{ "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": "2021-11-07T04:48:04.669401Z", "iopub.status.busy": "2021-11-07T04:48:04.669006Z", "iopub.status.idle": "2021-11-07T04:48:09.106364Z", "shell.execute_reply": "2021-11-07T04:48:09.106667Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Python implementation: CPython\n", "Python version : 3.8.1\n", "IPython version : 7.24.1\n", "\n", "qutip : 4.6.1\n", "matplotlib: 3.4.2\n", "numpy : 1.20.3\n", "krotov : 1.2.1+dev\n", "scipy : 1.6.3\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": "2021-11-07T04:48:09.110340Z", "iopub.status.busy": "2021-11-07T04:48:09.109976Z", "iopub.status.idle": "2021-11-07T04:48:09.111847Z", "shell.execute_reply": "2021-11-07T04:48:09.111483Z" } }, "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": "2021-11-07T04:48:09.114633Z", "iopub.status.busy": "2021-11-07T04:48:09.114278Z", "iopub.status.idle": "2021-11-07T04:48:09.115993Z", "shell.execute_reply": "2021-11-07T04:48:09.115636Z" } }, "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": "2021-11-07T04:48:09.118223Z", "iopub.status.busy": "2021-11-07T04:48:09.117874Z", "iopub.status.idle": "2021-11-07T04:48:09.119248Z", "shell.execute_reply": "2021-11-07T04:48:09.119528Z" }, "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": "2021-11-07T04:48:09.122340Z", "iopub.status.busy": "2021-11-07T04:48:09.121983Z", "iopub.status.idle": "2021-11-07T04:48:09.123657Z", "shell.execute_reply": "2021-11-07T04:48:09.123295Z" } }, "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": "2021-11-07T04:48:09.134678Z", "iopub.status.busy": "2021-11-07T04:48:09.134344Z", "iopub.status.idle": "2021-11-07T04:48:09.278047Z", "shell.execute_reply": "2021-11-07T04:48:09.277737Z" } }, "outputs": [ { "data": { "image/png": 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\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": "2021-11-07T04:48:09.281276Z", "iopub.status.busy": "2021-11-07T04:48:09.280900Z", "iopub.status.idle": "2021-11-07T04:48:09.283003Z", "shell.execute_reply": "2021-11-07T04:48:09.282739Z" } }, "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": "2021-11-07T04:48:09.285128Z", "iopub.status.busy": "2021-11-07T04:48:09.284839Z", "iopub.status.idle": "2021-11-07T04:48:09.286473Z", "shell.execute_reply": "2021-11-07T04:48:09.286180Z" }, "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": "2021-11-07T04:48:09.288467Z", "iopub.status.busy": "2021-11-07T04:48:09.288184Z", "iopub.status.idle": "2021-11-07T04:48:09.289776Z", "shell.execute_reply": "2021-11-07T04:48:09.289473Z" }, "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": "2021-11-07T04:48:09.292300Z", "iopub.status.busy": "2021-11-07T04:48:09.292010Z", "iopub.status.idle": "2021-11-07T04:48:09.293624Z", "shell.execute_reply": "2021-11-07T04:48:09.293328Z" } }, "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": "2021-11-07T04:48:09.368510Z", "iopub.status.busy": "2021-11-07T04:48:09.368199Z", "iopub.status.idle": "2021-11-07T04:48:09.369899Z", "shell.execute_reply": "2021-11-07T04:48:09.369588Z" } }, "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": "2021-11-07T04:48:09.372537Z", "iopub.status.busy": "2021-11-07T04:48:09.372241Z", "iopub.status.idle": "2021-11-07T04:48:09.373844Z", "shell.execute_reply": "2021-11