{ "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": [ "numpy 1.17.2\n", "qutip 4.5.0\n", "matplotlib 3.2.1\n", "scipy 1.3.1\n", "krotov 1.1.0\n", "matplotlib.pylab 1.17.2\n", "CPython 3.7.6\n", "IPython 7.13.0\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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"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 2\n", "1 9.24e-01 2.32e-03 9.27e-01 -2.70e-02 -2.47e-02 4\n", "2 8.83e-01 3.53e-03 8.87e-01 -4.11e-02 -3.75e-02 4\n", "3 8.23e-01 5.22e-03 8.28e-01 -6.06e-02 -5.54e-02 4\n", "4 7.38e-01 7.39e-03 7.45e-01 -8.52e-02 -7.78e-02 5\n", "5 6.26e-01 9.75e-03 6.36e-01 -1.11e-01 -1.01e-01 4\n", "6 4.96e-01 1.16e-02 5.07e-01 -1.31e-01 -1.19e-01 4\n", "7 3.62e-01 1.21e-02 3.74e-01 -1.34e-01 -1.22e-01 5\n", "8 2.44e-01 1.09e-02 2.55e-01 -1.18e-01 -1.07e-01 4\n", "9 1.53e-01 8.43e-03 1.62e-01 -9.03e-02 -8.19e-02 3\n", "10 9.20e-02 5.80e-03 9.78e-02 -6.14e-02 -5.56e-02 4\n", "11 5.35e-02 3.66e-03 5.72e-02 -3.85e-02 -3.48e-02 3\n", "12 3.06e-02 2.19e-03 3.28e-02 -2.29e-02 -2.07e-02 3\n", "13 1.73e-02 1.27e-03 1.86e-02 -1.33e-02 -1.20e-02 4\n", "14 9.79e-03 7.24e-04 1.05e-02 -7.55e-03 -6.82e-03 3\n", "15 5.52e-03 4.10e-04 5.93e-03 -4.27e-03 -3.86e-03 3\n", "16 3.11e-03 2.31e-04 3.35e-03 -2.41e-03 -2.18e-03 3\n", "17 1.76e-03 1.30e-04 1.89e-03 -1.36e-03 -1.23e-03 4\n", "18 9.92e-04 7.36e-05 1.07e-03 -7.65e-04 -6.91e-04 4\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 2020-03-24 14:43:50\n", "- Number of objectives: 1\n", "- Number of iterations: 18\n", "- Reason for termination: Reached convergence: J_T < 1e-3\n", "- Ended at 2020-03-24 14:45:10 (0:01:20)" ] }, "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", 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