{ "cells": [ { "cell_type": "markdown", "id": "aac525e9", "metadata": {}, "source": [ "# Rydiqule Performance #\n", "\n", "The primary purpose of this notebook is to provide a sense of how solve times in rydiqule scale with problem size. It also provides a practical example of the advantages of using rydiqule for large numbers of semi-classical master-equation solving relative to other tools." ] }, { "cell_type": "code", "execution_count": 1, "id": "e0a3c4d6", "metadata": {}, "outputs": [], "source": [ "import rydiqule as rq\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import time" ] }, { "cell_type": "markdown", "id": "1af9b0df", "metadata": {}, "source": [ "## Steady-state solve time scaling versus basis size ##" ] }, { "cell_type": "markdown", "id": "05e42f8f", "metadata": {}, "source": [ "We begin by showing how the solve time for a single set of Equations of Motion scales with the number of states in the basis $b$.\n", "\n", "For this benchmark, we randomize each problem to be solved, ensuring that there are around $b*\\log(b)$ couplings with a random coupling strength, and each state decays to the ground state with a random rate. All detunings are held to be 0." ] }, { "cell_type": "code", "execution_count": 2, "id": "8b218b07", "metadata": {}, "outputs": [], "source": [ "def random_ss_sensor(n_states, n_couplings, rabi_bounds=[0.1,10], detuning_bounds=[0,0], decoherence_bounds=[0,0.5]):\n", " if type(n_states) is not int:\n", " n_states = n_states.item()\n", " s = rq.Sensor(n_states)\n", " \n", " decoherences = np.random.uniform(decoherence_bounds[0], decoherence_bounds[1], size=n_states)\n", " gamma = np.zeros((n_states, n_states))\n", " gamma[:,0] = decoherences\n", " s.set_gamma_matrix(gamma)\n", " \n", " possible_coups = np.array(np.triu_indices(n_states, 1), dtype=int).T\n", " idx = np.random.choice(np.arange(len(possible_coups)), n_couplings, replace=False)\n", " coups = possible_coups[idx]\n", " \n", " rabis = np.random.uniform(rabi_bounds[0], rabi_bounds[1], size=n_couplings)\n", " detunings = np.random.uniform(detuning_bounds[0], detuning_bounds[1], size=n_couplings)\n", " \n", " lasers = []\n", " for i in range(n_couplings):\n", " lasers.append({\"states\": (int(coups[i][0]), int(coups[i][1])), \"rabi_frequency\": rabis[i], \"detuning\": detunings[i]})\n", "\n", " s.add_couplings(*lasers)\n", " \n", " return s" ] }, { "cell_type": "markdown", "id": "3cd86aa8", "metadata": {}, "source": [ "To provide some statistical measure without making the notebook run too long in a single sitting, we average 4 runs per point." ] }, { "cell_type": "code", "execution_count": 3, "id": "aff02378", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 2 3 4 8 16 32 64 96]\n", "[ 1 3 5 16 44 110 266 438]\n" ] } ], "source": [ "n_sims = 4\n", "\n", "n_states = np.array([2, 3, 4, 8, 16, 32, 64, 96])\n", "n_couplings = np.array(n_states*np.log(n_states), dtype=int)\n", "print(n_states)\n", "print(n_couplings)" ] }, { "cell_type": "code", "execution_count": 4, "id": "daa3b731", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Solving 96 states, round 4/4\r" ] } ], "source": [ "times = np.zeros((n_sims, len(n_states)))\n", "\n", "for j in range(len(n_states)):\n", " for i in range(n_sims):\n", " print(f'Solving {n_states[j]:d} states, round {i+1:d}/{n_sims:d}', end='\\r')\n", " s = random_ss_sensor(n_states[j], n_couplings[j])\n", " tic = time.perf_counter()\n", " _ = rq.solve_steady_state(s)\n", " toc = time.perf_counter()\n", " times[i,j] = (toc - tic)" ] }, { "cell_type": "code", "execution_count": 5, "id": "8fa28059", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1)\n", "\n", "ave_times = times.mean(axis=0)\n", "std_times = times.std(axis=0)\n", "\n", "ax.errorbar(n_states, ave_times, yerr=std_times, fmt='o')\n", "ax.set_title('Steady-State