-07T04:48:09.373540Z" } }, "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": "2021-11-07T04:48:09.386563Z", "iopub.status.busy": "2021-11-07T04:48:09.385648Z", "iopub.status.idle": "2021-11-07T04:48:09.458141Z", "shell.execute_reply": "2021-11-07T04:48:09.457839Z" } }, "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": "2021-11-07T04:48:09.462681Z", "iopub.status.busy": "2021-11-07T04:48:09.462385Z", "iopub.status.idle": "2021-11-07T04:48:35.442951Z", "shell.execute_reply": "2021-11-07T04:48:35.443200Z" }, "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 0\n", "1 9.24e-01 1.20e-02 9.36e-01 -2.71e-02 -1.50e-02 1\n", "2 8.83e-01 1.83e-02 9.02e-01 -4.11e-02 -2.28e-02 1\n", "3 8.23e-01 2.71e-02 8.50e-01 -6.06e-02 -3.35e-02 1\n", "4 7.37e-01 3.84e-02 7.76e-01 -8.52e-02 -4.68e-02 1\n", "5 6.26e-01 5.07e-02 6.77e-01 -1.11e-01 -6.05e-02 1\n", "6 4.96e-01 6.04e-02 5.56e-01 -1.31e-01 -7.02e-02 1\n", "7 3.62e-01 6.30e-02 4.25e-01 -1.34e-01 -7.09e-02 1\n", "8 2.44e-01 5.65e-02 3.00e-01 -1.18e-01 -6.15e-02 1\n", "9 1.53e-01 4.39e-02 1.97e-01 -9.03e-02 -4.64e-02 1\n", "10 9.20e-02 3.02e-02 1.22e-01 -6.14e-02 -3.12e-02 1\n", "11 5.35e-02 1.90e-02 7.25e-02 -3.85e-02 -1.94e-02 1\n", "12 3.06e-02 1.14e-02 4.20e-02 -2.29e-02 -1.15e-02 1\n", "13 1.73e-02 6.60e-03 2.39e-02 -1.32e-02 -6.64e-03 1\n", "14 9.78e-03 3.76e-03 1.35e-02 -7.54e-03 -3.78e-03 1\n", "15 5.52e-03 2.13e-03 7.65e-03 -4.26e-03 -2.13e-03 1\n", "16 3.11e-03 1.20e-03 4.31e-03 -2.40e-03 -1.20e-03 1\n", "17 1.76e-03 6.77e-04 2.43e-03 -1.36e-03 -6.78e-04 1\n", "18 9.91e-04 3.82e-04 1.37e-03 -7.64e-04 -3.82e-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": "2021-11-07T04:48:35.445864Z", "iopub.status.busy": "2021-11-07T04:48:35.445489Z", "iopub.status.idle": "2021-11-07T04:48:35.447517Z", "shell.execute_reply": "2021-11-07T04:48:35.447761Z" } }, "outputs": [ { "data": { "text/plain": [ "Krotov Optimization Result\n", "--------------------------\n", "- Started at 2021-11-07 05:48:09\n", "- Number of objectives: 1\n", "- Number of iterations: 18\n", "- Reason for termination: Reached convergence: J_T < 1e-3\n", "- Ended at 2021-11-07 05:48:35 (0:00:26)" ] }, "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": "2021-11-07T04:48:35.480265Z", "iopub.status.busy": "2021-11-07T04:48:35.479973Z", "iopub.status.idle": "2021-11-07T04:48:35.481202Z", "shell.execute_reply": "2021-11-07T04:48:35.481431Z" } }, "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": "2021-11-07T04:48:35.493803Z", "iopub.status.busy": "2021-11-07T04:48:35.493326Z", "iopub.status.idle": "2021-11-07T04:48:35.566066Z", "shell.execute_reply": "2021-11-07T04:48:35.565733Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "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": "2021-11-07T04:48:35.571155Z", "iopub.status.busy": "2021-11-07T04:48:35.570854Z", "iopub.status.idle": "2021-11-07T04:48:35.572696Z", "shell.execute_reply": "2021-11-07T04:48:35.572400Z" } }, "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": "2021-11-07T04:48:35.592948Z", "iopub.status.busy": "2021-11-07T04:48:35.582412Z", "iopub.status.idle": "2021-11-07T04:48:36.360539Z", "shell.execute_reply": "2021-11-07T04:48:36.360783Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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