diff --git a/examples/dbi/DBI_strategy_Pauli-Z_products.ipynb b/examples/dbi/DBI_strategy_Pauli-Z_products.ipynb index 0f76a36245..d89fdd5e74 100644 --- a/examples/dbi/DBI_strategy_Pauli-Z_products.ipynb +++ b/examples/dbi/DBI_strategy_Pauli-Z_products.ipynb @@ -28,7 +28,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -122,31 +122,16 @@ }, { "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "[Qibo 0.2.4|INFO|2024-01-24 19:59:31]: Using qibojit (numba) backend on /CPU:0\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Initial off diagonal norm 8.48528137423857\n" - ] - } - ], + "execution_count": null, + "metadata": {}, + "outputs": [], "source": [ "# set the qibo backend (we suggest qibojit if N >= 20)\n", "# alternatives: tensorflow (not optimized), numpy (when CPU not supported by jit)\n", "set_backend(\"qibojit\", \"numba\")\n", "\n", "# hamiltonian parameters\n", - "nqubits = 2\n", + "nqubits = 5\n", "h = 3\n", "\n", "# define the hamiltonian\n", @@ -160,20 +145,9 @@ }, { "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[-2.-0.j -0.-0.j -0.-0.j -0.-0.j]\n", - " [-0.-0.j 2.-0.j -0.-0.j -0.-0.j]\n", - " [-0.-0.j -0.-0.j 2.-0.j -0.-0.j]\n", - " [-0.-0.j -0.-0.j -0.-0.j -2.-0.j]]\n" - ] - } - ], + "execution_count": null, + "metadata": {}, + "outputs": [], "source": [ "print(H_TFIM.matrix)" ] @@ -219,8 +193,9 @@ "# add in initial values for plotting\n", "off_diagonal_norm_history = [dbi.off_diagonal_norm]\n", "steps = [0]\n", + "scheduling = DoubleBracketScheduling.use_hyperopt\n", "for _ in range(NSTEPS):\n", - " dbi, idx, step, flip_sign = select_best_dbr_generator(dbi, Z_ops, compare_canonical=False, max_evals=max_evals, step_max=step_max)\n", + " dbi, idx, step, flip_sign = select_best_dbr_generator(dbi, Z_ops, scheduling=scheduling, compare_canonical=False, max_evals=max_evals, step_max=step_max)\n", " off_diagonal_norm_history.append(dbi.off_diagonal_norm)\n", " steps.append(steps[-1]+step)\n", " if flip_sign < 0:\n", @@ -294,7 +269,6 @@ " step_max = 1,\n", " space = hp.uniform,\n", " optimizer = tpe,\n", - " max_evals = max_evals,\n", " )\n", " dbi_canonical(step=step)\n", " print(f\"New optimized step at iteration {s+1}/{NSTEPS}: {step}, loss {dbi_canonical.off_diagonal_norm}\")\n", @@ -389,7 +363,7 @@ "off_diagonal_norm_history_mixed = [dbi_mixed.off_diagonal_norm]\n", "steps = [0]\n", "for _ in range(NSTEPS):\n", - " dbi_mixed, idx, step, flip_sign = select_best_dbr_generator(dbi_mixed, Z_ops, compare_canonical=True, max_evals=max_evals)\n", + " dbi_mixed, idx, step, flip_sign = select_best_dbr_generator(dbi_mixed, Z_ops, scheduling=scheduling, compare_canonical=True, max_evals=max_evals, step_max=step_max)\n", " off_diagonal_norm_history_mixed.append(dbi_mixed.off_diagonal_norm)\n", " steps.append(steps[-1]+step)\n", " if idx == len(Z_ops):\n", @@ -479,7 +453,7 @@ "remaining_NSTEPS = NSTEPS - cannonical_NSTEPS\n", "dbi_mixed_can.mode = DoubleBracketGeneratorType.single_commutator\n", "for _ in range(remaining_NSTEPS):\n", - " dbi_mixed_can, idx, step, flip_sign = select_best_dbr_generator(dbi_mixed_can, Z_ops, compare_canonical=False)\n", + " dbi_mixed_can, idx, step, flip_sign = select_best_dbr_generator(dbi_mixed_can, Z_ops, scheduling=scheduling, compare_canonical=False, max_evals=max_evals, step_max=step_max)\n", " off_diagonal_norm_history_mixed_can.append(dbi_mixed_can.off_diagonal_norm)\n", " steps_mixed_can.append(step)\n", " if idx == len(Z_ops):\n", diff --git a/examples/dbi/dbi_costs.ipynb b/examples/dbi/dbi_costs.ipynb new file mode 100644 index 0000000000..558f74cff3 --- /dev/null +++ b/examples/dbi/dbi_costs.ipynb @@ -0,0 +1,548 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Double-bracket Iteration other cost functions and respective scheduling\n", + "\n", + "This notebook presents two additional cost functions for the double-bracket flow: least-squares and energy fluctuation with their respectice scheduling methods." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "from copy import deepcopy\n", + "\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from qibo import hamiltonians, set_backend\n", + "from qibo.models.dbi.double_bracket import DoubleBracketGeneratorType, DoubleBracketScheduling, DoubleBracketIteration, DoubleBracketCostFunction\n", + "from qibo.models.dbi.utils import *\n", + "from qibo.models.dbi.utils_scheduling import *" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Least-squares\n", + "\n", + "The cost function is defined as: $\\frac{1}{2}||D-H_k||^2 =\\frac{1}{2}(||D||^2+||H||^2) -Tr(D H_k)$ as in https://epubs.siam.org/doi/abs/10.1137/S0036141092229732?journalCode=sjmael. We seek to maximize this function at each iteration." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "[Qibo 0.2.5|INFO|2024-03-15 18:17:05]: Using qibojit (numba) backend on /CPU:0\n" + ] + } + ], + "source": [ + "# Hamiltonian\n", + "set_backend(\"qibojit\", \"numba\")\n", + "\n", + "# hamiltonian parameters\n", + "nqubits = 5\n", + "h = 3.0\n", + "\n", + "# define the hamiltonian\n", + "H_TFIM = hamiltonians.TFIM(nqubits=nqubits, h=h)\n", + "\n", + "# define the least-squares cost function\n", + "cost = DoubleBracketCostFunction.least_squares\n", + "# initialize class\n", + "dbi = DoubleBracketIteration(deepcopy(H_TFIM),mode=DoubleBracketGeneratorType.single_commutator,cost=cost)\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "grid_search step: 0.02021181818181818\n", + "hyperopt_search step: 0.2796044748864459\n", + "polynomial_approximation step: 0.016462159944159827\n" + ] + } + ], + "source": [ + "# generate data for plotting sigma decrease of the first step\n", + "d = np.diag(np.linspace(1,2**nqubits,2**nqubits))\n", + "s_space = np.linspace(1e-5, 0.6, 1000)\n", + "off_diagonal_norm_diff = []\n", + "potential = []\n", + "for s in s_space:\n", + " dbi_eval = deepcopy(dbi)\n", + " dbi_eval(s,d=d)\n", + " off_diagonal_norm_diff.append(dbi_eval.off_diagonal_norm - dbi.off_diagonal_norm)\n", + " potential.append(dbi_eval.least_squares(D=d))\n", + "\n", + "# grid_search\n", + "step_grid = dbi.choose_step(scheduling=DoubleBracketScheduling.grid_search,d=d)\n", + "print('grid_search step:', step_grid)\n", + "# hyperopt\n", + "step_hyperopt = dbi.choose_step(scheduling=DoubleBracketScheduling.hyperopt,d=d, max_evals=100, step_max=0.6)\n", + "print('hyperopt_search step:', step_hyperopt)\n", + "# polynomial\n", + "step_poly = dbi.choose_step(scheduling=DoubleBracketScheduling.polynomial_approximation,d=d, n=3)\n", + "print('polynomial_approximation step:', step_poly)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The minimum for cost function in the tested range is: 0.02021181818181818\n" + ] + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plot the results\n", + "plt.figure()\n", + "plt.plot(s_space, potential)\n", + "plt.xlabel('s')\n", + "plt.axvline(x=step_grid, color='r', linestyle='-',label='grid_search')\n", + "plt.axvline(x=step_hyperopt, color='g', linestyle='--',label='hyperopt')\n", + "plt.axvline(x=step_poly, color='m', linestyle='-.',label='polynomial')\n", + "plt.title('First DBI step')\n", + "plt.ylabel('Least squares cost function')\n", + "plt.legend()\n", + "plt.figure()\n", + "plt.plot(s_space, off_diagonal_norm_diff)\n", + "plt.axvline(x=step_grid, color='r', linestyle='-',label='grid_search')\n", + "plt.axvline(x=step_hyperopt, color='g', linestyle='--',label='hyperopt')\n", + "plt.axvline(x=step_poly, color='m', linestyle='-.',label='polynomial')\n", + "plt.ylabel(r'$||\\sigma(H_0)||-\\sigma(H_k)||$')\n", + "plt.xlabel('s')\n", + "plt.title('First DBI step')\n", + "plt.legend()\n", + "print('The