{ "cells": [ { "cell_type": "markdown", "id": "86c26a84", "metadata": {}, "source": [ "# Gibbs State" ] }, { "cell_type": "markdown", "id": "a444def8", "metadata": {}, "source": [ "## Overview" ] }, { "cell_type": "markdown", "id": "a4ab914e", "metadata": {}, "source": [ "The Gibbs state is an $n$-qubit mixed quantum state defined as a density matrix\n", "$$ \\rho := \\frac{1}{Z} e^{-\\beta H},\\quad Z=\\text{tr}(e^{-\\beta H}). $$\n", "This state is important in the application of quantum algorithms to quantum simulation, optimization, and machine learning.\n", "\n", "The preparation of the Gibbs state can be viewed as implementing the mapping $H \\mapsto \\exp(-\\beta H)$. Thus, the target function seemingly should be set to $f(x) = \\exp (-\\beta x)$. However, the parity condition is violated by this function and hence its implementation must be separated into even and odd components respectively, as in the Hamiltonian simulation example. The even/odd component of this function is hyperbolic cosine/sine, with values that blow up exponentially. Hence, naively implementing this function would cause an exponentially vanishing unnormalized quantum state. To remedy this, the Hamiltonian can first be shifted and scaled so as to be positive definite, i.e., there is a positive number $\\delta > 0$ so that $\\delta I \\prec H \\prec I$. Then, we only need a target function that agrees with $f$ on the interval $D = [\\delta, 1]$, i.e.,\n", "$$ \\max_{x \\in D} |h(x)- f(x)| < \\epsilon. $$\n", "Since the function is partially specified in a subinterval $D$, the best polynomial approximation $h(x)$ can be solved using our typical convex-optimization-based method." ] }, { "cell_type": "markdown", "id": "6a5f11c2", "metadata": {}, "source": [ "## Setup and approximate target function" ] }, { "cell_type": "code", "execution_count": 1, "id": "e94bd673", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "norm error = 7.1048080768587396e-09\n", "max of solution = 0.7346270305559349\n" ] }, { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from qsppack.utils import cvx_poly_coef\n", "\n", "beta = 2\n", "targ = lambda x: np.exp(-beta * x)\n", "deg = 151\n", "parity = deg % 2\n", "delta = 0.2\n", "\n", "opts = {\n", " 'intervals': [delta, 1],\n", " 'objnorm': 2,\n", " 'epsil': 0.2,\n", " 'npts': 500,\n", " 'fscale': 1,\n", " 'isplot': True,\n", " 'method': 'cvxpy',\n", " 'maxiter': 100,\n", " 'criteria': 1e-12,\n", " 'useReal': False,\n", " 'targetPre': True\n", "}\n", "\n", "coef_full = cvx_poly_coef(targ, deg, opts)\n", "coef = coef_full[parity::2]" ] }, { "cell_type": "markdown", "id": "722e4f20", "metadata": {}, "source": [ "## Solving the phase factors and verifying" ] }, { "cell_type": "code", "execution_count": 2, "id": "387bb391", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "iter err \n", " 1 +1.5632e-01\n", " 2 +8.4444e-03\n", " 3 +3.0174e-05\n", " 4 +3.7987e-10\n", "Stop criteria satisfied.\n", "The residual error is\n", "1.0658141036401503e-14\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "opts['method'] = 'Newton'\n", "\n", "from qsppack.solver import solve\n", "phi_proc, out = solve(coef, parity, opts)\n", "\n", "from qsppack.utils import chebyshev_to_func, get_entry\n", "import matplotlib.pyplot as plt\n", "\n", "xlist = np.linspace(0, np.sin(1), 500)\n", "func = lambda x: chebyshev_to_func(x, coef, parity, True)\n", "targ_value = targ(xlist)\n", "func_value = func(xlist)\n", "QSP_value = get_entry(xlist, phi_proc, out)\n", "err = np.linalg.norm(QSP_value - func_value, np.inf)\n", "print('The residual error is')\n", "print(err)\n", "\n", "plt.plot(xlist, QSP_value - func_value)\n", "plt.xlabel('$x$', fontsize=12)\n", "plt.ylabel('$g(x,\\\\Phi^*)-f_\\\\mathrm{poly}(x)$', fontsize=12)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "5e9d5b71", "metadata": {}, "source": [ "## Reference\n", "1. Gilyén, A., Su, Y., Low, G. H., & Wiebe, N. (2019, June). Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics. In *Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing* (pp. 193-204).\n", "\n", "2. Dong, Y., Meng, X., Whaley, K. B., & Lin, L. (2021). Efficient phase-factor evaluation in quantum signal processing. *Physical Review A*, 103(4), 042419." ] } ], "metadata": { "kernelspec": { "display_name": "qspy", "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": "3.13.2" } }, "nbformat": 4, "nbformat_minor": 5 }