Solve Time vs Basis Size')\n", "ax.set_xlabel('Basis Size ($n$)')\n", "ax.set_ylabel('Solve Time (s)')\n", "ax.set_yscale('log')\n", "ax.set_xscale('log')" ] }, { "cell_type": "markdown", "id": "8828af11", "metadata": {}, "source": [ "## Steady-state solve time scaling versus stack size ##" ] }, { "cell_type": "markdown", "id": "fc946e92", "metadata": {}, "source": [ "Here we see how solve time scales versus the number of Equations of Motion to be solved for a system with a basis size of 3. This is done by varying how many probe detuning points we sample." ] }, { "cell_type": "code", "execution_count": 6, "id": "73020264", "metadata": {}, "outputs": [], "source": [ "couple = {'states': (1,2), 'rabi_frequency':2*np.pi*1, 'detuning':2*np.pi*0, 'label':'couple'}\n", "\n", "sts = rq.Sensor(3)\n", "sts.add_couplings(couple)\n", "sts.add_decoherence((1,0), 2*np.pi*6.0666)\n", "sts.add_decoherence((2,1), 2*np.pi*0.1)" ] }, { "cell_type": "code", "execution_count": 7, "id": "a164f5d9", "metadata": {}, "outputs": [], "source": [ "n_sims = 4\n", "ssize = np.array([2, 10, 20, 40, 80, 160, 300, 600, 1200, 2400, 4800, 10000])" ] }, { "cell_type": "code", "execution_count": 8, "id": "05581b56", "metadata": {}, "outputs": [], "source": [ "times_stack = np.zeros((len(ssize), n_sims), dtype=float)\n", "\n", "for i, p_pts in enumerate(ssize):\n", " for j in range(n_sims):\n", " probe = {'states': (0,1), 'rabi_frequency':2*np.pi*0.1,\n", " 'detuning':2*np.pi*np.linspace(-100, 100, p_pts), 'label':'probe'}\n", " sts.add_couplings(probe)\n", " tic = time.perf_counter()\n", " _ = rq.solve_steady_state(sts)\n", " toc = time.perf_counter()\n", " times_stack[i,j] = (toc-tic)" ] }, { "cell_type": "code", "execution_count": 9, "id": "7e707a3b", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1)\n", "\n", "ave_times = times_stack.mean(axis=1)\n", "std_times = times_stack.std(axis=1)\n", "\n", "ax.errorbar(ssize, ave_times, yerr=std_times, fmt='o')\n", "ax.set_title('Steady-State Solve Time vs Parameter Size')\n", "ax.set_xlabel('Parameter Size ($d$)')\n", "ax.set_ylabel('Solve Time (s)')\n", "ax.set_yscale('log')\n", "ax.set_xscale('log')" ] }, { "cell_type": "markdown", "id": "6692e4dd", "metadata": {}, "source": [ "## Time-dependent solve times versus stack size ##" ] }, { "cell_type": "markdown", "id": "f0e558fc", "metadata": {}, "source": [ "Here we repeat the test, but with a time-dependent coupling. Note that time-dependent solving is slower than steady-state by a fair bit. This is not aided by our insistence on allowing arbitrary python functions for the time dependence, which makes the back-end implementations tricky." ] }, { "cell_type": "code", "execution_count": 10, "id": "bde869a5", "metadata": {}, "outputs": [], "source": [ "couple = {'states': (1,2), 'rabi_frequency':2*np.pi*1, 'detuning':2*np.pi*0, 'label':'couple',\n", " 'time_dependence': lambda t: np.sin(2*np.pi*2*t)}\n", "\n", "tts = rq.Sensor(3)\n", "tts.add_couplings(couple)\n", "tts.add_decoherence((1,0), 2*np.pi*6.0666)\n", "tts.add_decoherence((2,1), 2*np.pi*0.1)" ] }, { "cell_type": "code", "execution_count": 11, "id": "f171cc50", "metadata": {}, "outputs": [], "source": [ "n_sims = 4\n", "tsize = np.array([2, 10, 20, 40, 80, 160, 320])" ] }, { "cell_type": "markdown", "id": "3a2335c7", "metadata": {}, "source": [ "Rydiqule's standard time-solving backend is scipy's `solve_ivp`." ] }, { "cell_type": "code", "execution_count": 12, "id": "004518db", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Solving 320 detunings, round 4/4\r" ] } ], "source": [ "ttimes_stack = np.zeros((len(tsize), n_sims), dtype=float)\n", "\n", "for i, p_pts in enumerate(tsize):\n", " for j in range(n_sims):\n", " print(f'Solving {p_pts} detunings, round {j+1}/{n_sims}', end='\\r')\n", " probe = {'states': (0,1), 'rabi_frequency':2*np.pi*0.1,\n", " 'detuning':2*np.pi*np.linspace(-100, 100, p_pts), 'label':'probe'}\n", " tts.add_couplings(probe)\n", " tic = time.perf_counter()\n", " _ = rq.solve_time(tts, end_time=10, num_pts=100)\n", " toc = time.perf_counter()\n", " ttimes_stack[i,j] = (toc-tic)" ] }, { "cell_type": "markdown", "id": "619912b9", "metadata": {}, "source": [ "Rydiqule also has some support for a compiled version of `solve_ivp` provided by the `CyRK` package. It can be faster for some kinds of problems, but it is not compatible with all problems in rydiqule. For example, the optional `flat` argument used here provides the best performance, but is not compatible with doppler-broadened solves." ] }, { "cell_type": "code", "execution_count": 13, "id": "b347d4ea", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Solving 320 detunings, round 4/4\r" ] } ], "source": [ "cttimes_stack = np.zeros((len(tsize), n_sims), dtype=float)\n", "\n", "for i, p_pts in enumerate(tsize):\n", " for j in range(n_sims):\n", " print(f'Solving {p_pts} detunings, round {j+1}/{n_sims}', end='\\r')\n", " probe = {'states': (0,1), 'rabi_frequency':2*np.pi*0.1,\n", " 'detuning':2*np.pi*np.linspace(-100, 100, p_pts), 'label':'probe'}\n", " tts.add_couplings(probe)\n", " tic = time.perf_counter()\n", " _ = rq.solve_time(tts, end_time=10, num_pts=100, solver='cyrk', eqns='flat')\n", " toc = time.perf_counter()\n", " cttimes_stack[i,j] = (toc-tic)" ] }, { "cell_type": "code", "execution_count": 14, "id": "272cbe63", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1)\n", "\n", "ave_times = ttimes_stack.mean(axis=1)\n", "std_times = ttimes_stack.std(axis=1)\n", "\n", "ax.errorbar(tsize, ave_times, yerr=std_times, fmt='o', label='scipy')\n", "ax.errorbar(tsize, cttimes_stack.mean(axis=1), yerr=cttimes_stack.std(axis=1), fmt='o', label='cyrk')\n", "ax.legend()\n", "ax.set_title('Time-dependent Solve Time vs Parameter Size')\n", "ax.set_xlabel('Parameter Size ($d$)')\n", "ax.set_ylabel('Solve Time (s)')\n", "ax.set_yscale('log')\n", "ax.set_xscale('log')" ] }, { "cell_type": "markdown", "id": "520c83b2", "metadata": {}, "source": [ "## Comparison to qutip ##\n", "\n", "While qutip primarily targets a different (and wider) set of problems, we can compare solving a simple 2-level system over a set of parameters. We note that qutip is not designed or advertised to be effective at solving semi-classical quantum systems with large numbers of atomic levels or iterated over many parameters. Rydiqule, on the other hand, is specifically designed to solve that subset of problems, as will be seen below." ] }, { "cell_type": "markdown", "id": "790de91a", "metadata": {}, "source": [ "First, we solve the demonstration system in rydiqule. It has 101 detunings and 10 rabi frequencies, and we want to plot the imaginary part of $\\rho_{1,0}$." ] }, { "cell_type": "code", "execution_count": 15, "id": "68100ac1", "metadata": {}, "outputs": [], "source": [ "detunings = np.linspace(-50, 50, 101)\n", "rabis = np.geomspace(0.1, 25, 10)\n", "gamma = 6.0666\n", "\n", "probe = {'states': (0,1), 'rabi_frequency':2*np.pi*rabis, 'detuning':2*np.pi*detunings, 'label':'probe'}\n", "\n", "s2 = rq.Sensor(2)\n", "s2.add_couplings(probe)\n", "s2.add_decoherence((1,0), 2*np.pi*gamma)" ] }, { "cell_type": "code", "execution_count": 16, "id": "767b4d90", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "12.6 ms ± 908 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" ] } ], "source": [ "%%timeit\n", "_ = rq.solve_steady_state(s2)" ] }, { "cell_type": "code", "execution_count": 17, "id": "3866284e", "metadata": {}, "outputs": [], "source": [ "sols_rq2 = rq.solve_steady_state(s2)" ] }, { "cell_type": "code", "execution_count": 