{ "cells": [ { "cell_type": "markdown", "id": "86c26a84", "metadata": {}, "source": [ "# Gaussian State" ] }, { "cell_type": "markdown", "id": "a444def8", "metadata": {}, "source": [ "## Overview" ] }, { "cell_type": "markdown", "id": "a4ab914e", "metadata": {}, "source": [ "A Gaussian state is an $n$-qubit quantum state defined as\n", "$$ |\\Psi \\rangle := \\frac{1}{\\sqrt{\\sum_x |f(x)|^2}} \\sum_{x=0}^{N-1} f(x) |x\\rangle, $$\n", "where $N=2^n$ and $f(x) = \\text{exp}(-\\beta x^2 /2)$ is the Gaussian function. Gaussian states are ubiquitous in the application of quantum algorithms to quantum chemistry, quantum field theory simulation, and finance applications.\n", "\n", "A recent preprint [1] proposed a procedure for preparing Gaussian states. It leverges the block encoding of the sine value of equally spaced sample points $\\sum_x \\sin(x/N)|x\\rangle \\langle x|$. By applying the quantum eigenvalue transformation on this block encoding, a Gaussian state is prepared. Consequently, the problem is reduced to finding the phase factors generating the following function:\n", "$$ h(z) = f(\\arcsin(z)) \\propto \\exp(-\\beta \\arcsin^2(x)/2), $$\n", "where $z=\\sin(x)$ transforms the domain to $z \\in [0, \\sin(1)]$." ] }, { "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 = 4.2473472425764815e-10\n", "max of solution = 0.9899999997914414\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 = 100\n", "targ = lambda x: np.exp(-beta/2 * np.arcsin(x)**2)\n", "deg = 100\n", "parity = deg % 2\n", "\n", "opts = {\n", " 'intervals': [0, np.sin(1)],\n", " 'objnorm': np.inf,\n", " 'epsil': 0.01,\n", " 'npts': 500,\n", " 'fscale': 0.99,\n", " 'isplot': True,\n", " 'method': 'cvxpy',\n", " 'maxiter': 100,\n", " 'criteria': 1e-12,\n", " 'useReal': True,\n", " 'targetPre': True,\n", " 'print': 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 +1.5414e-01\n", " 2 +3.4730e-02\n", " 3 +6.6586e-03\n", " 4 +6.6105e-04\n", " 5 +1.0191e-05\n", " 6 +2.5796e-09\n", "Stop criteria satisfied.\n", "The residual error is\n", "7.327471962526033e-15\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. McArdle, S., Gilyén, A., & Berta, M. (2022). Quantum state preparation without coherent arithmetic. *arXiv:2210.14892*." ] } ], "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 }