " ax.set_ylabel('pulse amplitude')\n", " plt.show(fig)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2019-07-14T20:35:02.628919Z", "start_time": "2019-07-14T20:35:02.413216Z" }, "attributes": { "classes": [], "id": "", "n": "11" }, "execution": { "iopub.execute_input": "2021-01-13T19:19:46.517368Z", "iopub.status.busy": "2021-01-13T19:19:46.515875Z", "iopub.status.idle": "2021-01-13T19:19:46.829993Z", "shell.execute_reply": "2021-01-13T19:19:46.830896Z" } }, "outputs": [ { "data": { "image/png": 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akdPNjnsp8OvACkmfLNrVhVcAnFR+2djGrMMwszmoPfluqfWmqj1AH3AZ8GBR+QDwv9IMqh7lTowzPDbu9cbNLBWdyXdLLTwEeLrZcX8E/EjSF5OObjuNQvWx3TUOM0tBXdQ4JN0ZEW8BHpYUE/dHxMtSjazODI56gkMzS09TYwOtTQ21nTiA9yV/31SNQOrdkCc4NLOUdbbVxnxVp2uq2pv8fap64dSvwhA5Jw4zS0utzJB7uqaqAaC4iUrJtoCIiK6UY6srhX/MTicOM0tJe0uNJ46I6Jxqn53KTVVmlraOtqaaeACwpG85SS8HfoV8jeMHpSzkNN8MeNlYM0tZR2sT+waGsw5j+ifHJd1EfqnYpeTnhvqcpD9KO7B6M+TEYWYpyy8fW8NPjhd5O/BLETEMIOnPgS3U0OSCtcBNVWaWtvbW2miqKmWuqj1AW9F2K2WsqzFfDIzkaGlsoKXJy8aaWTo6Whtru3O8yFFgq6R7yPdxvAF4oDB/VUT8Torx1Y2hkdzJhVbMzNLQ0drM8bETnBgPGhuUWRylfNN9LXkVfDedUOrb0MgJTzdiZqkqfMcMjuRYtCC7efGmTRwR8flqBFLvBoZznuDQzFLVUbSYU5aJo5RRVW+S9LCkQ5L6JQ1I6i/l4pLWS9omabukGyfZf7GkhyTlJF0xYd81kn6avK4pKn+FpEeTa34yWUI2c0OeUt3MUlZoDh/MuJ+jlJ7cvwSuAZZGRFdEdJby1LikRuAW4FJgHXC1pHUTDnsauBb40oRzlwAfAi4CLgQ+JKk72f03wLuBtclrfQn3kLqhUS/iZGbpKtQ46iFxPAM8FhGnzJA7jQuB7RGxIyJGgTuYsFZ5ROyMiEeA8QnnvhG4JyIORcRh4B5gvaQzga6IuC+J53bg8jLjSsXgsJeNNbN0FWbfHsx4SG4p33S/B2yS9D1gpFAYER+f5rwV5JNOwS7yNYhSTHbuiuS1a5LyU0i6HrgeYNWqVSV+7MwNer1xM0tZex3VOD4KHCP/LEdn0aumRcStEdEbEb09PT2pf57XGzeztJ1sqqqDGsfzIuLcGVx7N3BW0fZKSn9wcDfwqxPO/W5SvnKG10zN+HhwbPSEaxxmlqpaWT62lBrHJkmXzODam4G1ktZIagGuAjaWeO7dwCWSupNO8UuAu5M1QvolvTIZTfUu4OsziK2ihkY9T5WZpe/kcxwZ1zhKSRz/HfhnScfLGY6brFN+A/kk8ARwZ0RslXSzpMsAJF0gaRdwJfApSVuTcw8Bf0o++WwGbk7KAN4D/B2wHfgZ8K0y7jcVg56nysyqoKmxgQXNjQyOjGUbx3QHzGZdjojYBGyaUHZT0fvN/HzTU/FxtwG3TVLeB8yk6Sw1J2fG9ZQjZpayjrYmBjOeIbfU9Ti6yT8zcXKyw4j4flpB1ZvCP6IfADSztHW2NmU+qmraxCHpvwHvI18z2AK8Evgh8NpUI6sjhfZGTzliZmnraGticDjbpqpS+jjeB1wAPBURvwacDxxJM6h681wfh2scZpaujhqocZSSOIaLFnFqjYgfAy9KN6z64tX/zKxaOmpgMadSvul2SVoM/CNwj6TDwFNpBlVvBp04zKxKaqHGUcqoqv+cvP2wpHuBRcA/pxpVnfFwXDOrlvyoqhpPHMUi4ntpBVLPhkZyNDWIVi8ba2Yp62htYnA4R0SQ1aoS/qargMFk2dgaWRrEzOawjrYmcuPBSG7ipOLV48RRAYMjOdpb3ExlZunrTJrEs+wgLylxSDpb0uuT9wsk1fzsuNU05CnVzaxKamEVwFKWjn03cBfwqaRoJfkRVpYoNFWZmaWt8KBxlhMdllLjeC/wKqAfICJ+CpyRZlD1ZnDkhEdUmVlVFFo3BjKc6LCUxDGSLP0KgKQmoNxlZOe0oZHcyXZHM7M01cLysaUkju9J+gNggaQ3AF8B/indsOrL4HDO042YWVUUahyFdYCyUEriuBHYDzwK/Bb5adL/KM2g6s2Ql401syppr4HlY0t5cnwc+DTwaUlLgJUR4aaqxPh4MDiao7PNM+OaWfoKTVVZLh9byqiq70rqSpLGg+QTyCdKubik9ZK2Sdou6cZJ9rdK+nKy/35Jq5Pyt0vaUvQal3ReUTzbivZl2lE/OJojAro8qsrMqqC1qYGmBtV8H8eiiOgHfhO4PSIuAl433UmSGoFbgEuBdcDVktZNOOw64HBEvAD4BPAxgIj4YkScFxHnAe8EnoyILUXnvb2wPyL2lXAPqSk8hNPpxGFmVSAp8/mqSkkcTZLOBN4CfKOMa18IbI+IHcmorDuADROO2QB8Pnl/F/A6nTpvx9XJuTVpIFlQxU1VZlYthfmqslJK4rgZuJt8Etgs6RzgpyWctwJ4pmh7V1I26TERkQOOAksnHPNW4B8mlH02aab640kSDQCSrpfUJ6lv//79JYQ7M65xmFm1dbQ21XYfR0R8JSJeFhHvSbZ3RMSb0w8NJF0EHIuIx4qK3x4RLwVenbzeOdm5EXFrRPRGRG9PT09qMbrGYWbV1tmWbY1jyp/Jkv6K0zzoFxG/M821dwNnFW2vTMomO2ZX8mDhIuBg0f6rmFDbiIjdyd8BSV