minimum for cost function in the tested range is:', step_grid)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Comparison of the least-squares cost function with the original cost function using the polynomial scheduling method" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "d = np.diag(np.linspace(1,2**nqubits,2**nqubits))\n", + "off_diagonal_norm_diff = [dbi.off_diagonal_norm]\n", + "off_diagonal_norm_diff_least_squares = [dbi.off_diagonal_norm]\n", + "iters = 100\n", + "dbi_ls = deepcopy(dbi)\n", + "cost = DoubleBracketCostFunction.off_diagonal_norm\n", + "dbi_od = DoubleBracketIteration(deepcopy(H_TFIM),mode=DoubleBracketGeneratorType.single_commutator,cost=cost)\n", + "for _ in range(iters):\n", + " step_poly = dbi_od.choose_step(scheduling=DoubleBracketScheduling.polynomial_approximation, d=d, n=3)\n", + " dbi_od(step_poly,d=d)\n", + " step_poly = dbi_ls.choose_step(scheduling=DoubleBracketScheduling.polynomial_approximation, d=d, n=3)\n", + " dbi_ls(step_poly,d=d)\n", + " off_diagonal_norm_diff.append(dbi_od.off_diagonal_norm)\n", + " off_diagonal_norm_diff_least_squares.append(dbi_ls.off_diagonal_norm)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure()\n", + "plt.plot(range(iters+1), off_diagonal_norm_diff, label=r'Off-diagonal norm')\n", + "plt.plot(range(iters+1), off_diagonal_norm_diff_least_squares, label=r'Least squares')\n", + "plt.xlabel('Iterations')\n", + "plt.ylabel(r'$||\\sigma(H_k)||$')\n", + "plt.legend()\n" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Energy fluctuation\n", + "\n", + "This cost function is defined as: $\\Xi_k^2 (\\mu) = \\langle \\mu | H_k^2| \\mu \\rangle - \\langle \\mu | H_k| \\mu \\rangle^2$" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "[Qibo 0.2.5|INFO|2024-03-15 18:17:12]: Using qibojit (numba) backend on /CPU:0\n" + ] + } + ], + "source": [ + "# Hamiltonian\n", + "set_backend(\"qibojit\", \"numba\")\n", + "\n", + "# hamiltonian parameters\n", + "nqubits = 3\n", + "h = 3.0\n", + "\n", + "# define the hamiltonian\n", + "H_TFIM = hamiltonians.TFIM(nqubits=nqubits, h=h)\n", + "\n", + "# define the energy fluctuation cost function\n", + "cost = DoubleBracketCostFunction.energy_fluctuation\n", + "# define the state\n", + "state = 0\n", + "# initialize class\n", + "dbi = DoubleBracketIteration(deepcopy(H_TFIM),mode=DoubleBracketGeneratorType.single_commutator,cost=cost, state=state)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "grid_search step: 0.8585872727272726\n", + "hyperopt_search step: 0.3413442272248831\n", + "polynomial_approximation step: 0.028303853122485182\n" + ] + } + ], + "source": [ + "# generate data for plotting sigma decrease of the first step\n", + "d = np.diag(np.linspace(1,2**nqubits,2**nqubits))\n", + "s_space = np.linspace(1e-5, 0.9, 1000)\n", + "off_diagonal_norm_diff = []\n", + "fluctuation = []\n", + "for s in s_space:\n", + " dbi_eval = deepcopy(dbi)\n", + " dbi_eval(s,d=d)\n", + " off_diagonal_norm_diff.append(dbi_eval.off_diagonal_norm - dbi.off_diagonal_norm)\n", + " fluctuation.append(dbi_eval.energy_fluctuation(state=state))\n", + "\n", + "# grid_search\n", + "step_grid = dbi.choose_step(scheduling=DoubleBracketScheduling.grid_search,d=d)\n", + "print('grid_search step:', step_grid)\n", + "# hyperopt\n", + "step_hyperopt = dbi.choose_step(scheduling=DoubleBracketScheduling.hyperopt,d=d, max_evals=100, step_max=0.6)\n", + "print('hyperopt_search step:', step_hyperopt)\n", + "# polynomial\n", + "step_poly = dbi.choose_step(scheduling=DoubleBracketScheduling.polynomial_approximation,d=d, n=3)\n", + "print('polynomial_approximation step:', step_poly)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The minimum for cost function in the tested range is: 0.8585872727272726\n" + ] + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plot the results\n", + "plt.figure()\n", + "plt.plot(s_space, fluctuation)\n", + "plt.xlabel('s')\n", + "plt.axvline(x=step_grid, color='r', linestyle='-',label='grid_search')\n", + "plt.axvline(x=step_hyperopt, color='g', linestyle='--',label ='hyperopt')\n", + "plt.axvline(x=step_poly, color='m', linestyle='-.',label='polynomial')\n", + "plt.title('First DBI step')\n", + "plt.ylabel('Energy fluctuation')\n", + "plt.legend()\n", + "plt.figure()\n", + "plt.plot(s_space, off_diagonal_norm_diff)\n", + "plt.axvline(x=step_grid, color='r', linestyle='-',label='grid_search')\n", + "plt.axvline(x=step_hyperopt, color='g', linestyle='--',label='hyperopt')\n", + "plt.axvline(x=step_poly, color='m', linestyle='-.',label='polynomial')\n", + "plt.ylabel(r'$||\\sigma(H_0)||-\\sigma(H_k)||$')\n", + "plt.xlabel('s')\n", + "plt.title('First DBI step')\n", + "plt.legend()\n", + "print('The minimum for cost function in the tested range is:', step_grid)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "d = np.diag(np.linspace(1,2**nqubits,2**nqubits))\n", + "off_diagonal_norm_diff = [dbi.off_diagonal_norm]\n", + "energy_fluc = [dbi.energy_fluctuation(state=state)]\n", + "iters = 50\n", + "dbi_ = deepcopy(dbi)\n", + "for _ in range(iters):\n", + " step_poly = dbi_.choose_step(scheduling=DoubleBracketScheduling.polynomial_approximation, d=d, n=3)\n", + " dbi_(step_poly,d=d)\n", + " off_diagonal_norm_diff.append(dbi_.off_diagonal_norm)\n", + " energy_fluc.append(dbi_.energy_fluctuation(state=state))" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'Energy fluctuation')" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure()\n", + "plt.plot(range(iters+1), off_diagonal_norm_diff)\n", + "plt.xlabel('Iterations')\n", + "plt.ylabel(r'$||\\sigma(H_k)||$')\n", + "\n", + "plt.figure()\n", + "plt.plot(range(iters+1), energy_fluc)\n", + "plt.xlabel('Iterations')\n", + "plt.ylabel(r'Energy fluctuation')\n" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "iters = 10\n", + "columnNorm = np.empty((2**nqubits,iters))\n", + "d = (np.diag(np.linspace(1,2**nqubits,2**nqubits)))\n", + "for i in range(2**nqubits):\n", + " dbi_ = deepcopy(dbi)\n", + " dbi_.state = i\n", + " for j in range(iters):\n", + " step_poly = dbi_.choose_step(scheduling=DoubleBracketScheduling.polynomial_approximation, d=d, n=3)\n", + " dbi_(step_poly,d=d)\n", + " columnNorm[i,j] = np.linalg.norm(dbi_.h.matrix[:,i])\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5, 0, 'Iterations')" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "eigvals = np.linalg.eigh(dbi_.h.matrix)[0]\n", + "plt.figure()\n", + "for i in range(2**nqubits):\n", + " plt.plot(range(iters), columnNorm[i], label='State ' + str(i))\n", + " plt.axhline(y=eigvals[i], color='r', linestyle='--')\n", + "plt.xlabel('Iterations')\n" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "ename": "ValueError", + "evalue": "The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()", + "output_type": "error", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[1;32mIn[20], line 8\u001b[0m\n\u001b[0;32m 5\u001b[0m step \u001b[39m=\u001b[39m \u001b[39m1e-2\u001b[39m\n\u001b[0;32m 6\u001b[0m iterations \u001b[39m=\u001b[39m \u001b[39m100\u001b[39m\n\u001b[1;32m----> 8\u001b[0m d, loss, grad, diags \u001b[39m=\u001b[39m gradient_ascent(dbi, d,step, iterations)\n\u001b[0;32m 10\u001b[0m n \u001b[39m=\u001b[39m \u001b[39m3\u001b[39m\n", + "File \u001b[1;32m~\\Documents\\GitHub\\qibo\\src\\qibo\\models\\dbi\\utils_scheduling.py:253\u001b[0m, in \u001b[0;36mgradient_ascent\u001b[1;34m(dbi_object, d, step, iterations)\u001b[0m\n\u001b[0;32m 250\u001b[0m diagonals[:,\u001b[39m0\u001b[39m] \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39mdiag(d)\n\u001b[0;32m 252\u001b[0m \u001b[39mfor\u001b[39;00m i \u001b[39min\u001b[39;00m \u001b[39mrange\u001b[39m(iterations):\n\u001b[1;32m--> 253\u001b[0m grad[i,:] \u001b[39m=\u001b[39m gradientDiagonal(dbi_object, d, H)\n\u001b[0;32m 254\u001b[0m \u001b[39mfor\u001b[39;00m j \u001b[39min\u001b[39;00m \u001b[39mrange\u001b[39m(\u001b[39mlen\u001b[39m(d)):\n\u001b[0;32m 255\u001b[0m d[j,j] \u001b[39m=\u001b[39m d[j,j] \u001b[39m+\u001b[39m step\u001b[39m*\u001b[39mgrad[i,j] \u001b[39m# note the plus sign as we maximize the potential\u001b[39;00m\n", + "File \u001b[1;32m~\\Documents\\GitHub\\qibo\\src\\qibo\\models\\dbi\\utils_scheduling.py:237\u001b[0m, in \u001b[0;36mgradientDiagonal\u001b[1;34m(dbi_object, d, H)\u001b[0m\n\u001b[0;32m 235\u001b[0m grad \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39mzeros(\u001b[39mlen\u001b[39m(d))\n\u001b[0;32m 236\u001b[0m \u001b[39mfor\u001b[39;00m i \u001b[39min\u001b[39;00m \u001b[39mrange\u001b[39m(\u001b[39mlen\u001b[39m(d)):\n\u001b[1;32m--> 237\u001b[0m derivative \u001b[39m=\u001b[39m dpolynomial_diDiagonal(dbi_object,d,H,i)\n\u001b[0;32m 238\u001b[0m grad[i] \u001b[39m=\u001b[39m derivative\u001b[39m-\u001b[39md[i,i]\n\u001b[0;32m 239\u001b[0m \u001b[39mreturn\u001b[39;00m grad\n", + "File \u001b[1;32m~\\Documents\\GitHub\\qibo\\src\\qibo\\models\\dbi\\utils_scheduling.py:224\u001b[0m, in \u001b[0;36mdpolynomial_diDiagonal\u001b[1;34m(dbi_object, d, H, i)\u001b[0m\n\u001b[0;32m 220\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39mdpolynomial_diDiagonal\u001b[39m(dbi_object, d,H,i):\n\u001b[0;32m 221\u001b[0m \u001b[39m# Derivative of polynomial approximation of potential function with respect to diagonal elements of d (full-diagonal ansatz)\u001b[39;00m\n\u001b[0;32m 222\u001b[0m \u001b[39m# Formula can be expanded easily to any order, with n=3 corresponding to cubic approximation\u001b[39;00m\n\u001b[0;32m 223\u001b[0m derivative \u001b[39m=\u001b[39m \u001b[39m0\u001b[39m\n\u001b[1;32m--> 224\u001b[0m s \u001b[39m=\u001b[39m polynomial_step(dbi_object, d, H, i)\n\u001b[0;32m 225\u001b[0m A \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39mzeros(d\u001b[39m.\u001b[39mshape)\n\u001b[0;32m 226\u001b[0m Gamma_list \u001b[39m=\u001b[39m dbi_object\u001b[39m.\u001b[39mgenerate_Gamma_list(\u001b[39m4\u001b[39m, d)\n", + "File \u001b[1;32m~\\Documents\\GitHub\\qibo\\src\\qibo\\models\\dbi\\utils_scheduling.py:127\u001b[0m, in \u001b[0;36mpolynomial_step\u001b[1;34m(dbi_object, n, n_max, d, coef, cost)\u001b[0m\n\u001b[0;32m 124\u001b[0m \u001b[39mif\u001b[39;00m d \u001b[39mis\u001b[39;00m \u001b[39mNone\u001b[39;00m:\n\u001b[0;32m 125\u001b[0m d \u001b[39m=\u001b[39m dbi_object\u001b[39m.\u001b[39mdiagonal_h_matrix\n\u001b[1;32m--> 127\u001b[0m \u001b[39mif\u001b[39;00m n \u001b[39m>\u001b[39;49m n_max:\n\u001b[0;32m 128\u001b[0m \u001b[39mraise\u001b[39;00m \u001b[39mValueError\u001b[39;00m(\n\u001b[0;32m 129\u001b[0m \u001b[39m\"\u001b[39m\u001b[39mNo solution can be found with polynomial approximation. Increase `n_max` or use other scheduling methods.\u001b[39m\u001b[39m\"\u001b[39m\n\u001b[0;32m 130\u001b[0m )\n\u001b[0;32m 131\u001b[0m \u001b[39mif\u001b[39;00m coef \u001b[39mis\u001b[39;00m \u001b[39mNone\u001b[39;00m:\n", + "\u001b[1;31mValueError\u001b[0m: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()" + ] + } + ], + "source": [ + "cost = DoubleBracketCostFunction.least_squares\n", + "dbi = DoubleBracketIteration(deepcopy(H_TFIM),mode=DoubleBracketGeneratorType.single_commutator,cost=cost)\n", + "d = np.diag(np.linspace(1,2**nqubits,2**nqubits))\n", + "\n", + "step = 1e-2\n", + "iterations = 100\n", + "\n", + "d, loss, grad, diags = gradient_ascent(dbi, d,step, iterations)\n", + "\n", + "n = 3" + ] + } + ], + "metadata": { + "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": "3.9.18" + }, + "orig_nbformat": 4, + "vscode": { + "interpreter": { + "hash": "c4f92193806e2908606a5f23edd55a5282f2f433b73b1c504507f9256ed9f0b4" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/examples/dbi/dbi_scheduling.ipynb b/examples/dbi/dbi_scheduling.ipynb new file mode 100644 index 0000000000..1953c1272d --- /dev/null +++ b/examples/dbi/dbi_scheduling.ipynb @@ -0,0 +1,474 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Double-bracket Iteration Scheduling Strategies\n", + "\n", + "This notebook presents the different strategies for scheduling the step durations for the double-bracket iteration algorithm and their resepctive accuracies." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Import the dependencies" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "from copy import deepcopy\n", + "\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from qibo import hamiltonians, set_backend\n", + "from qibo.models.dbi.double_bracket import DoubleBracketGeneratorType, DoubleBracketScheduling, DoubleBracketIteration\n", + "from qibo.models.dbi.utils import *\n", + "from qibo.models.dbi.utils_scheduling import *" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Canonical\n", + "Set up the basic test case with the transverse field ising model hamiltonian and the canonical bracket as the generator." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "[Qibo 0.2.5|INFO|2024-03-12 17:24:06]: Using qibojit (numba) backend on /CPU:0\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Initial off diagonal norm 37.94733192202055\n" + ] + } + ], + "source": [ + "# Hamiltonian\n", + "set_backend(\"qibojit\", \"numba\")\n", + "\n", + "# hamiltonian parameters\n", + "nqubits = 5\n", + "h = 3\n", + "\n", + "# define the hamiltonian\n", + "H_TFIM = hamiltonians.TFIM(nqubits=nqubits, h=h)\n", + "\n", + "# initialize class\n", + "dbi = DoubleBracketIteration(deepcopy(H_TFIM),mode=DoubleBracketGeneratorType.canonical)\n", + "print(\"Initial off diagonal norm\", dbi.off_diagonal_norm)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We first run a sweep of step duration to map the off-diagonal norm in this range." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "# generate data for plotting sigma decrease of the first step\n", + "s_space = np.linspace(1e-5, 0.6, 100)\n", + "off_diagonal_norm_diff = []\n", + "for s in s_space:\n", + " dbi_eval = deepcopy(dbi)\n", + " dbi_eval(s)\n", + " off_diagonal_norm_diff.append(dbi_eval.off_diagonal_norm - dbi.off_diagonal_norm)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The default scheduling strategy is grid search: `DoubleBracketScheduling.\n", + "grid_serach`. This strategy specifies a list of step durations to test one by one and finds the one that maximizes the cost function (off-digonal norm of Hamiltonian)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "ename": "TypeError", + "evalue": "loss() got an unexpected keyword argument 'state'", + "output_type": "error", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[1;31mTypeError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[1;32mIn[16], line 2\u001b[0m\n\u001b[0;32m 1\u001b[0m \u001b[39m# grid_search\u001b[39;00m\n\u001b[1;32m----> 2\u001b[0m step_grid \u001b[39m=\u001b[39m dbi\u001b[39m.\u001b[39;49mchoose_step(scheduling\u001b[39m=\u001b[39;49mDoubleBracketScheduling\u001b[39m.