{ "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" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "matplotlib 3.1.2\n", "matplotlib.pylab 1.17.2\n", "scipy 1.3.1\n", "numpy 1.17.2\n", "qutip 4.4.1\n", "krotov 1.0.0\n", "CPython 3.7.3\n", "IPython 7.10.2\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" } }, "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" } }, "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" }, "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" } }, "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" } }, "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" } }, "outputs": [ { "data": { "text/plain": [ "[Objective[|Ψ₀(2)⟩ to |Ψ₁(2)⟩ via [H₀[2,2], [H₁[2,2], u₁(t)]]]]" ] }, "execution_count": 7, "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" }, "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" }, "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" } }, "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" } }, "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" } }, "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" } }, "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" }, "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 -2.70e-02 -2.47e-02 2\n", "2 8.83e-01 3.53e-03 8.87e-01 -4.11e-02 -3.75e-02 2\n", "3 8.23e-01 5.22e-03 8.28e-01 -6.06e-02 -5.54e-02 2\n", "4 7.38e-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 -1.01e-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 2\n", "9 1.53e-01 8.43e-03 1.62e-01 -9.03e-02 -8.19e-02 2\n", "10 9.20e-02 5.80e-03 9.78e-02 -6.14e-02 -5.56e-02 2\n", "11 5.35e-02 3.66e-03 5.72e-02 -3.85e-02 -3.48e-02 2\n", "12 3.06e-02 2.19e-03 3.28e-02 -2.29e-02 -2.07e-02 2\n", "13 1.73e-02 1.27e-03 1.86e-02 -1.33e-02 -1.20e-02 2\n", "14 9.79e-03 7.24e-04 1.05e-02 -7.55e-03 -6.82e-03 2\n", "15 5.52e-03 4.10e-04 5.93e-03 -4.27e-03 -3.86e-03 2\n", "16 3.11e-03 2.31e-04 3.35e-03 -2.41e-03 -2.18e-03 2\n", "17 1.76e-03 1.30e-04 1.89e-03 -1.36e-03 -1.23e-03 1\n", "18 9.92e-04 7.36e-05 1.07e-03 -7.65e-04 -6.91e-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" } }, "outputs": [ { "data": { "text/plain": [ "Krotov Optimization Result\n", "--------------------------\n", "- Started at 2019-12-15 22:36:37\n", "- Number of objectives: 1\n", "- Number of iterations: 18\n", "- Reason for termination: Reached convergence: J_T < 1e-3\n", "- Ended at 2019-12-15 22:37:16 (0:00:39)" ] }, "execution_count": 15, "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" } }, "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" } }, "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": {}, "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" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_iterations(opt_result)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The initial guess (dashed) and final optimized (solid) control amplitude and resulting dynamics are shown with full opacity, whereas the curves corresponding intermediate iterations are shown with decreasing transparency." ] } ], "metadata": { "hide_input": false, "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" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false }, "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": 2 }