8i3yR2+zSxpKb/uGscZlZdHa1NHBgcnf7AlJzu265vltfeDKyVtIZ8grgKeNuEYzYC1wA/BK4AvlMY6iupgXy/yqsLByfJZXFEHJDUDLwJ+H+zjHNWnqtxOHGYWXV0tDWz8+CxzD5/ym+7iPj8VPtKERE5STeQ7x9pBG6LiK2Sbgb6ImIj8BngC5K2A4fIJ5eCi4FnImJHUVkrcHeSNBrJJ41PzybO2epPqotdbqoysyrpaG3MdFr1aX8mJ8vFntJkFRGvne7ciNhE/knz4rKbit4PA1dOce53gVdOKBsCXjHd51bTwHCO5kav/mdm1ZNfdzy7SQ5LaV/5QNH7NuDNQLYL3taQgeExOtuavfqfmVVNR2szw2PjjJ0Yp7mx+j9aS5ly5MEJRf8m6YGU4qk7A8M592+YWVUtWvDcKoBL2luq/vmlNFUtKdpsIN9UtCi1iOpMvsbhxGFm1dO1IN+n2n98rDYTB/n5qQIQ+SaqJ8lPFWIkNY5Wd4ybWfUUBuMcPZ5NP0cpTVVrqhFIvRoYznH20oVZh2Fm88jJGsdwjSYOSW3Ae4BfIV/z+Ffgb5MRUfNeoXPczKxaFp1sqspmnFIpTVW3AwPAXyXbbwO+wBTDaOcbd46bWbV1JZ3jNVvjAM6NiOLp0O+V9HhaAdWTE+PBwEjOa3GYWVUV+jj6M+rjKGUA8EOSTj6Il0w8ONvpSOaEwnz4bqoys2pa2NJIY4Nqt3Oc/PDbf5f0dLK9Ctgm6VEgIuJlqUVX4zxPlZllQRJdbU013VS1PvUo6tRza3G4xmFm1bVoQXPtdo5HxFPVCKQeHTmWz/bdC504zKy6uhY0Z1bj8Mx8s1BoXyyMqTYzq5autuaa7hy3KRw9nl9IZbFrHGZWZV0LmjLrHHfimIVCU9XihdWfK8bM5rdFC5pPrgdUbakmDknrJW2TtF3SjZPsb5X05WT//ZJWJ+WrJR2XtCV5/W3ROa+Q9GhyzieV4XzmR4+P0dQg2lsaswrBzOapOdlUJakRuAW4FFgHXC1p3YTDrgMOR8QLgE8AHyva97OIOC95/XZR+d8A7wbWJq/MRn0dOT7GogVei8PMqq9rQTMjuXGGx05U/bPTrHFcCGyPiB0RMQrcAWyYcMwGoLBE7V3A605Xg5B0JtAVEfcla5PfDlxe8chLdPTYGIvcv2FmGSjMWJHFErJpJo4VwDNF27uSskmPiYgccBRYmuxbI+lhSd+T9Oqi43dNc00AJF0vqU9S3/79+2d3J1M4cnyUxR5RZWYZKIzmzKKDvFY7x/cCqyLifOD9wJckdZVzgYi4NSJ6I6K3p6cnlSCPHh9zx7iZZWKuJo7dwFlF2yuTskmPkdREfmXBgxExEhEH4eTStT8DXpgcv3Kaa1bNkWNjJ6c3NjOrpu7kR2vhsYBqSjNxbAbWSlojqQW4Ctg44ZiNwDXJ+yuA70RESOpJOteRdA75TvAdEbEX6Jf0yqQv5F3A11O8h9M66sRhZhkpzFhxaKj6NY7UZueLiJykG4C7gUbgtojYKulmoC8iNgKfAb4gaTtwiHxyAbgYuFnSGDAO/HZEHEr2vQf4HLAA+FbyqrrciXEGRnJ++M/MMtGdrDV+eKj6NY5Up3WNiE3ApgllNxW9H2aSBaEi4qvAV6e4Zh9wbmUjLV/hwRt3jptZFjpbm2hqEIePza2mqjntSPKP5eG4ZpYFSSxe2OLEUU+OJCMZFi/wqCozy8aS9mYOZdBU5cQxQ4UhcK5xmFlWuhe2cPjY3BqOO6cdLUxw6D4OM8tI98KWTDrHnThmqFA97PYDgGaWke5293HUlYNDIzQ1yM9xmFlmlrQ3c/jYGPmp+6rHiWOGDgyMsqS9hYYGz4xrZtnoXtjCifGo+rocThwzdHBohKUdrVmHYWbzWKGpvNr9HE4cM3RgcJRlHe7fMLPsLCk8PV7lfg4njhk6ODTC0nYnDjPLTmHKIyeOOnFwcNRNVWaWqUKNo9oTHTpxzMCx0RzHRk+wzInDzDLUfTJxjFT1c504ZuDgYL5auNR9HGaWoc7WJtqaG9g/4MRR8w4M5v+R3DluZlmSxBmdbTzb78RR807WONrdVGVm2Vre1cq+geGqfqYTxwwUahxuqjKzrJ3R2ca+uVTjkLRe0jZJ2yXdOMn+VklfTvbfL2l1Uv4GSQ9KejT5+9qic76bXHNL8jojzXuYzMHkYRt3jptZ1no6W9lX5T6O1FYATNYMvwV4A7AL2CxpY0Q8XnTYdcDhiHiBpKuAjwFvBQ4AvxEReySdS3752RVF5709WQkwEwcGR+hobaKtuTGrEMzMAFje1cbgSI6hkRztraku6npSmjWOC4HtEbEjIkaBO4ANE47ZAHw+eX8X8DpJioiHI2JPUr4VWCCpZn7e7+sfoaezZsIxs3nsjOS7qJq1jjQTxwrgmaLtXfx8reHnjomIHHAUWDrhmDcDD0VE8f8qn02aqf5Y0qSzDEq6XlKfpL79+/fP5j5OsfvIcZ63uK2i1zQzm4nlXfnvomf7q9dBXtOd45J+kXzz1W8VFb89Il4KvDp5vXOycyPi1ojojYjenp6eisa19+hxzly0oKLXNDObiTO65laNYzdwVtH2yqRs0mMkNQGLgIPJ9krga8C7IuJnhRMiYnfydwD4EvkmsaoZzY2zb2CE5y124jCz7C3vzNc49s2RGsdmYK2kNZJagKuAjROO2Qhck7y/AvhORISkxcA3gRsj4t8KB0tqkrQsed8MvAl4LMV7OMWz/cNEwAo3VZlZDeha0ERLU8PcqHEkfRY3kB8R9QRwZ0RslXSzpMuSwz4DLJW0HXg/UBiyewPwAuCmCcNuW4G7JT0CbCFfY/l0WvcwmT1HjgO4xmFmNUESy7ta+Y+j1atxpDp2KyI2AZsmlN1U9H4YuHKS8z4CfGSKy76ikjGWa8/RfOJwH4eZ1YqVixey6/Cxqn1eTXeO16I9R/JZ3aOqzKxWnL10IU8ddOKoWXuOHKd7YTMLW6rzoI2Z2XRWLV3IwaFRBkeqs/a4E0eZ9hzxUFwzqy1nL2kH4KmDQ1X5PCeOMu05MuyOcTOrKWcvXQjA01VqrnLiKMP4eLDz4BBrli3MOhQzs5MKiWOnE0ft2X3kOCO5cc7p6cg6FDOzkzrbmlnS3sLTh9xUVXN2HMj/o