{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Optimization of an X-Gate for a Transmon Qubit" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "krotov 0.3.0\n", "scipy 1.2.1\n", "matplotlib 3.0.3\n", "qutip 4.3.1\n", "matplotlib.pylab 1.15.4\n", "numpy 1.15.4\n", "CPython 3.6.8\n", "IPython 7.3.0\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", "from scipy.fftpack import fft\n", "from scipy.interpolate import interp1d\n", "%watermark -v --iversions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\newcommand{tr}[0]{\\operatorname{tr}}\n", "\\newcommand{diag}[0]{\\operatorname{diag}}\n", "\\newcommand{abs}[0]{\\operatorname{abs}}\n", "\\newcommand{pop}[0]{\\operatorname{pop}}\n", "\\newcommand{aux}[0]{\\text{aux}}\n", "\\newcommand{opt}[0]{\\text{opt}}\n", "\\newcommand{tgt}[0]{\\text{tgt}}\n", "\\newcommand{init}[0]{\\text{init}}\n", "\\newcommand{lab}[0]{\\text{lab}}\n", "\\newcommand{rwa}[0]{\\text{rwa}}\n", "\\newcommand{bra}[1]{\\langle#1\\vert}\n", "\\newcommand{ket}[1]{\\vert#1\\rangle}\n", "\\newcommand{Bra}[1]{\\left\\langle#1\\right\\vert}\n", "\\newcommand{Ket}[1]{\\left\\vert#1\\right\\rangle}\n", "\\newcommand{Braket}[2]{\\left\\langle #1\\vphantom{#2} \\mid #2\\vphantom{#1}\\right\\rangle}\n", "\\newcommand{op}[1]{\\hat{#1}}\n", "\\newcommand{Op}[1]{\\hat{#1}}\n", "\\newcommand{dd}[0]{\\,\\text{d}}\n", "\\newcommand{Liouville}[0]{\\mathcal{L}}\n", "\\newcommand{DynMap}[0]{\\mathcal{E}}\n", "\\newcommand{identity}[0]{\\mathbf{1}}\n", "\\newcommand{Norm}[1]{\\lVert#1\\rVert}\n", "\\newcommand{Abs}[1]{\\left\\vert#1\\right\\vert}\n", "\\newcommand{avg}[1]{\\langle#1\\rangle}\n", "\\newcommand{Avg}[1]{\\left\\langle#1\\right\\rangle}\n", "\\newcommand{AbsSq}[1]{\\left\\vert#1\\right\\vert^2}\n", "\\newcommand{Re}[0]{\\operatorname{Re}}\n", "\\newcommand{Im}[0]{\\operatorname{Im}}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Define the Hamiltonian" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The effective Hamiltonian of a single transmon depends on the capacitive energy $E_C=e^2/2C$ and the Josephson energy $E_J$, an energy due to the Josephson junction working as a nonlinear inductor periodic with the flux $\\Phi$. In the so-called transmon limit the ratio between these two energies lie around $E_J / E_C \\approx 45$. The time-independent Hamiltonian can be described then as\n", "\n", "\\begin{equation*}\n", "\\op{H}_{0} = 4 E_C (\\hat{n}-n_g)^2 - E_J \\cos(\\hat{\\Phi})\n", "\\end{equation*}\n", "\n", "where $\\hat{n}$ is the number operator, which count how many Cooper pairs cross the junction, and $n_g$ being the effective offset charge measured in Cooper pair charge units. The aforementioned equation can be written in a truncated charge basis defined by the number operator $\\op{n} \\ket{n} = n \\ket{n}$ such that\n", "\n", "\\begin{equation*}\n", "\\op{H}_{0} = 4 E_C \\sum_{j=-N} ^N (j-n_g)^2 |j \\rangle \\langle j| - \\frac{E_J}{2} \\sum_{j=-N} ^{N-1} ( |j+1\\rangle\\langle j| + |j\\rangle\\langle j+1|).\n", "\\end{equation*}\n", "\n", "If we apply a potential $V(t)$ to the qubit the complete Hamiltonian is changed to\n", "\n", "\\begin{equation*}\n", "\\op{H} = \\op{H}_{0} + V(t) \\cdot \\op{H}_{1}\n", "\\end{equation*}\n", "\n", "The interaction Hamiltonian $\\op{H}_1$ is then equivalent to the charge operator $\\op{q}$, which in the truncated charge basis can be written as\n", "\n", "\\begin{equation*}\n", "\\op{H}_1 = \\op{q} = \\sum_{j=-N} ^N -2n \\ket{n} \\bra{n}.\n", "\\end{equation*}\n", "\n", "Note that the -2 coefficient is just indicating that the charge carriers here are Cooper pairs, each with a charge of $-2e$.\n", "\n", "We define the logic states $\\ket{0_l}$ and $\\ket{1_l}$ (not to be confused with the charge states $\\ket{n=0}$ and $\\ket{n=1}$) as the eigenstates of the free Hamiltonian $\\op{H}_0$ with the lowest energy. The problem to solve is find a potential $V_{opt}(t)$ such that after a given final time $T$ can implement an X-gate.