\u001b[39;49mgrid_search)\n\u001b[0;32m 3\u001b[0m \u001b[39mprint\u001b[39m(\u001b[39m'\u001b[39m\u001b[39mgrid_search step:\u001b[39m\u001b[39m'\u001b[39m, step_grid)\n\u001b[0;32m 4\u001b[0m \u001b[39m# hyperopt\u001b[39;00m\n", + "File \u001b[1;32mc:\\Users\\andre\\Documents\\GitHub\\qibo\\.conda\\lib\\site-packages\\qibo\\models\\dbi\\double_bracket.py:164\u001b[0m, in \u001b[0;36mDoubleBracketIteration.choose_step\u001b[1;34m(self, d, scheduling, **kwargs)\u001b[0m\n\u001b[0;32m 162\u001b[0m \u001b[39mif\u001b[39;00m scheduling \u001b[39mis\u001b[39;00m \u001b[39mNone\u001b[39;00m:\n\u001b[0;32m 163\u001b[0m scheduling \u001b[39m=\u001b[39m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39mscheduling\n\u001b[1;32m--> 164\u001b[0m step \u001b[39m=\u001b[39m scheduling(\u001b[39mself\u001b[39m, d\u001b[39m=\u001b[39md, \u001b[39m*\u001b[39m\u001b[39m*\u001b[39mkwargs)\n\u001b[0;32m 165\u001b[0m \u001b[39mif\u001b[39;00m (\n\u001b[0;32m 166\u001b[0m step \u001b[39mis\u001b[39;00m \u001b[39mNone\u001b[39;00m\n\u001b[0;32m 167\u001b[0m \u001b[39mand\u001b[39;00m scheduling \u001b[39m==\u001b[39m DoubleBracketScheduling\u001b[39m.\u001b[39mpolynomial_approximation\n\u001b[0;32m 168\u001b[0m ):\n\u001b[0;32m 169\u001b[0m kwargs[\u001b[39m\"\u001b[39m\u001b[39mn\u001b[39m\u001b[39m\"\u001b[39m] \u001b[39m=\u001b[39m kwargs\u001b[39m.\u001b[39mget(\u001b[39m\"\u001b[39m\u001b[39mn\u001b[39m\u001b[39m\"\u001b[39m, \u001b[39m3\u001b[39m)\n", + "File \u001b[1;32mc:\\Users\\andre\\Documents\\GitHub\\qibo\\.conda\\lib\\site-packages\\qibo\\models\\dbi\\utils_scheduling.py:47\u001b[0m, in \u001b[0;36mgrid_search_step\u001b[1;34m(dbi_object, step_min, step_max, num_evals, space, d, state)\u001b[0m\n\u001b[0;32m 44\u001b[0m \u001b[39mif\u001b[39;00m d \u001b[39mis\u001b[39;00m \u001b[39mNone\u001b[39;00m:\n\u001b[0;32m 45\u001b[0m d \u001b[39m=\u001b[39m dbi_object\u001b[39m.\u001b[39mdiagonal_h_matrix\n\u001b[1;32m---> 47\u001b[0m loss_list \u001b[39m=\u001b[39m [dbi_object\u001b[39m.\u001b[39mloss(step, d\u001b[39m=\u001b[39md, state\u001b[39m=\u001b[39mstate) \u001b[39mfor\u001b[39;00m step \u001b[39min\u001b[39;00m space]\n\u001b[0;32m 48\u001b[0m idx_max_loss \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39margmin(loss_list)\n\u001b[0;32m 49\u001b[0m \u001b[39mreturn\u001b[39;00m space[idx_max_loss]\n", + "File \u001b[1;32mc:\\Users\\andre\\Documents\\GitHub\\qibo\\.conda\\lib\\site-packages\\qibo\\models\\dbi\\utils_scheduling.py:47\u001b[0m, in \u001b[0;36m\u001b[1;34m(.0)\u001b[0m\n\u001b[0;32m 44\u001b[0m \u001b[39mif\u001b[39;00m d \u001b[39mis\u001b[39;00m \u001b[39mNone\u001b[39;00m:\n\u001b[0;32m 45\u001b[0m d \u001b[39m=\u001b[39m dbi_object\u001b[39m.\u001b[39mdiagonal_h_matrix\n\u001b[1;32m---> 47\u001b[0m loss_list \u001b[39m=\u001b[39m [dbi_object\u001b[39m.\u001b[39;49mloss(step, d\u001b[39m=\u001b[39;49md, state\u001b[39m=\u001b[39;49mstate) \u001b[39mfor\u001b[39;00m step \u001b[39min\u001b[39;00m space]\n\u001b[0;32m 48\u001b[0m idx_max_loss \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39margmin(loss_list)\n\u001b[0;32m 49\u001b[0m \u001b[39mreturn\u001b[39;00m space[idx_max_loss]\n", + "\u001b[1;31mTypeError\u001b[0m: loss() got an unexpected keyword argument 'state'" + ] + } + ], + "source": [ + "# grid_search\n", + "step_grid = dbi.choose_step(scheduling=DoubleBracketScheduling.grid_search)\n", + "print('grid_search step:', step_grid)\n", + "# hyperopt\n", + "step_hyperopt = dbi.choose_step(scheduling=DoubleBracketScheduling.hyperopt, max_evals=100, step_max=0.6)\n", + "print('hyperopt_search step:', step_hyperopt)\n", + "step_poly = dbi.choose_step(scheduling=DoubleBracketScheduling.polynomial_approximation, n=5)\n", + "print('polynomial_approximation step:', step_poly)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Plot the results\n", + "plt.plot(s_space, off_diagonal_norm_diff)\n", + "plt.axvline(x=step_grid, color='r', linestyle='-',label='grid_search')\n", + "plt.axvline(x=step_hyperopt, color='g', linestyle='--',label='hyperopt')\n", + "plt.axvline(x=step_poly, color='m', linestyle='-.',label='polynomial')\n", + "plt.ylabel(r'$||\\sigma(H_0)||-\\sigma(H_k)||$')\n", + "plt.xlabel('s')\n", + "plt.title('First DBI step')\n", + "plt.legend()\n", + "print('The minimum for cost function in the tested range is:', step_grid)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Specified diagonal operator\n", + "\n", + "While for the cannonical case, all the scheduling methods are accurate, it is important to realize that the global minimum of the loss function is not always so obvious. It is thus necessary to show whether the 3 converges to an agreeable step duration using different iteration generators, such as the Pauli 'ZZ..Z' operator and 'ZZ..I' operator." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Generate the digaonal operators\n", + "Z_str = \"Z\"*nqubits\n", + "ZI_str = \"Z\"*(nqubits-1)+\"I\"\n", + "Z_op = SymbolicHamiltonian(str_to_symbolic(Z_str)).dense.matrix\n", + "ZI_op = SymbolicHamiltonian(str_to_symbolic(ZI_str)).dense.matrix\n", + "op_dict = {Z_str:Z_op, ZI_str: ZI_op}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "dbi = DoubleBracketIteration(deepcopy(H_TFIM),mode=DoubleBracketGeneratorType.single_commutator)\n", + "d_str = ZI_str\n", + "d = op_dict[d_str]\n", + "# generate data for plotting sigma decrease of the first step\n", + "s_space = np.linspace(1e-5, 0.6, 100)\n", + "off_diagonal_norm_diff = []\n", + "for s in s_space:\n", + " dbi_eval = deepcopy(dbi)\n", + " dbi_eval(s,d=d)\n", + " off_diagonal_norm_diff.append(dbi_eval.off_diagonal_norm - dbi.off_diagonal_norm)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# grid_search\n", + "step_grid = dbi.choose_step(scheduling=DoubleBracketScheduling.grid_search, step_max=0.6, d=d)\n", + "grid_min = dbi.loss(step=step_grid, d=d)-dbi.off_diagonal_norm\n", + "print('grid_search step:', step_grid, 'loss', grid_min)\n", + "# hyperopt\n", + "step_hyperopt = dbi.choose_step(scheduling=DoubleBracketScheduling.hyperopt, d=d, max_evals=100, step_max=0.6)\n", + "hyperopt_min = dbi.loss(step=step_hyperopt, d=d)-dbi.off_diagonal_norm\n", + "print('hyperopt_search step:', step_hyperopt, 'loss', hyperopt_min)\n", + "# polynomial expansion\n", + "step_poly = dbi.choose_step(scheduling=DoubleBracketScheduling.polynomial_approximation, d=d, n=5)\n", + "poly_min = dbi.loss(step=step_poly, d=d)-dbi.off_diagonal_norm\n", + "print('polynomial_approximation step:', step_poly, 'loss', poly_min)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Plot the results\n", + "plt.plot(s_space, off_diagonal_norm_diff)\n", + "plt.axvline(x=step_grid, color='r', linestyle='-',label='grid_search')\n", + "plt.text(x=step_grid, y=grid_min, s=f'grid min \\n{round(grid_min,3)}')\n", + "plt.text(x=step_poly, y=poly_min, s=f'grid min \\n{round(poly_min,3)}')\n", + "plt.axvline(x=step_hyperopt, color='g', linestyle='--',label='hyperopt')\n", + "plt.axvline(x=step_poly, color='m', linestyle='-.',label='polynomial')\n", + "plt.ylabel(r'$||\\sigma(H_0)||-\\sigma(H_k)||$')\n", + "plt.xlabel('s')\n", + "plt.title(f'First DBI step with D={d_str}')\n", + "plt.legend()\n", + "print('The minimum for cost function in the tested range is:', step_grid)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that there are two similar \"minimal point\" at 0.03 and 0.22, with the latter being the absolute minimum by an insignificant advantage. However, for practical reasons, we prefer taking the first close-minimum calculated by polynomial approximation. Hence, we can use the polynomial approximation to restrict the search area and obtain better results. For example, we define a search range of 0.1 around the polynomial step." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Use polynomial expansion as an restriction for hyperopt/grid range" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "search_range = 0.1\n", + "if step_poly < search_range/2:\n", + " step_min = 0\n", + " step_max = search_range\n", + "else:\n", + " step_min = step_poly - search_range/2\n", + " step_max = step_poly + search_range/2\n", + "# grid_search\n", + "step_grid = dbi.choose_step(scheduling=DoubleBracketScheduling.grid_search, step_min=step_min, step_max=step_max, d=d)\n", + "print('grid_search step:', step_grid)\n", + "# hyperopt\n", + "step_hyperopt = dbi.choose_step(scheduling=DoubleBracketScheduling.hyperopt, step_min=step_min, step_max=step_max, max_evals=100, d=d,)\n", + "print('hyperopt_search step:', step_hyperopt)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Plot the results\n", + "plt.plot(s_space, off_diagonal_norm_diff)\n", + "plt.axvline(x=step_grid, color='r', linestyle='-',label='grid_search')\n", + "plt.axvline(x=step_hyperopt, color='g', linestyle='--',label='hyperopt')\n", + "plt.axvline(x=step_poly, color='m', linestyle='-.',label='polynomial')\n", + "plt.ylabel(r'$||\\sigma(H_0)||-\\sigma(H_k)||$')\n", + "plt.xlabel('s')\n", + "plt.title(r'Restrict $s$ with polynomial')\n", + "plt.legend()\n", + "print('The minimum for cost function in the tested range is:', step_grid)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Hence, we see that the strategy is indeed effective for finding the first minimum of the loss funciton for both the Z operator and the ZI operator." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compare in Pauli-Z strategy" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "from qibo.quantum_info import random_hermitian\n", + "from qibo.hamiltonians import Hamiltonian" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Hamiltonian\n", + "set_backend(\"qibojit\", \"numba\")\n", + "nqubits = 4\n", + "h0 = random_hermitian(2**nqubits)\n", + "\n", + "# initialize class\n", + "dbi = DoubleBracketIteration(deepcopy(Hamiltonian(nqubits=nqubits, matrix=h0)),mode=DoubleBracketGeneratorType.single_commutator)\n", + "print(\"Initial off diagonal norm\", dbi.off_diagonal_norm)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "generate_local_Z = generate_Z_operators(nqubits)\n", + "Z_ops = list(generate_local_Z.values())\n", + "Z_names = list(generate_local_Z.keys())" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "NSTEPS = 8\n", + "scheduling_list = [DoubleBracketScheduling.grid_search,\n", + " DoubleBracketScheduling.hyperopt,\n", + " DoubleBracketScheduling.polynomial_approximation,]\n", + "scheduling_labels = ['grid search',\n", + " 'hyperopt',\n", + " 'polynomial',]\n", + "Z_optimal_scheduling = []\n", + "s_scheduling = []\n", + "off_norm_scheduling =[]\n", + "for i,scheduling in enumerate(scheduling_list):\n", + " # reinitialize\n", + " dbi = DoubleBracketIteration(Hamiltonian(nqubits=nqubits, matrix=deepcopy(h0)), mode=DoubleBracketGeneratorType.single_commutator)\n", + " Z_optimal = []\n", + " # add in initial values for plotting\n", + " off_diagonal_norm_history = [dbi.off_diagonal_norm]\n", + " steps = [0]\n", + " print(f'----------Scheduling {scheduling_labels[i]}----------')\n", + " for _ in range(NSTEPS):\n", + " dbi, idx, step, flip_sign = select_best_dbr_generator(dbi, Z_ops, scheduling=scheduling, compare_canonical=False)\n", + " off_diagonal_norm_history.append(dbi.off_diagonal_norm)\n", + " steps.append(steps[-1]+step)\n", + " if flip_sign < 0:\n", + " Z_optimal.append('-' + Z_names[idx])\n", + " else:\n", + " Z_optimal.append(Z_names[idx])\n", + " print(f\"New optimized step at iteration {_+1}/{NSTEPS}: {step} with operator {Z_optimal[-1]}, loss {dbi.off_diagonal_norm}\")\n", + " Z_optimal_scheduling.append(Z_optimal)\n", + " s_scheduling.append(steps)\n", + " off_norm_scheduling.append(off_diagonal_norm_history)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt.figure()\n", + "for i, scheduling in enumerate(scheduling_labels):\n", + " plt.plot(s_scheduling[i], off_norm_scheduling[i], '-o', label=scheduling)\n", + "plt.xlabel(\"Step durations\")\n", + "plt.ylabel(\"Norm off-diagonal restriction\")\n", + "plt.title(\"Compare Variational Pauli-Z using different scheduling strategies\")\n", + "plt.legend()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## When polynomial approximation has no solution\n", + "\n", + "In some cases, the prescribed taylor expansion order `n` may not be sufficient to produce a meaningful step duration (real positive). In these cases, we rely on a backup scheduling method in `choose_step`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Hamiltonian\n", + "set_backend(\"qibojit\", \"numba\")\n", + "\n", + "# hamiltonian parameters\n", + "nqubits = 5\n", + "h = 3\n", + "\n", + "# define the hamiltonian\n", + "H_TFIM = hamiltonians.TFIM(nqubits=nqubits, h=h)\n", + "\n", + "# initialize class\n", + "dbi = DoubleBracketIteration(deepcopy(H_TFIM),mode=DoubleBracketGeneratorType.canonical)\n", + "dbi.scheduling = DoubleBracketScheduling.polynomial_approximation\n", + "print(\"Initial off diagonal norm\", dbi.off_diagonal_norm)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For demonstration purposes, we let `n=1` which is a linear fit to the loss function. This results in no valid solutions and function `polynomial_step` returns `None`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "for n in range (5):\n", + " step = polynomial_step(dbi, n=n)\n", + " print(n, step)\n", + "print(dbi.choose_step(n=1))" + ] + } + ], + "metadata": { + "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": "3.9.18" + }, + "vscode": { + "interpreter": { + "hash": "48caf7dabad7b721a854729228548373f17e53f40870080394d552284aea7c35" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/src/qibo/models/dbi/double_bracket.py b/src/qibo/models/dbi/double_bracket.py index f9248bc469..2069296058 100644 --- a/src/qibo/models/dbi/double_bracket.py +++ b/src/qibo/models/dbi/double_bracket.py @@ -1,11 +1,16 @@ from copy import deepcopy from enum import Enum, auto -from functools import partial +from typing import Optional import hyperopt import numpy as np from qibo.hamiltonians import Hamiltonian +from qibo.models.dbi.utils_scheduling import ( + grid_search_step, + hyperopt_step, + polynomial_step, +) class DoubleBracketGeneratorType(Enum): @@ -20,6 +25,26 @@ class DoubleBracketGeneratorType(Enum): # TODO: add double commutator (does it converge?) +class DoubleBracketScheduling(Enum): + """Define the DBI scheduling strategies.""" + + hyperopt = hyperopt_step + """Use hyperopt package.""" + grid_search = grid_search_step + """Use greedy grid search.""" + polynomial_approximation = polynomial_step + """Use polynomial expansion (analytical) of the loss function.""" + +class DoubleBracketCostFunction(Enum): + """Define the DBI cost function.""" + + off_diagonal_norm = auto() + """Use off-diagonal norm as cost function.""" + least_squares = auto() + """Use least squares as cost function.""" + energy_fluctuation = auto() + """Use energy fluctuation as cost function.""" + class DoubleBracketIteration: """ Class implementing the Double Bracket iteration algorithm. @@ -48,10 +73,16 @@ def __init__( self, hamiltonian: Hamiltonian, mode: DoubleBracketGeneratorType = DoubleBracketGeneratorType.canonical, + scheduling: DoubleBracketScheduling = DoubleBracketScheduling.grid_search, + cost: DoubleBracketCostFunction = DoubleBracketCostFunction.off_diagonal_norm, + state: int = 0, ): self.h = hamiltonian self.h0 = deepcopy(self.h) self.mode = mode + self.scheduling = scheduling + self.cost = cost + self.state = state def __call__( self, step: float, mode: DoubleBracketGeneratorType = None, d: np.array = None @@ -68,7 +99,7 @@ def __call__( if d is None: d = self.diagonal_h_matrix operator = self.backend.calculate_matrix_exp( - 1.0j * step, + 1.0j*step, self.commutator(d, self.h.matrix), ) elif mode is DoubleBracketGeneratorType.group_commutator: @@ -83,6 +114,7 @@ def __call__( operator_dagger = self.backend.cast( np.matrix(self.backend.to_numpy(operator)).getH() ) + self.h.matrix = operator @ self.h.matrix @ operator_dagger @staticmethod @@ -114,47 +146,29 @@ def backend(self): """Get Hamiltonian's backend.""" return self.h0.backend - def hyperopt_step( + def least_squares(self, D: np.array): + """Least squares cost function.""" + H = self.h.matrix + return -np.real(np.trace(H@D)-0.5*(np.linalg.norm(H)**2+np.linalg.norm(D)**2)) + + def choose_step( self, - step_min: float = 1e-5, - step_max: float = 1, - max_evals: int = 1000, - space: callable = None, - optimizer: callable = None, - look_ahead: int = 1, - verbose: bool = False, - d: np.array = None, + d: Optional[np.array] = None, + scheduling: Optional[DoubleBracketScheduling] = None, + **kwargs, ): - """ - Optimize iteration step. - - Args: - step_min: lower bound of the search grid; - step_max: upper bound of the search grid; - max_evals: maximum number of iterations done by the hyperoptimizer; - space: see hyperopt.hp possibilities; - optimizer: see hyperopt algorithms; - look_ahead: number of iteration steps to compute the loss function; - verbose: level of verbosity; - d: diagonal operator for generating double-bracket iterations. - - Returns: - (float): optimized best iteration step. - """ - if space is None: - space = hyperopt.hp.uniform - if optimizer is None: - optimizer = hyperopt.tpe - - space = space("step", step_min, step_max) - best = hyperopt.fmin( - fn=partial(self.loss, d=d, look_ahead=look_ahead), - space=space, - algo=optimizer.suggest, - max_evals=max_evals, - verbose=verbose, - ) - return best["step"] + if scheduling is None: + scheduling = self.scheduling + step = scheduling(self, d=d, **kwargs) + if ( + step is None + and scheduling == DoubleBracketScheduling.polynomial_approximation + ): + kwargs["n"] = kwargs.get("n", 3) + kwargs["n"] += 1 + # if n==n_max, return None + step = scheduling(self, d=d, **kwargs) + return step def loss(self, step: float, d: np.array = None, look_ahead: int = 1): """ @@ -171,8 +185,13 @@ def loss(self, step: float, d: np.array = None, look_ahead: int = 1): for _ in range(look_ahead): self.__call__(mode=self.mode, step=step, d=d) - # off_diagonal_norm's value after the steps - loss = self.off_diagonal_norm + # loss values depending on the cost function + if self.cost == DoubleBracketCostFunction.off_diagonal_norm: + loss = self.off_diagonal_norm + elif self.cost == DoubleBracketCostFunction.least_squares: + loss = self.least_squares(d) + else: + loss = self.energy_fluctuation(self.state) # set back the initial configuration self.h = h_copy @@ -191,4 +210,17 @@ def energy_fluctuation(self, state): Args: state (np.ndarray): quantum state to be used to compute the energy fluctuation with H. """ - return self.h.energy_fluctuation(state) + state_vector = np.zeros(len(self.h.matrix)) + state_vector[state] = 1.0 + return np.real(self.h.energy_fluctuation(state_vector)) + + def sigma(self, h: np.array): + return h - self.backend.cast(np.diag(np.diag(self.backend.to_numpy(h)))) + + def generate_Gamma_list(self, n: int, d: np.array): + r"""Computes the n-nested Gamma functions, where $\Gamma_k=[W,...,[W,[W,H]]...]$, where we take k nested commutators with $W = [D, H]$""" + W = self.commutator(d, self.sigma(self.h.matrix)) + Gamma_list = [self.h.matrix] + for _ in range(n - 1): + Gamma_list.append(self.commutator(W, Gamma_list[-1])) + return Gamma_list diff --git a/src/qibo/models/dbi/utils.py b/src/qibo/models/dbi/utils.py index 461e660b78..b1dd5daf61 100644 --- a/src/qibo/models/dbi/utils.py +++ b/src/qibo/models/dbi/utils.py @@ -1,9 +1,10 @@ +import math from copy import deepcopy from itertools import product from typing import Optional +import hyperopt import numpy as np -from hyperopt import hp, tpe from qibo import symbols from qibo.config import raise_error @@ -11,6 +12,7 @@ from qibo.models.dbi.double_bracket import ( DoubleBracketGeneratorType, DoubleBracketIteration, + DoubleBracketScheduling, ) @@ -71,11 +73,9 @@ def select_best_dbr_generator( dbi_object: DoubleBracketIteration, d_list: list, step: Optional[float] = None, - step_min: float = 1e-5, - step_max: float = 1, - max_evals: int = 200, compare_canonical: bool = True, - mode: DoubleBracketGeneratorType = DoubleBracketGeneratorType.single_commutator, + scheduling: DoubleBracketScheduling = None, + **kwargs, ): """Selects the best double bracket rotation generator from a list and runs the @@ -83,16 +83,15 @@ def select_best_dbr_generator( dbi_object (`DoubleBracketIteration`): the target DoubleBracketIteration object. d_list (list): list of diagonal operators (np.array) to run from. step (float): fixed iteration duration. - Defaults to ``None``, uses hyperopt. - step_min (float): minimally allowed iteration duration. - step_max (float): maximally allowed iteration duration. - max_evals (int): maximally allowed number of evaluation in hyperopt. - compare_canonical (bool): if `True`, the optimal diagonal operator chosen from "d_list" is compared with the canonical bracket. - mode (`DoubleBracketGeneratorType`): DBI generator type used for the selection. + Defaults to ``None``, optimize with `scheduling` method and `choose_step` function. + compare_canonical (boolean): if `True`, the diagonalization effect with operators from `d_list` is compared with the canonical bracket. + scheduling (`DoubleBracketScheduling`): scheduling method for finding the optimal step. Returns: The updated dbi_object, index of the optimal diagonal operator, respective step duration, and evolution direction. """ + if scheduling is None: + scheduling = dbi_object.scheduling norms_off_diagonal_restriction = [ dbi_object.off_diagonal_norm for _ in range(len(d_list)) ] @@ -104,13 +103,8 @@ def select_best_dbr_generator( flip_list[i] = cs_angle_sgn(dbi_eval, d) if flip_list[i] != 0: if step is None: - step_best = dbi_eval.hyperopt_step( - d=flip_list[i] * d, - step_min=step_min, - step_max=step_max, - space=hp.uniform, - optimizer=tpe, - max_evals=max_evals, + step_best = dbi_eval.choose_step( + d=flip_list[i] * d, scheduling=scheduling, **kwargs ) else: step_best = step @@ -123,13 +117,7 @@ def select_best_dbr_generator( dbi_eval = deepcopy(dbi_object) dbi_eval.mode = DoubleBracketGeneratorType.canonical if step is None: - step_best = dbi_eval.hyperopt_step( - step_min=step_min, - step_max=step_max, - space=hp.uniform, - optimizer=tpe, - max_evals=max_evals, - ) + step_best = dbi_eval.choose_step(scheduling=scheduling, **kwargs) else: step_best = step dbi_eval(step=step_best) @@ -163,3 +151,27 @@ def cs_angle_sgn(dbi_object, d): ) ) return np.sign(norm) + + +def off_diagonal_norm_polynomial_expansion_coef(dbi_object, d, n): + if d is None: + d = dbi_object.diagonal_h_matrix + # generate Gamma's where $\Gamma_{k+1}=[W, \Gamma_{k}], $\Gamma_0=H + W = dbi_object.commutator(d, dbi_object.sigma(dbi_object.h.matrix)) + Gamma_list = dbi_object.generate_Gamma_list(n + 2, d) + sigma_Gamma_list = list(map(dbi_object.sigma, Gamma_list)) + exp_list = np.array([1 / math.factorial(k) for k in range(n + 1)]) + # coefficients for rotation with [W,H] and H + c1 = exp_list.reshape((-1, 1, 1)) * sigma_Gamma_list[1:] + c2 = exp_list.reshape((-1, 1, 1)) * sigma_Gamma_list[:-1] + # product coefficient + trace_coefficients = [0] * (2 * n + 1) + for k in range(n + 1): + for j in range(n + 1): + power = k + j + product_matrix = c1[k] @ c2[j] + trace_coefficients[power] += 2 * np.trace(product_matrix) + # coefficients from high to low (n:0) + coef = list(reversed(trace_coefficients[: n + 1])) + return coef + diff --git