5yzrD3jSMzMfl41R1Y5cZRhx/5BANc4zKzmrF7azs4DrnHUnCf29rO0vcVrjZtZzVm7vIM9R4c5enws9c9y4ijDE3sHeMmZXUwxk7uZWWZecmYXAD/e25/6ZzlxlGjsxDjbnh3gJWd2Zh2Kmdkp1iWJY+seJ46a8cTefkZz47x05eKsQzEzO8UZna0s72plyzNHUv8sJ44S9e08DMAFq7szjsTM7FSS6F29hAefOpz6ZzlxlOj+Jw+ysnuBpxsxs5p1wdnd7D5ynGcOpTss14mjBCO5E/zgpwd4zQsruwStmVklveZFZwDwnR/vS/VznDhK8K8/OcDQ6Ale95Izsg7FzGxKa5a1c05PO996bG+qn5Nq4pC0XtI2Sdsl3TjJ/lZJX0723y9pddG+Dybl2yS9sdRrpuFLDzxNT2crr17rGoeZ1bY3v3wl9+04xPZ9g6l9RmqJQ1IjcAtwKbAOuFrSugmHXQccjogXAJ8APpacu478GuW/CKwH/lpSY4nXrKjv/2Q/3/nxPt75yrNpbnQFzcxq21svOIuFLY189JuPc2I8UvmMNL8JLwS2R8SOiBgF7gA2TDhmA/D55P1dwOuUf7puA3BHRIxExJPA9uR6pVyzYv7ga4/yXz+3mef3tPPuV5+T1seYmVXMso5Wfu+NL+Lebft5/ce/x0+eHaj4Z6S5jN0K4Jmi7V3ARVMdExE5SUeBpUn5fRPOXZG8n+6aAEi6HrgeYNWqVTO6gZXdC7jml1fz2695PgtaGmd0DTOzarv2VWtYvLCFrz28mxUprB80Z9c/jYhbgVsBent7Z1Rfe8+vvqCiMZmZVcvl56/g8vNXTH/gDKTZVLUbOKtoe2VSNukxkpqARcDB05xbyjXNzCxFaSaOzcBaSWsktZDv7N444ZiNwDXJ+yuA70REJOVXJaOu1gBrgQdKvKaZmaUotaaqpM/iBuBuoBG4LSK2SroZ6IuIjcBngC9I2g4cIp8ISI67E3gcyAHvjYgTAJNdM617MDOzUyn/A39u6+3tjb6+vqzDMDOrK5IejIjeieV+MMHMzMrixGFmZmVx4jAzs7I4cZiZWVnmRee4pP3AUzM8fRlwoILh1APf8/zge577Znu/Z0fEKbO7zovEMRuS+iYbVTCX+Z7nB9/z3JfW/bqpyszMyuLEYWZmZXHimN6tWQeQAd/z/OB7nvtSuV/3cZiZWVlc4zAzs7I4cZiZWVmcOE5D0npJ2yRtl3Rj1vGkTdJtkvZJeizrWKpB0lmS7pX0uKStkt6XdUxpk9Qm6QFJP0ru+U+yjqlaJDVKeljSN7KOpRok7ZT0qKQtkio6y6v7OKYgqRH4CfAG8kvUbgaujojHMw0sRZIuBgaB2yPi3KzjSZukM4EzI+IhSZ3Ag8Dlc/zfWEB7RAxKagZ+ALwvIu6b5tS6J+n9QC/QFRFvyjqetEnaCfRGRMUfeHSNY2oXAtsjYkdEjAJ3ABsyjilVEfF98uuizAsRsTciHkreDwBP8Nza9nNS5A0mm83Ja87/epS0EvhPwN9lHctc4MQxtRXAM0Xbu5jjXyrzmaTVwPnA/RmHkrqkyWYLsA+4JyLm/D0Dfwn8HjCecRzVFMC/SHpQ0vWVvLATh817kjqArwL/MyL6s44nbRFxIiLOA1YCF0qa082Skt4E7IuIB7OOpcp+JSJeDlwKvDdpiq4IJ46p7QbOKtpemZTZHJK0838V+GJE/N+s46mmiDgC3AuszziUtL0KuCxp878DeK2kv882pPRFxO7k7z7ga+Sb3yvCiWNqm4G1ktZIaiG/HvrGjGOyCko6ij8DPBERH886nmqQ1CNpcfJ+AfnBHz/ONKiURcQHI2JlRKwm/9/xdyLiHRmHlSpJ7cmADyS1A5cAFRst6cQxhYjIATcAd5PvNL0zIrZmG1W6JP0D8EPgRZJ2Sbou65hS9irgneR/gW5JXr+edVApOxO4V9Ij5H8c3RMR82J46jyzHPiBpB8BDwDfjIh/rtTFPRzXzMzK4hqHmZmVxYnDzMzK4sRhZmZlceIwM7OyOHGYmVlZnDjMKkzSYknvSd4/T9JdWcdkVkkejmtWYcm8V9+YDzMM2/zUlHUAZnPQnwPPTyYS/Cnwkog4V9K1wOVAO7AW+D9AC/mHEEeAX4+IQ5KeD9wC9ADHgHdHxJx+utvqi5uqzCrvRuBnyUSCvzth37nAbwIXAB8FjkXE+eSf2H9XcsytwP+IiFcAHwD+uhpBm5XKNQ6z6ro3WftjQNJR4J+S8keBlyUz9f4y8JX8VFoAtFY/TLOpOXGYVddI0fvxou1x8v89NgBHktqKWU1yU5VZ5Q0AnTM5MVkP5ElJV0J+Bl9Jv1TJ4Mxmy4nDrMIi4iDwb5IeA/5iBpd4O3BdMrPpVub4ksVWfzwc18zMyuIah5mZlcWJw8zMyuLEYWZmZXHiMDOzsjhxmJlZWZw4zMysLE4cZmZWlv8PGfdd/VcJB5EAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_pulse(H[1][1], tlist)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Optimization target" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `krotov` package requires the goal of the optimization to be described by a\n", "list of `Objective` instances. In this example, there is only a single\n", "objective: the state-to-state transfer from initial state $\\ket{\\Psi_{\\init}} =\n", "\\ket{0}$ to the target state $\\ket{\\Psi_{\\tgt}} = \\ket{1}$, under the dynamics\n", "of the Hamiltonian $\\op{H}(t)$:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2019-07-14T20:35:02.638222Z", "start_time": "2019-07-14T20:35:02.631007Z" }, "execution": { "iopub.execute_input": "2021-01-13T19:19:46.841392Z", "iopub.status.busy": "2021-01-13T19:19:46.840244Z", "iopub.status.idle": "2021-01-13T19:19:46.844821Z", "shell.execute_reply": "2021-01-13T19:19:46.845680Z" } }, "outputs": [ { "data": { "text/plain": [ "[Objective[|Ψ₀(2)⟩ to |Ψ₁(2)⟩ via [H₀[2,2], [H₁[2,2], u₁(t)]]]]" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "objectives = [\n", " krotov.Objective(\n", " initial_state=qutip.ket(\"0\"), target=qutip.ket(\"1\"), H=H\n", " )\n", "]\n", "\n", "objectives" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In addition, we would like to maintain the property of the control field to be\n", "zero at $t=0$ and $t=T$, with a smooth switch-on and switch-off. We can define\n", "an \"update shape\" $S(t) \\in [0, 1]$ for this purpose: Krotov's method will\n", "update the field at each point in time proportionally to $S(t)$; wherever\n", "$S(t)$ is zero, the optimization will not change the value of the control from\n", "the original guess." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2019-07-14T20:35:02.647393Z", "start_time": "2019-07-14T20:35:02.642363Z" }, "execution": { "iopub.execute_input": "2021-01-13T19:19:46.853270Z", "iopub.status.busy": "2021-01-13T19:19:46.849902Z", "iopub.status.idle": "2021-01-13T19:19:46.857772Z", "shell.execute_reply": "2021-01-13T19:19:46.858640Z" }, "lines_to_next_cell": 2 }, "outputs": [], "source": [ "def S(t):\n", " \"\"\"Shape function for the field update\"\"\"\n", " return krotov.shapes.flattop(\n", " t, t_start=0, t_stop=5, t_rise=0.3, t_fall=0.3, func='blackman'\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Beyond the shape, Krotov's method uses a parameter $\\lambda_a$ for each control\n", "field that determines the overall magnitude of the respective field in each\n", "iteration (the smaller $\\lambda_a$, the larger the update; specifically, the\n", "update is proportional to $\\frac{S(t)}{\\lambda_a}$). Both the update-shape\n", "$S(t)$ and the $\\lambda_a$ parameter must be passed to the optimization routine\n", "as \"pulse options\":" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2019-07-14T20:35:02.654998Z", "start_time": "2019-07-14T20:35:02.651951Z" }, "execution": { "iopub.execute_input": "2021-01-13T19:19:46.864597Z", "iopub.status.busy": "2021-01-13T19:19:46.863114Z", "iopub.status.idle": "2021-01-13T19:19:46.869516Z", "shell.execute_reply": "2021-01-13T19:19:46.871919Z" }, "lines_to_next_cell": 0 }, "outputs": [], "source": [ "pulse_options = {\n", " H[1][1]: dict(lambda_a=5, update_shape=S)\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simulate dynamics under the guess field" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before running the optimization procedure, we first simulate the dynamics under the\n", "guess field $\\epsilon_{0}(t)$. The following solves equation of motion for the\n", "defined objective, which contains the initial state $\\ket{\\Psi_{\\init}}$ and\n", "the Hamiltonian $\\op{H}(t)$ defining its evolution. This delegates to QuTiP's\n", "usual `mesolve` function." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use the projectors $\\op{P}_0 = \\ket{0}\\bra{0}$ and $\\op{P}_1 = \\ket{1}\\bra{1}$ for calculating the population:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2019-07-14T20:35:02.663991Z", "start_time": "2019-07-14T20:35:02.658095Z" }, "execution": { "iopub.execute_input": "2021-01-13T19:19:46.879910Z", "iopub.status.busy": "2021-01-13T19:19:46.877805Z", "iopub.status.idle": "2021-01-13T19:19:46.883375Z", "shell.execute_reply": "2021-01-13T19:19:46.884311Z" } }, "outputs": [], "source": [ "proj0 = qutip.ket2dm(qutip.ket(\"0\"))\n", "proj1 = qutip.ket2dm(qutip.ket(\"1\"))" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "ExecuteTime": { "end_time": "2019-07-14T20:35:02.860043Z", "start_time": "2019-07-14T20:35:02.666497Z" }, "attributes": { "classes": [], "id": "", "n": "12" }, "execution": { "iopub.execute_input": "2021-01-13T19:19:47.061381Z", "iopub.status.busy": "2021-01-13T19:19:47.059865Z", "iopub.status.idle": "2021-01-13T19:19:47.063073Z", "shell.execute_reply": "2021-01-13T19:19:47.063965Z" } }, "outputs": [], "source": [ "guess_dynamics = objectives[0].mesolve(tlist, e_ops=[proj0, proj1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plot of the population dynamics shows that the guess field does not transfer\n", "the initial state $\\ket{\\Psi_{\\init}} = \\ket{0}$ to the desired target state\n", "$\\ket{\\Psi_{\\tgt}} = \\ket{1}$ (so the optimization will have something to do)." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "ExecuteTime": { "end_time": "2019-07-14T20:35:02.869215Z", "start_time": "2019-07-14T20:35:02.862523Z" }, "attributes": { "classes": [], "id": "", "n": "13" }, "execution": { "iopub.execute_input": "2021-01-13T19:19:47.071001Z", "iopub.status.busy": "2021-01-13T19:19:47.069947Z", "iopub.status.idle": "2021-01-13T19:19:47.072686Z", "shell.execute_reply": "2021-01-13T19:19:47.073366Z" } }, "outputs": [], "source": [ "def plot_population(result):\n", " fig, ax = plt.subplots()\n", " ax.plot(result.times, result.expect[0], label='0')\n", " ax.plot(result.times, result.expect[1], label='1')\n", " ax.legend()\n", " ax.set_xlabel('time')\n", " ax.set_ylabel('population')\n", " plt.show(fig)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "ExecuteTime": { "end_time": "2019-07-14T20:35:03.080846Z", "start_time": "2019-07-14T20:35:02.871928Z" }, "attributes": { "classes": [], "id": "", "n": "14" }, "execution": { "iopub.execute_input": "2021-01-13T19:19:47.104604Z", "iopub.status.busy": "2021-01-13T19:19:47.103399Z", "iopub.status.idle": "2021-01-13T19:19:47.271946Z", "shell.execute_reply": "2021-01-13T19:19:47.272416Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_population(guess_dynamics)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Optimize" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the following we optimize the guess field $\\epsilon_{0}(t)$ such\n", "that the intended state-to-state transfer $\\ket{\\Psi_{\\init}} \\rightarrow\n", "\\ket{\\Psi_{\\tgt}}$ is solved, via the `krotov` package's central\n", "`optimize_pulses` routine. It requires, besides the previously defined\n", "`objectives`, information about the optimization functional $J_T$ (implicitly,\n", "via `chi_constructor`, which calculates the states $\\ket{\\chi} =\n", "\\frac{J_T}{\\bra{\\Psi}}$).