\n", "\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def transmon_ham_and_states(Ec=0.386, EjEc=45, nstates=8, ng=0.0, T=10.0):\n", " \"\"\"Transmon Hamiltonian\"\"\"\n", " # Ec : capacitive energy\n", " # EjEc : ratio Ej / Ec\n", " # nstates : defines the maximum and minimum states for the basis. The truncated basis\n", " # will have a total of 2*nstates + 1 states\n", "\n", " Ej = EjEc * Ec\n", " n = np.arange(-nstates, nstates + 1)\n", " up = np.diag(np.ones(2 * nstates), k=-1)\n", " do = up.T\n", " H0 = qutip.Qobj(np.diag(4 * Ec * (n - ng) ** 2) - Ej * (up + do) / 2.0)\n", " H1 = qutip.Qobj(-2 * np.diag(n))\n", "\n", " eigenvals, eigenvecs = scipy.linalg.eig(H0.full())\n", " ndx = np.argsort(eigenvals.real)\n", " E = eigenvals[ndx].real\n", " V = eigenvecs[:, ndx]\n", " w01 = E[1] - E[0] # Transition energy between states\n", "\n", " psi0 = qutip.Qobj(V[:, 0])\n", " psi1 = qutip.Qobj(V[:, 1])\n", "\n", " profile = lambda t: np.exp(-40.0 * (t / T - 0.5) ** 2)\n", " eps0 = lambda t, args: 8 * profile(t) * np.cos(2 * np.pi * w01 * t)\n", " return ([H0, [H1, eps0]], psi0, psi1)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2019-01-31T00:29:08.524967Z", "start_time": "2019-01-31T00:29:08.509095Z" } }, "outputs": [], "source": [ "H, psi0, psi1 = transmon_ham_and_states()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We introduce the projectors $P_i = \\ket{\\psi _i}\\bra{\\psi _i}$ for the logic states $\\ket{\\psi _i} \\in \\{\\ket{0_l}, \\ket{1_l}\\}$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2019-01-31T00:29:08.538557Z", "start_time": "2019-01-31T00:29:08.530210Z" } }, "outputs": [], "source": [ "proj0 = psi0 * psi0.dag()\n", "proj1 = psi1 * psi1.dag()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Optimization target" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We choose our X-gate to be defined during a time interval starting at $t_{0} = 0$ and ending at $T = 10$, with a total of $nt = 1000$ time steps." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2019-01-31T00:29:08.555125Z", "start_time": "2019-01-31T00:29:08.542874Z" } }, "outputs": [], "source": [ "tlist = np.linspace(0, 10, 1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We make use of the $\\sigma _{x}$ operator included in QuTiP to define our objective:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2019-01-31T00:29:08.569805Z", "start_time": "2019-01-31T00:29:08.557781Z" } }, "outputs": [], "source": [ "objectives = krotov.gate_objectives(\n", " basis_states=[psi0, psi1], gate=qutip.operators.sigmax(), H=H\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We define the desired shape of the pulse and the update factor $\\lambda _a$" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2019-01-31T00:29:08.583127Z", "start_time": "2019-01-31T00:29:08.573188Z" } }, "outputs": [], "source": [ "def S(t):\n", " \"\"\"Shape function for the pulse update\"\"\"\n", " dt = tlist[1] - tlist[0]\n", " steps = len(tlist)\n", " return np.exp(-40.0 * (t / ((steps - 1) * dt) - 0.5) ** 2)\n", "\n", "\n", "pulse_options = {H[1][1]: dict(lambda_a=1, shape=S)}\n" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 2 }, "source": [ "It may be useful to check the fidelity after each iteration. To achieve this, we define a simple function that will be used by the main routine\n", "\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2019-01-31T00:29:08.593176Z", "start_time": "2019-01-31T00:29:08.587397Z" } }, "outputs": [], "source": [ "def print_fidelity(**args):\n", " F_re = np.average(np.array(args['tau_vals']).real)\n", " print(\"Iteration %d: \\tF = %f\" % (args['iteration'], F_re))\n", " return F_re" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 2 }, "source": [ "## Simulate dynamics of the guess pulse\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def plot_pulse(pulse, tlist, xlimit=None):\n", " fig, ax = plt.subplots()\n", " if callable(pulse):\n", " pulse = np.array([pulse(t, None) for t in tlist])\n", " ax.plot(tlist, pulse)\n", " ax.set_xlabel('time (ns)')\n", " ax.set_ylabel('pulse amplitude')\n", " if xlimit is not None:\n", " ax.set_xlim(xlimit)\n", " plt.show(fig)\n", "\n", "\n", "def plot_spectrum(pulse, tlist):\n", "\n", " if callable(pulse):\n", " pulse = np.array([pulse(t, None) for t in tlist])\n", "\n", " tstep = tlist[1] - tlist[0]\n", " F = 1 / tstep\n", " n = len(tlist)\n", " k = np.arange(n)\n", " T = tlist[-1]\n", "\n", " frequency = k / T\n", " frequency = frequency[range(int(n / 2))]\n", " freq_amp = np.fft.fft(pulse) / n\n", " freq_amp = freq_amp[range(int(n / 2))]\n", "\n", " fig, ax = plt.subplots()\n", " ax.plot(frequency, abs(freq_amp)) # plotting the spectrum\n", " ax.set_xlabel('frequency')\n", " ax.set_ylabel('amplitude')\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_pulse(H[1][1], tlist)\n", "plot_spectrum(H[1][1], tlist)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For our guess pulse we have chosen to use an oscillating potential which is resonant with the energy gap between our states $\\Delta E = E_1 - E_0 \\approx 6.914$, shaped with a Gaussian function. The spectrum of the pulse shows this exact thing in the frequency decomposition. It is important to recall that this pulse is actually not referring to an electrical signal, but rather the electric potential that will be applied to the transmon circuit in which we are basing our system.