a/src/qibo/models/dbi/utils_scheduling.py b/src/qibo/models/dbi/utils_scheduling.py new file mode 100644 index 0000000000..5f217cc948 --- /dev/null +++ b/src/qibo/models/dbi/utils_scheduling.py @@ -0,0 +1,260 @@ +import math +from functools import partial +from typing import Optional +from copy import deepcopy +import hyperopt +import numpy as np + + +error = 1e-3 + +def commutator(A, B): + """Compute commutator between two arrays.""" + return A@B-B@A + +def variance(A, state): + """Calculates the variance of a matrix A with respect to a state: Var($A$) = $\langle\mu|A^2|\mu\rangle-\langle\mu|A|\mu\rangle^2$""" + B = A@A + return B[state,state]-A[state,state]**2 + +def covariance(A, B, state): + """Calculates the covariance of two matrices A and B with respect to a state: Cov($A,B$) = $\langle\mu|AB|\mu\rangle-\langle\mu|A|\mu\rangle\langle\mu|B|\mu\rangle$""" + C = A@B+B@A + return C[state,state]-2*A[state,state]*B[state,state] + +def grid_search_step( + dbi_object, + step_min: float = 1e-5, + step_max: float = 1, + num_evals: int = 100, + space: Optional[np.array] = None, + d: Optional[np.array] = None, +): + """ + Greedy optimization of the iteration step. + + Args: + step_min: lower bound of the search grid; + step_max: upper bound of the search grid; + mnum_evals: number of iterations between step_min and step_max; + d: diagonal operator for generating double-bracket iterations. + + Returns: + (float): optimized best iteration step (minimizing off-diagonal norm). + """ + if space is None: + space = np.linspace(step_min, step_max, num_evals) + + if d is None: + d = dbi_object.diagonal_h_matrix + + loss_list = [dbi_object.loss(step, d=d) for step in space] + + idx_max_loss = np.argmin(loss_list) + return space[idx_max_loss] + + +def hyperopt_step( + dbi_object, + step_min: float = 1e-5, + step_max: float = 1, + max_evals: int = 500, + space: callable = None, + optimizer: callable = None, + look_ahead: int = 1, + verbose: bool = False, + d: Optional[np.array] = None, +): + """ + Optimize iteration step using hyperopt. + + Args: + step_min: lower bound of the search grid; + step_max: upper bound of the search grid; + max_evals: maximum number of iterations done by the hyperoptimizer; + space: see hyperopt.hp possibilities; + optimizer: see hyperopt algorithms; + look_ahead: number of iteration steps to compute the loss function; + verbose: level of verbosity; + d: diagonal operator for generating double-bracket iterations. + + Returns: + (float): optimized best iteration step (minimizing loss function). + """ + if space is None: + space = hyperopt.hp.uniform + if optimizer is None: + optimizer = hyperopt.tpe + if d is None: + d = dbi_object.diagonal_h_matrix + + space = space("step", step_min, step_max) + + + best = hyperopt.fmin( + fn=partial(dbi_object.loss, d=d, look_ahead=look_ahead), + space=space, + algo=optimizer.suggest, + max_evals=max_evals, + verbose=verbose, + ) + return best["step"] + + +def polynomial_step( + dbi_object, + n: int = 2, + n_max: int = 5, + d: np.array = None, + coef: Optional[list] = None, + cost: str = None, +): + r""" + Optimizes iteration step by solving the n_th order polynomial expansion of the loss function. + e.g. $n=2$: $2\Trace(\sigma(\Gamma_1 + s\Gamma_2 + s^2/2\Gamma_3)\sigma(\Gamma_0 + s\Gamma_1 + s^2/2\Gamma_2)) + Args: + n (int, optional): the order to which the loss function is expanded. Defaults to 4. + n_max (int, optional): maximum order allowed for recurring calls of `polynomial_step`. Defaults to 5. + d (np.array, optional): diagonal operator, default as $\delta(H)$. + backup_scheduling (`DoubleBracketScheduling`): the scheduling method to use in case no real positive roots are found. + """ + if cost is None: + cost = dbi_object.cost.name + + if d is None: + d = dbi_object.diagonal_h_matrix + + if n > n_max: + raise ValueError( + "No solution can be found with polynomial approximation. Increase `n_max` or use other scheduling methods." + ) + if coef is None: + if cost == "off_diagonal_norm": + coef = off_diagonal_norm_polynomial_expansion_coef(dbi_object, d, n) + elif cost == "least_squares": + coef = least_squares_polynomial_expansion_coef(dbi_object, d, n) + elif cost == "energy_fluctuation": + coef = energy_fluctuation_polynomial_expansion_coef(dbi_object, d, n, dbi_object.state) + else: + raise ValueError(f"Cost function {cost} not recognized.") + + roots = np.roots(coef) + real_positive_roots = [ + np.real(root) for root in roots if np.imag(root) < error and np.real(root) > 0 + ] + # solution exists, return minimum s + if len(real_positive_roots) > 0: + sol = min(real_positive_roots) + for s in real_positive_roots: + if dbi_object.loss(s, d) < dbi_object.loss(sol, d): + sol = s + return sol + # solution does not exist, return None + else: + return None + + +def off_diagonal_norm_polynomial_expansion_coef(dbi_object, d, n): + if d is None: + d = dbi_object.diagonal_h_matrix + # generate Gamma's where $\Gamma_{k+1}=[W, \Gamma_{k}], $\Gamma_0=H + W = dbi_object.commutator(d, dbi_object.sigma(dbi_object.h.matrix)) + Gamma_list = dbi_object.generate_Gamma_list(n + 2, d) + sigma_Gamma_list = list(map(dbi_object.sigma, Gamma_list)) + exp_list = np.array([1 / math.factorial(k) for k in range(n + 1)]) + # coefficients for rotation with [W,H] and H + c1 = exp_list.reshape((-1, 1, 1)) * sigma_Gamma_list[1:] + c2 = exp_list.reshape((-1, 1, 1)) * sigma_Gamma_list[:-1] + # product coefficient + trace_coefficients = [0] * (2 * n + 1) + for k in range(n + 1): + for j in range(n + 1): + power = k + j + product_matrix = c1[k] @ c2[j] + trace_coefficients[power] += 2 * np.trace(product_matrix) + # coefficients from high to low (n:0) + coef = list(reversed(trace_coefficients[: n + 1])) + return coef + +def least_squares_polynomial_expansion_coef(dbi_object, d, n): + if d is None: + d = dbi_object.diagonal_h_matrix + # generate Gamma's where $\Gamma_{k+1}=[W, \Gamma_{k}], $\Gamma_0=H + Gamma_list = dbi_object.generate_Gamma_list(n+1, d) + exp_list = np.array([1 / math.factorial(k) for k in range(n + 1)]) + # coefficients + coef = np.empty(n) + for i in range(n): + coef[i] = np.real(exp_list[i]*np.trace(d@Gamma_list[i+1])) + coef = list(reversed(coef)) + return coef + +#TODO: add a general expansion formula not stopping at 3rd order +def energy_fluctuation_polynomial_expansion_coef(dbi_object, d, n, state): + if d is None: + d = dbi_object.diagonal_h_matrix + # generate Gamma's where $\Gamma_{k+1}=[W, \Gamma_{k}], $\Gamma_0=H + Gamma_list = dbi_object.generate_Gamma_list(n+1, d) + # coefficients + coef = np.empty(3) + coef[0] = np.real(2*covariance(Gamma_list[0], Gamma_list[1],state)) + coef[1] = np.real(2*variance(Gamma_list[1],state)) + coef[2] = np.real(covariance(Gamma_list[0], Gamma_list[3],state)+3*covariance(Gamma_list[1], Gamma_list[2],state)) + coef = list(reversed(coef)) + return coef + +def dGamma_diDiagonal(dbi_object, d, H, n, i,dGamma, Gamma_list): + # Derivative of gamma with respect to diagonal elements of D (full-diagonal ansatz) + A = np.zeros(d.shape) + A[i,i] = 1 + B = commutator(commutator(A,H),Gamma_list[n-1]) + W = commutator(d,H) + return B + commutator(W,dGamma[-1]) + +def dpolynomial_diDiagonal(dbi_object, d,H,i): + # Derivative of polynomial approximation of potential function with respect to diagonal elements of d (full-diagonal ansatz) + # Formula can be expanded easily to any order, with n=3 corresponding to cubic approximation + derivative = 0 + s = polynomial_step(dbi_object, n=3, d=d) + A = np.zeros(d.shape) + Gamma_list = dbi_object.generate_Gamma_list(4, d) + A[i,i] = 1 + dGamma = [commutator(A,H)] + derivative += np.real(np.trace(Gamma_list[0]@A)+np.trace(dGamma[0]@d+Gamma_list[1]@A)*s) + for n in range(2,4): + dGamma.append(dGamma_diDiagonal(dbi_object,d,H,n,i,dGamma,Gamma_list)) + derivative += np.real(np.trace(dGamma[-1]@d + Gamma_list[n]@A)*s**n/math.factorial(n)) + + return derivative + +def gradientDiagonal(dbi_object,d,H): + # Gradient of potential function with respect to diagonal elements of D (full-diagonal ansatz) + grad = np.zeros(len(d)) + for i in range(len(d)): + derivative = dpolynomial_diDiagonal(dbi_object,d,H,i) + grad[i] = d[i,i]-derivative + return grad + +def gradient_ascent(dbi_object, d, step, iterations): + H = dbi_object.h.matrix + loss = np.zeros(iterations+1) + grad = np.zeros((iterations,len(d))) + dbi_new = deepcopy(dbi_object) + s = polynomial_step(dbi_object, n = 3, d=d) + dbi_new(s,d=d) + loss[0] = dbi_new(d) + diagonals = np.empty((len(d),iterations+1)) + diagonals[:,0] = np.diag(d) + + for i in range(iterations): + dbi_new = deepcopy(dbi_object) + grad[i,:] = gradientDiagonal(dbi_object, d, H) + for j in range(len(d)): + d[j,j] = d[j,j] - step*grad[i,j] + s = polynomial_step(dbi_object, n = 3, d=d) + dbi_new(s,d=d) + loss[i+1] = dbi_new.least_squares(d) + diagonals[:,i+1] = np.diag(d) + + + return d,loss,grad,diagonals \ No newline at end of file diff --git a/tests/test_models_dbi.py b/tests/test_models_dbi.py index 43f3034d4d..5fa277f7ac 100644 --- a/tests/test_models_dbi.py +++ b/tests/test_models_dbi.py @@ -7,16 +7,18 @@ from qibo.models.dbi.double_bracket import ( DoubleBracketGeneratorType, DoubleBracketIteration, + DoubleBracketScheduling, ) from qibo.quantum_info import random_hermitian -NSTEPS = 50 +NSTEPS = 1 +seed = 10 """Number of steps for evolution.""" @pytest.mark.parametrize("nqubits", [3, 4, 5]) def test_double_bracket_iteration_canonical(backend, nqubits): - h0 = random_hermitian(2**nqubits, backend=backend) + h0 = random_hermitian(2**nqubits, backend=backend, seed=seed) dbi = DoubleBracketIteration( Hamiltonian(nqubits, h0, backend=backend), mode=DoubleBracketGeneratorType.canonical, @@ -30,7 +32,7 @@ def test_double_bracket_iteration_canonical(backend, nqubits): @pytest.mark.parametrize("nqubits", [3, 4, 5]) def test_double_bracket_iteration_group_commutator(backend, nqubits): - h0 = random_hermitian(2**nqubits, backend=backend) + h0 = random_hermitian(2**nqubits, backend=backend, seed=seed) d = backend.cast(np.diag(np.diag(backend.to_numpy(h0)))) dbi = DoubleBracketIteration( Hamiltonian(nqubits, h0, backend=backend), @@ -40,7 +42,6 @@ def test_double_bracket_iteration_group_commutator(backend, nqubits): # test first iteration with default d dbi(mode=DoubleBracketGeneratorType.group_commutator, step=0.01) - for _ in range(NSTEPS): dbi(step=0.01, d=d) @@ -49,7 +50,7 @@ def test_double_bracket_iteration_group_commutator(backend, nqubits): @pytest.mark.parametrize("nqubits", [3, 4, 5]) def test_double_bracket_iteration_single_commutator(backend, nqubits): - h0 = random_hermitian(2**nqubits, backend=backend) + h0 = random_hermitian(2**nqubits, backend=backend, seed=seed) d = backend.cast(np.diag(np.diag(backend.to_numpy(h0)))) dbi = DoubleBracketIteration( Hamiltonian(nqubits, h0, backend=backend), @@ -68,28 +69,28 @@ def test_double_bracket_iteration_single_commutator(backend, nqubits): @pytest.mark.parametrize("nqubits", [3, 4, 5]) def test_hyperopt_step(backend, nqubits): - h0 = random_hermitian(2**nqubits, backend=backend) + h0 = random_hermitian(2**nqubits, backend=backend, seed=seed) d = backend.cast(np.diag(np.diag(backend.to_numpy(h0)))) dbi = DoubleBracketIteration(Hamiltonian(nqubits, h0, backend=backend)) - + dbi.scheduling = DoubleBracketScheduling.hyperopt # find initial best step with look_ahead = 1 initial_step = 0.01 delta = 0.02 - step = dbi.hyperopt_step( + step = dbi.choose_step( step_min=initial_step - delta, step_max=initial_step + delta, max_evals=100 ) assert step != initial_step - # evolve following the optimized first step + # evolve following with optimized first step for generator in DoubleBracketGeneratorType: dbi(mode=generator, step=step, d=d) # find the following step size with look_ahead look_ahead = 3 - step = dbi.hyperopt_step( + step = dbi.choose_step( step_min=initial_step - delta, step_max=initial_step + delta, max_evals=100, @@ -107,3 +108,43 @@ def test_energy_fluctuations(backend): dbi = DoubleBracketIteration(Hamiltonian(1, matrix=h0, backend=backend)) energy_fluctuation = dbi.energy_fluctuation(state=state) assert energy_fluctuation == 0 + + +@pytest.mark.parametrize( + "scheduling", + [DoubleBracketScheduling.grid_search, DoubleBracketScheduling.hyperopt], +) +@pytest.mark.parametrize("nqubits", [3, 4, 5]) +def test_double_bracket_iteration_scheduling_grid_hyperopt( + backend, nqubits, scheduling +): + h0 = random_hermitian(2**nqubits, backend=backend, seed=seed) + d = backend.cast(np.diag(np.diag(backend.to_numpy(h0)))) + dbi = DoubleBracketIteration( + Hamiltonian(nqubits, h0, backend=backend), + mode=DoubleBracketGeneratorType.single_commutator, + ) + initial_off_diagonal_norm = dbi.off_diagonal_norm + for _ in range(NSTEPS): + step1 = dbi.choose_step(d=d, scheduling=scheduling) + dbi(d=d, step=step1) + step2 = dbi.choose_step() + dbi(step=step2) + assert initial_off_diagonal_norm > dbi.off_diagonal_norm + + +@pytest.mark.parametrize("nqubits", [3, 4, 6]) +@pytest.mark.parametrize("n", [2, 4]) +def test_double_bracket_iteration_scheduling_polynomial(backend, nqubits, n): + h0 = random_hermitian(2**nqubits, backend=backend, seed=seed) + dbi = DoubleBracketIteration( + Hamiltonian(nqubits, h0, backend=backend), + mode=DoubleBracketGeneratorType.single_commutator, + scheduling=DoubleBracketScheduling.polynomial_approximation, + ) + initial_off_diagonal_norm = dbi.off_diagonal_norm + for _ in range(NSTEPS): + # by default, d is the diagonal resctriction of H + step1 = dbi.choose_step(n=n) + dbi(step=step1) + assert initial_off_diagonal_norm > dbi.off_diagonal_norm diff --git a/tests/test_models_dbi_utils.py b/tests/test_models_dbi_utils.py index cd9f74e9de..a19ee502c5 100644 --- a/tests/test_models_dbi_utils.py +++ b/tests/test_models_dbi_utils.py @@ -37,6 +37,7 @@ def test_select_best_dbr_generator(backend, nqubits, step): dbi = DoubleBracketIteration( Hamiltonian(nqubits, h0, backend=backend), mode=DoubleBracketGeneratorType.single_commutator, + scheduling=DoubleBracketScheduling.grid_search, ) generate_Z = generate_Z_operators(nqubits) Z_ops = list(generate_Z.values()) diff --git a/tests/test_models_dbi_utils_scheduling.py b/tests/test_models_dbi_utils_scheduling.py new file mode 100644 index 0000000000..392727f144 --- /dev/null +++ b/tests/test_models_dbi_utils_scheduling.py @@ -0,0 +1,30 @@ +"""Unit testing for utils_scheduling.py for Double Bracket Iteration""" + +import numpy as np +import pytest + +from qibo.hamiltonians import Hamiltonian +from qibo.models.dbi.double_bracket import ( + DoubleBracketGeneratorType, + DoubleBracketIteration, + DoubleBracketScheduling, +) +from qibo.models.dbi.utils_scheduling import polynomial_step +from qibo.quantum_info import random_hermitian + +NSTEPS = 1 +seed = 10 +"""Number of steps for evolution.""" + + +@pytest.mark.parametrize("nqubits", [5, 6]) +def test_polynomial_fail_cases(backend, nqubits): + h0 = random_hermitian(2**nqubits, backend=backend, seed=seed) + dbi = DoubleBracketIteration( + Hamiltonian(nqubits, h0, backend=backend), + mode=DoubleBracketGeneratorType.single_commutator, + scheduling=DoubleBracketScheduling.polynomial_approximation, + ) + with pytest.raises(ValueError): + polynomial_step(dbi, n=2, n_max=1) + assert polynomial_step(dbi, n=1) == None