\n", "\n", "Here, we choose $J_T = J_{T,\\text{ss}} = 1 - F_{\\text{ss}}$ with $F_{\\text{ss}}\n", "= \\Abs{\\Braket{\\Psi_{\\tgt}}{\\Psi(T)}}^2$, with $\\ket{\\Psi(T)}$ the forward\n", "propagated state of $\\ket{\\Psi_{\\init}}$. Even though $J_T$ is not explicitly\n", "required for the optimization, it is nonetheless useful to be able to calculate\n", "and print it as a way to provide some feedback about the optimization progress.\n", "Here, we pass as an `info_hook` the function `krotov.info_hooks.print_table`,\n", "using `krotov.functionals.J_T_ss` (which implements the above functional; the\n", "`krotov` library contains implementations of all the \"standard\" functionals used in\n", "quantum control). This `info_hook` prints a tabular overview after each\n", "iteration, containing the value of $J_T$, the magnitude of the integrated pulse\n", "update, and information on how much $J_T$ (and the full Krotov functional $J$)\n", "changes between iterations. It also stores the value of $J_T$ internally in the\n", "`Result.info_vals` attribute.\n", "\n", "The value of $J_T$ can also be used to check the convergence. In this example,\n", "we limit the number of total iterations to 10, but more generally, we could use\n", "the `check_convergence` parameter to stop the optimization when $J_T$ falls below\n", "some threshold. Here, we only pass a function that checks that the value of\n", "$J_T$ is monotonically decreasing. The\n", "`krotov.convergence.check_monotonic_error` relies on\n", "`krotov.info_hooks.print_table` internally having stored the value of $J_T$ to\n", "the `Result.info_vals` in each iteration." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "ExecuteTime": { "end_time": "2019-07-14T20:35:28.180958Z", "start_time": "2019-07-14T20:35:03.083981Z" }, "attributes": { "classes": [], "id": "", "n": "15" }, "execution": { "iopub.execute_input": "2021-01-13T19:19:47.283227Z", "iopub.status.busy": "2021-01-13T19:19:47.277756Z", "iopub.status.idle": "2021-01-13T19:20:24.011943Z", "shell.execute_reply": "2021-01-13T19:20:24.012611Z" }, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "iter. J_T ∫gₐ(t)dt J ΔJ_T ΔJ secs\n", "0 9.51e-01 0.00e+00 9.51e-01 n/a n/a 1\n", "1 9.24e-01 2.32e-03 9.27e-01 -2.71e-02 -2.47e-02 1\n", "2 8.83e-01 3.53e-03 8.87e-01 -4.11e-02 -3.76e-02 1\n", "3 8.23e-01 5.22e-03 8.28e-01 -6.06e-02 -5.54e-02 1\n", "4 7.37e-01 7.39e-03 7.45e-01 -8.52e-02 -7.78e-02 2\n", "5 6.26e-01 9.75e-03 6.36e-01 -1.11e-01 -1.02e-01 2\n", "6 4.96e-01 1.16e-02 5.07e-01 -1.31e-01 -1.19e-01 2\n", "7 3.62e-01 1.21e-02 3.74e-01 -1.34e-01 -1.22e-01 2\n", "8 2.44e-01 1.09e-02 2.55e-01 -1.18e-01 -1.07e-01 1\n", "9 1.53e-01 8.42e-03 1.62e-01 -9.03e-02 -8.18e-02 2\n", "10 9.20e-02 5.79e-03 9.78e-02 -6.14e-02 -5.56e-02 2\n", "11 5.35e-02 3.66e-03 5.71e-02 -3.85e-02 -3.48e-02 1\n", "12 3.06e-02 2.19e-03 3.28e-02 -2.29e-02 -2.07e-02 1\n", "13 1.73e-02 1.27e-03 1.86e-02 -1.32e-02 -1.20e-02 2\n", "14 9.78e-03 7.24e-04 1.05e-02 -7.54e-03 -6.82e-03 1\n", "15 5.52e-03 4.10e-04 