\n", "\n", "We can also make sure that the oscillations are being computed with enough resolution:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_pulse(H[1][1], tlist, xlimit=[4, 5])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once we are sure to have obtained the desired guess pulse, the dynamics for the initial guess can be found easily:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "guess_dynamics = [\n", " objectives[x].mesolve(tlist, e_ops=[proj0, proj1]) for x in [0, 1]\n", "]" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "def plot_population(result):\n", " '''Representation of the expected values for the initial states'''\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": 14, "metadata": { "ExecuteTime": { "end_time": "2019-01-31T00:29:10.291810Z", "start_time": "2019-01-31T00:29:09.942317Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_population(guess_dynamics[0])\n", "plot_population(guess_dynamics[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The initial guess can alter the population during the evolution of the system, but in the end it is not achieving the result that we are aiming for. Even though it is not an ideal pulse, we will try to optimize it.\n", "\n", "As a test, we can check whether our time step is sufficiently small by comparing the states that we are obtaining after the propagation with the ones that we would obtain with twice the amount of time steps." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "guess_states = [objectives[x].mesolve(tlist) for x in [0, 1]]" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "tlist2 = np.linspace(0, tlist[-1], len(tlist) * 2)\n", "guess_states2 = [objectives[x].mesolve(tlist2) for x in [0, 1]]" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "def print_errors(result1, result2, index1, index2):\n", " err1 = 1 - abs(\n", " result1[0].states[index1].overlap(result2[0].states[index2])\n", " )\n", " err2 = 1 - abs(\n", " result1[1].states[index1].overlap(result2[1].states[index2])\n", " )\n", " print(\"%.1e\" % err1)\n", " print(\"%.1e\" % err2)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.5e-14\n", "2.8e-12\n" ] } ], "source": [ "print_errors(guess_states, guess_states2, -1, -1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Optimize" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now use all the information that we have gathered to initialize\n", "the optimization routine. That is:\n", "\n", "* The `objectives`: creating an X-gate in the given basis.\n", "\n", "* The `pulse_options`: initial pulses and their shapes restrictions.\n", "\n", "* The `tlist`: time grid used for the propagation.\n", "\n", "* The `propagator`: propagation method that will be used.\n", "\n", "* The `chi_constructor`: the optimization functional to use.\n", "\n", "* The `info_hook`: the subroutines to be called and data to be analized inbetween iterations.\n", "\n", "* The `iter_stop`: the number of iterations to perform the optimization." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "lines_to_next_cell": 2 }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Iteration 0: \tF = -0.000010\n", "Iteration 1: \tF = 0.653868\n", "Iteration 2: \tF = 0.749174\n", "Iteration 3: \tF = 0.786936\n", "Iteration 4: \tF = 0.803851\n", "Iteration 5: \tF = 0.815087\n", "Iteration 6: \tF = 0.823723\n", "Iteration 7: \tF = 0.830559\n", "Iteration 8: \tF = 0.836098\n", "Iteration 9: \tF = 0.840722\n", "Iteration 10: \tF = 0.844699\n" ] } ], "source": [ "oct_result = krotov.optimize_pulses(\n", " objectives,\n", " pulse_options,\n", " tlist,\n", " propagator=krotov.propagators.expm,\n", " chi_constructor=krotov.functionals.chis_re,\n", " info_hook=print_fidelity,\n", " iter_stop=10,\n", " parallel_map=(\n", " qutip.parallel_map,\n", " qutip.parallel_map,\n", " krotov.parallelization.parallel_map_fw_prop_step,\n", " ),\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The