18, "id": "61ce0e54", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$Im(\\\\rho_{1,0})$')" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1)\n", "\n", "ax.plot(detunings, sols_rq2.rho_ij(1,0).imag)\n", "ax.set_xlabel('Probe Detuning (MHz)')\n", "ax.set_ylabel('$Im(\\\\rho_{1,0})$')" ] }, { "cell_type": "markdown", "id": "2caefde6", "metadata": {}, "source": [ "Constructing the same hamiltonian in qutip is done by expressing it as sums of Pauli matrices. Note that each parameter set requires re-building the Hamiltonian at each point, done via a nested python loop. It is difficult to scale the problem configuration to large numbers of atomic levels. And each set of parameters to be iterated over requires a separate python loop. The incurred interpreter overhead is substantial, giving a solve time more than 3 orders of magnitude slower." ] }, { "cell_type": "code", "execution_count": 19, "id": "9220c6a1", "metadata": {}, "outputs": [], "source": [ "import qutip" ] }, { "cell_type": "code", "execution_count": 20, "id": "3d5056a9", "metadata": {}, "outputs": [], "source": [ "sm = qutip.destroy(2)\n", "c_op_list = [np.sqrt(2*np.pi*gamma) * sm] # note: qutip wants root of the rate\n", "\n", "psi0 = qutip.basis(2, 0)\n", "psi1 = qutip.basis(2, 1)\n", "\n", "def q_solve(det, rabi):\n", "\n", " H0 = (2*np.pi*det*qutip.sigmaz() + 2*np.pi*rabi*qutip.sigmax())/2\n", "\n", " rho_ss = qutip.steadystate(H0, c_op_list, method='direct', solver='solve').full()\n", "\n", " return rho_ss\n" ] }, { "cell_type": "code", "execution_count": 21, "id": "cfaa88bd", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: total: 20 s\n", "Wall time: 20 s\n" ] } ], "source": [ "%%time\n", "sols_qtp = np.empty((len(detunings), len(rabis), 2, 2), dtype = np.complex128)\n", "\n", "for i, det in enumerate(detunings):\n", " for j, rabi in enumerate(rabis):\n", " sols_qtp[i,j] = q_solve(det, rabi)" ] }, { "cell_type": "code", "execution_count": 22, "id": "8cbf71a6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$Im(\\\\rho_{1,0})$')" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1)\n", "\n", "ax.plot(detunings, sols_qtp[:,:,0,1].imag)\n", "ax.set_xlabel('Probe Detuning (MHz)')\n", "ax.set_ylabel('$Im(\\\\rho_{1,0})$')" ] }, { "cell_type": "markdown", "id": "7b67ee3f", "metadata": {}, "source": [ "### Time-dependence comparison ###\n", "\n", "We compare the same problem, but this time with a time-dependent Hamiltonian. Here QuTiP provides many highly-optimized time-integrators and is generally faster for a solve on a single set of parameters." ] }, { "cell_type": "markdown", "id": "20af815f", "metadata": {}, "source": [ "We start by solving the simple system in rydiqule for a single set of parameters." ] }, { "cell_type": "code", "execution_count": 23, "id": "86005d8e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0. 0. 0.]\n" ] } ], "source": [ "gamma = 6.0666\n", "\n", "probe = {'states': (0,1), 'rabi_frequency':2*np.pi*1, 'detuning':2*np.pi*0, 'label':'probe',\n", " 'time_dependence': lambda t: np.sin(2*np.pi*2*t)}\n", "\n", "s2t = rq.Sensor(2)\n", "s2t.add_couplings(probe)\n", "s2t.add_decoherence((1,0), 2*np.pi*gamma)\n", "\n", "init_cond_complex = np.array(((1,0),\n", " (0,0)), dtype=float)\n", "init_cond = rq.sensor_utils.convert_complex_to_dm(init_cond_complex)\n", "print(init_cond)\n", "end_time = 10 # us\n", "n_pts = 400" ] }, { "cell_type": "code", "execution_count": 24, "id": "ed13e4c6", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: total: 93.8 ms\n", "Wall time: 98.8 ms\n" ] } ], "source": [ "%%time\n", "sols_rq2t = rq.solve_time(s2t, end_time, n_pts, init_cond=init_cond)" ] }, { "cell_type": "code", "execution_count": 25, "id": "d04da3ca", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$\\\\rho_{1,1}$')" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1)\n", "\n", "ax.plot(sols_rq2t.t, sols_rq2t.rho_ij(1,1))\n", "ax.set_xlabel('Time (us)')\n", "ax.set_ylabel('$\\\\rho_{1,1}$')" ] }, { "cell_type": "markdown", "id": "90ebc55c", "metadata": {}, "source": [ "We solve the same problem in qutip, using its standard `mesolve` with the optional cython-compiled backend enabled." ] }, { "cell_type": "code", "execution_count": 26, "id": "0615e3d6", "metadata": {}, "outputs": [], "source": [ "sm = qutip.destroy(2)\n", "c_op_list = [np.sqrt(2*np.pi*gamma) * sm]\n", "\n", "psi0 = qutip.basis(2, 0)\n", "psi1 = qutip.basis(2, 1)\n", "w = 2\n", "\n", "t_list = np.linspace(0, end_time, n_pts)\n", "\n", "def q_tsolve(det, rabi):\n", "\n", " H0 = (2*np.pi*det*qutip.sigmaz())/2\n", " H1 = 2*np.pi*rabi*qutip.sigmax()/2\n", " args = {'w': w}\n", "\n", " H = [H0, [H1, \"np.sin(2*np.pi*w*t)\"]]\n", "\n", " rho_t = qutip.mesolve(H, psi0, t_list, c_op_list, args=args)\n", "\n", " return rho_t\n" ] }, { "cell_type": "markdown", "id": "4a70fc87", "metadata": {}, "source": [ "Ensure a first run to allow first compilation to occur. Requires optional dependencies: `cython` and `filelock`." ] }, { "cell_type": "code", "execution_count": 27, "id": "b10ed205", "metadata": {}, "outputs": [], "source": [ "sols_qtp2 = q_tsolve(0, 1.0)" ] }, { "cell_type": "markdown", "id": "8edf19e8", "metadata": {}, "source": [ "QuTiP's (mostly) standard solver is over x4 faster." ] }, { "cell_type": "code", "execution_count": 28, "id": "7c1aa54d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "22.3 ms ± 1.07 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n" ] } ], "source": [ "%%timeit\n", "sols_qtp2 = q_tsolve(0, 1.0)" ] }, { "cell_type": "code", "execution_count": 29, "id": "2a4de97d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$\\\\rho_{1,1}$')" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1)\n", "\n", "prob_11 = qutip.expect(psi1 * psi1.dag(), sols_qtp2.states)\n", "\n", "ax.plot(t_list, prob_11)\n", "ax.set_xlabel('Time (us)')\n", "ax.set_ylabel('$\\\\rho_{1,1}$')" ] }, { "cell_type": "markdown", "id": "9da95d42", "metadata": {}, "source": [ "### Time-dependent comparison over many parameters ###" ] }, { "cell_type": "markdown", "id": "dae9872b", "metadata": {}, "source": [ "If we want to solve the same time-dependent problem for many parameters, this is easy to set up in rydiqule but uses nested for loops for qutip (which incurs interpreted overhead similar to the steady-state example above)." ] }, { "cell_type": "code", "execution_count": 30, "id": "82b29ddc", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(101, 10, 3)\n" ] } ], "source": [ "detunings = np.linspace(-50, 50, 101)\n", "rabis = np.geomspace(0.1, 25, 10)\n", "gamma = 6.0666\n", "\n", "probe = {'states': (0,1), 'rabi_frequency':2*np.pi*rabis, 'detuning':2*np.pi*detunings, 'label':'probe',\n", " 'time_dependence': lambda t: np.sin(2*np.pi*2*t)}\n", "\n", "s2t = rq.Sensor(2)\n", "s2t.add_couplings(probe)\n", "s2t.add_decoherence((1,0), 2*np.pi*gamma)\n", "\n", "init_cond = rq.solve_steady_state(s2t).rho\n", "print(init_cond.shape)\n", "end_time = 10 # us\n", "n_pts = 400" ] }, { "cell_type": "code", "execution_count": 31, "id": "a79df520", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: total: 1.56 s\n", "Wall time: 1.56 s\n" ] } ], "source": [ "%%time\n", "sols_rq2t = rq.solve_time(s2t, end_time, n_pts, init_cond=init_cond)" ] }, { "cell_type": "markdown", "id": "66412e1b", "metadata": {}, "source": [ "To make pre-allocating the results easier, we use qutip's ability to automatically calculate expectation values for a desired parameter at solve time." ] }, { "cell_type": "code", "execution_count": 32, "id": "87aa26c7", "metadata": {}, "outputs": [], "source": [ "sm = qutip.destroy(2)\n", "c_op_list = [np.sqrt(2*np.pi*gamma) * sm]\n", "\n", "psi0 = qutip.basis(2, 0)\n", "psi1 = qutip.basis(2, 1)\n", "w = 2\n", "\n", "t_list = np.linspace(0, end_time, n_pts)\n", "\n", "def q_tsolve(det, rabi):\n", "\n", " H0 = (2*np.pi*det*qutip.sigmaz())/2\n", " H1 = 2*np.pi*rabi*qutip.sigmax()/2\n", " args = {'w': w}\n", "\n", " H = [H0, [H1, \"np.sin(2*np.pi*w*t)\"]]\n", "\n", " # calculate desired output here since pre-allocating and storing density matrices is annoying\n", " rho11_t = qutip.mesolve(H, psi0, t_list, c_op_list, e_ops = [psi1*psi1.dag()], args=args).expect[0]\n", "\n", " return rho11_t\n" ] }, { "cell_type": "markdown", "id": "8dad9a3b", "metadata": {}, "source": [ "We see that the interpreter overhead is significant, leading to over an order of magnitude slower total calculation time versus rydiqule." ] }, { "cell_type": "code", "execution_count": 33, "id": "58672296", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: total: 58.1 s\n", "Wall time: 56.5 s\n" ] } ], "source": [ "%%time\n", "sols_qtp2p = np.empty((len(detunings), len(rabis), n_pts), dtype = np.complex128)\n", "size = len(detunings)*len(rabis)\n", "\n", "for i, det in enumerate(detunings):\n", " for j, rabi in enumerate(rabis):\n", " print(f'Solving {(i)*len(rabis)+(j+1)}/{size}', end='\\r')\n", " sols_qtp2p[i,j,:] = q_tsolve(det, rabi)" ] }, { "cell_type": "code", "execution_count": 35, "id": "32840ae3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " Rydiqule\n", " ================\n", " \n", "Rydiqule Version: 2.1.1.dev37\n", "Installation Path: ~\\src\\rydiqule_public\\src\\rydiqule\n", "\n", " Dependencies\n", " ================\n", " \n", "NumPy Version: 2.0.1\n", "SciPy Version: 1.16.0\n", "Matplotlib Version: 3.10.5\n", "ARC Version: 3.9.0\n", "Python Version: 3.12.3\n", "Python Install Path: ~\\miniconda3\\envs\\qutip\n", "Platform Info: Windows (AMD64)\n", "CPU Count and Freq: 16 @ 3.91 GHz\n", "Total System Memory: 256 GB\n" ] } ], "source": [ "rq.about()" ] }, { "cell_type": "code", "execution_count": 36, "id": "2887f96e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "QuTiP: Quantum Toolbox in Python\n", "================================\n", "Copyright (c) QuTiP team 2011 and later.\n", "Current admin team: Alexander Pitchford, Nathan Shammah, Shahnawaz Ahmed, Neill Lambert, Eric Giguère, Boxi Li, Simon Cross, Asier Galicia, Paul Menczel, and Patrick Hopf.\n", "Board members: Daniel Burgarth, Robert Johansson, Anton F. Kockum, Franco Nori and Will Zeng.\n", "Original developers: R. J. Johansson & P. D. Nation.\n", "Previous lead developers: Chris Granade & A. Grimsmo.\n", "Currently developed through wide collaboration. See https://github.com/qutip for details.\n", "\n", "QuTiP Version: 5.2.1\n", "Numpy Version: 2.0.1\n", "Scipy Version: 1.16.0\n", "Cython Version: 3.1.3\n", "Matplotlib Version: 3.10.5\n", "Python Version: 3.12.3\n", "Number of CPUs: 16\n", "BLAS Info: Generic\n", "INTEL MKL Ext: None\n", "Platform Info: Windows (AMD64)\n", "Installation path: c:\\Users\\naqsL\\miniconda3\\envs\\qutip\\Lib\\site-packages\\qutip\n", "\n", "Installed QuTiP family packages\n", "-------------------------------\n", "\n", "No QuTiP family packages installed.\n", "\n", "================================================================================\n", "Please cite QuTiP in your publication.\n", "================================================================================\n", "For your convenience a bibtex reference can be easily generated using `qutip.cite()`\n" ] } ], "source": [ "qutip.about()" ] }, { "cell_type": "code", "execution_count": null, "id": "fbaf1d09", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "qutip", "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": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 5 }