5.92e-03 -4.26e-03 -3.86e-03 1\n", "16 3.11e-03 2.31e-04 3.34e-03 -2.40e-03 -2.17e-03 1\n", "17 1.76e-03 1.30e-04 1.89e-03 -1.36e-03 -1.22e-03 1\n", "18 9.91e-04 7.35e-05 1.06e-03 -7.64e-04 -6.90e-04 1\n" ] } ], "source": [ "opt_result = krotov.optimize_pulses(\n", " objectives,\n", " pulse_options=pulse_options,\n", " tlist=tlist,\n", " propagator=krotov.propagators.expm,\n", " chi_constructor=krotov.functionals.chis_ss,\n", " info_hook=krotov.info_hooks.print_table(J_T=krotov.functionals.J_T_ss),\n", " check_convergence=krotov.convergence.Or(\n", " krotov.convergence.value_below('1e-3', name='J_T'),\n", " krotov.convergence.check_monotonic_error,\n", " ),\n", " store_all_pulses=True,\n", ")" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "ExecuteTime": { "end_time": "2019-07-14T20:35:28.188546Z", "start_time": "2019-07-14T20:35:28.182914Z" }, "attributes": { "classes": [], "id": "", "n": "16" }, "execution": { "iopub.execute_input": "2021-01-13T19:20:24.017864Z", "iopub.status.busy": "2021-01-13T19:20:24.016620Z", "iopub.status.idle": "2021-01-13T19:20:24.020480Z", "shell.execute_reply": "2021-01-13T19:20:24.021053Z" } }, "outputs": [ { "data": { "text/plain": [ "Krotov Optimization Result\n", "--------------------------\n", "- Started at 2021-01-13 14:19:47\n", "- Number of objectives: 1\n", "- Number of iterations: 18\n", "- Reason for termination: Reached convergence: J_T < 1e-3\n", "- Ended at 2021-01-13 14:20:24 (0:00:37)" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "opt_result" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simulate the dynamics under the optimized field" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Having obtained the optimized control field, we can simulate the dynamics to\n", "verify that the optimized field indeed drives the initial state\n", "$\\ket{\\Psi_{\\init}} = \\ket{0}$ to the desired target state\n", "$\\ket{\\Psi_{\\tgt}} = \\ket{1}$." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "ExecuteTime": { "end_time": "2019-07-14T20:35:28.702476Z", "start_time": "2019-07-14T20:35:28.429551Z" }, "attributes": { "classes": [], "id": "", "n": "18" }, "execution": { "iopub.execute_input": "2021-01-13T19:20:24.180368Z", "iopub.status.busy": "2021-01-13T19:20:24.179669Z", "iopub.status.idle": "2021-01-13T19:20:24.181940Z", "shell.execute_reply": "2021-01-13T19:20:24.182439Z" } }, "outputs": [], "source": [ "opt_dynamics = opt_result.optimized_objectives[0].mesolve(\n", " tlist, e_ops=[proj0, proj1])" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "ExecuteTime": { "end_time": "2019-07-14T20:35:28.937680Z", "start_time": "2019-07-14T20:35:28.705190Z" }, "attributes": { "classes": [], "id": "", "n": "19" }, "execution": { "iopub.execute_input": "2021-01-13T19:20:24.224283Z", "iopub.status.busy": "2021-01-13T19:20:24.222618Z", "iopub.status.idle": "2021-01-13T19:20:24.408840Z", "shell.execute_reply": "2021-01-13T19:20:24.409310Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_population(opt_dynamics)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To gain some intuition on how the controls and the dynamics change throughout the optimization