fidelity in each step is then stored in the `info_vals` that are defined by the subroutines in `info_hook`:\n" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "def plot_convergence(result):\n", " fig, ax = plt.subplots()\n", " ax.semilogy(result.iters, 1 - np.array(result.info_vals))\n", " ax.set_xlabel('OCT iteration')\n", " ax.set_ylabel('error')\n", " plt.show(fig)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_convergence(oct_result)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simulate dynamics of the optimized pulse" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We want to see how much the results have improved after the optimization." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_pulse(oct_result.optimized_controls[0], tlist)\n", "plot_spectrum(oct_result.optimized_controls[0], tlist)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "ExecuteTime": { "end_time": "2019-01-31T00:30:10.080643Z", "start_time": "2019-01-31T00:30:08.679560Z" } }, "outputs": [], "source": [ "opt_dynamics = [\n", " oct_result.optimized_objectives[x].mesolve(tlist, e_ops=[proj0, proj1])\n", " for x in [0, 1]\n", "]" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "ExecuteTime": { "end_time": "2019-01-31T00:30:12.041672Z", "start_time": "2019-01-31T00:30:10.083759Z" } }, "outputs": [], "source": [ "opt_states = [\n", " oct_result.optimized_objectives[x].mesolve(tlist) for x in [0, 1]\n", "]" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "ExecuteTime": { "end_time": "2019-01-31T00:30:12.263068Z", "start_time": "2019-01-31T00:30:12.043673Z" } }, "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[0])" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "ExecuteTime": { "end_time": "2019-01-31T00:30:12.460131Z", "start_time": "2019-01-31T00:30:12.266370Z" }, "lines_to_next_cell": 2 }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_population(opt_dynamics[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case we do not only care about the expected value for the states, but since we want to implement a gate it is necessary to check whether we are performing a coherent control. We are then interested in the phase difference that we obtain after propagating the states from the logic basis, which should be near to 0.\n" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "def relative_phase(result):\n", "\n", " overlap_0 = np.angle(result[0].states[-1].overlap(psi1))\n", " overlap_1 = np.angle(result[1].states[-1].overlap(psi0))\n", "\n", " rel_phase = (overlap_0 - overlap_1) % (2 * np.pi)\n", " print(\"Final relative phase = %.2e\" % rel_phase)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Final relative phase = 2.70e-02\n" ] } ], "source": [ "relative_phase(opt_states)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We may also propagate the optimization result using the same propagator that was\n", "used in the optimization (instead of `qutip.mesolve`). The main difference\n", "between the two propagations is that `mesolve` assumes piecewise constant pulses\n", "that switch between two points in `tlist`, whereas `propagate` assumes that\n", "pulses are constant on the intervals of `tlist`, and thus switches *on* the\n", "points in `tlist`." ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "ExecuteTime": { "end_time": "2019-01-31T00:30:15.558501Z", "start_time": "2019-01-31T00:30:12.715401Z" } }, "outputs": [], "source": [ "opt_dynamics2 = [\n", " oct_result.optimized_objectives[x].propagate(\n", " tlist, e_ops=[proj0, proj1], propagator=krotov.propagators.expm\n", " )\n", " for x in [0, 1]\n", "]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The difference between the two propagations gives an indication of the \"time\n", "discretization error\". If this error were unacceptably large, we would need a\n", "smaller time step." ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "ExecuteTime": { "end_time": "2019-01-31T00:30:15.565275Z", "start_time": "2019-01-31T00:30:15.560602Z" } }, "outputs": [ { "data": { "text/plain": [ "'2.81e-04'" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\"%.2e\" % abs(opt_dynamics2[0].expect[1][-1] - opt_dynamics[0].expect[1][-1])" ] } ], "metadata": { "hide_input": false, "jupytext": { "formats": "" }, "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": "3.6.8" }, "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 }