procedure, we can generate a plot of the control fields and the dynamics after each iteration of the optimization algorithm. This is possible because we set `store_all_pulses=True` in the call to `optimize_pulses`, which allows to recover the optimized controls from each iteration from `Result.all_pulses`. The flag is not set to True by default, as for long-running optimizations with thousands or tens of thousands iterations, the storage of all control fields may require significant memory." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "execution": { "iopub.execute_input": "2021-01-13T19:20:24.421916Z", "iopub.status.busy": "2021-01-13T19:20:24.420852Z", "iopub.status.idle": "2021-01-13T19:20:24.423448Z", "shell.execute_reply": "2021-01-13T19:20:24.423968Z" } }, "outputs": [], "source": [ "def plot_iterations(opt_result):\n", " \"\"\"Plot the control fields in population dynamics over all iterations.\n", "\n", " This depends on ``store_all_pulses=True`` in the call to\n", " `optimize_pulses`.\n", " \"\"\"\n", " fig, [ax_ctr, ax_dyn] = plt.subplots(nrows=2, figsize=(8, 10))\n", " n_iters = len(opt_result.iters)\n", " for (iteration, pulses) in zip(opt_result.iters, opt_result.all_pulses):\n", " controls = [\n", " krotov.conversions.pulse_onto_tlist(pulse)\n", " for pulse in pulses\n", " ]\n", " objectives = opt_result.objectives_with_controls(controls)\n", " dynamics = objectives[0].mesolve(\n", " opt_result.tlist, e_ops=[proj0, proj1]\n", " )\n", " if iteration == 0:\n", " ls = '--' # dashed\n", " alpha = 1 # full opacity\n", " ctr_label = 'guess'\n", " pop_labels = ['0 (guess)', '1 (guess)']\n", " elif iteration == opt_result.iters[-1]:\n", " ls = '-' # solid\n", " alpha = 1 # full opacity\n", " ctr_label = 'optimized'\n", " pop_labels = ['0 (optimized)', '1 (optimized)']\n", " else:\n", " ls = '-' # solid\n", " alpha = 0.5 * float(iteration) / float(n_iters) # max 50%\n", " ctr_label = None\n", " pop_labels = [None, None]\n", " ax_ctr.plot(\n", " dynamics.times,\n", " controls[0],\n", " label=ctr_label,\n", " color='black',\n", " ls=ls,\n", " alpha=alpha,\n", " )\n", " ax_dyn.plot(\n", " dynamics.times,\n", " dynamics.expect[0],\n", " label=pop_labels[0],\n", " color='#1f77b4', # default blue\n", " ls=ls,\n", " alpha=alpha,\n", " )\n", " ax_dyn.plot(\n", " dynamics.times,\n", " dynamics.expect[1],\n", " label=pop_labels[1],\n", " color='#ff7f0e', # default orange\n", " ls=ls,\n", " alpha=alpha,\n", " )\n", " ax_dyn.legend()\n", " ax_dyn.set_xlabel('time')\n", " ax_dyn.set_ylabel('population')\n", " ax_ctr.legend()\n", " ax_ctr.set_xlabel('time')\n", " ax_ctr.set_ylabel('control amplitude')\n", " plt.show(fig)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "ExecuteTime": { "end_time": "2019-07-14T21:07:26.245866Z", "start_time": "2019-07-14T21:07:20.914008Z" }, "execution": { "iopub.execute_input": "2021-01-13T19:20:24.551224Z", "iopub.status.busy": "2021-01-13T19:20:24.550324Z", "iopub.status.idle": "2021-01-13T19:20:27.395973Z", "shell.execute_reply": "2021-01-13T19:20:27.396514Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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