{ "cells": [ { "cell_type": "markdown", "id": "86c26a84", "metadata": {}, "source": [ "# Singular Value Threshold Projector" ] }, { "cell_type": "markdown", "id": "a444def8", "metadata": {}, "source": [ "## Overview" ] }, { "cell_type": "markdown", "id": "a4ab914e", "metadata": {}, "source": [ "Singular value threshold projectors project out singular vectors with singular values below or above a certain threshold. Suppose that we have access to a unitary $U$, its inverse $U^\\dagger$ and the controlled reflection operators $(2\\Pi - I)$, $(2\\tilde{\\Pi} - I)$. We are primarily interested in $A := \\tilde{\\Pi}U\\Pi$, which has a singular value decomposition $A = W\\Sigma V$. For $S \\subset R$, let $\\Sigma_S$ be the matrix obtained from $\\Sigma$ by replacing all diagonal entries $\\Sigma_{ii} \\in S$ by one and all diagonal entries $\\Sigma_{ii} \\notin S$ by zero. We define $\\Pi_S := \\Pi V \\Sigma_S V^\\dagger \\Pi$, and similarly $\\tilde{\\Pi}_S := \\tilde{\\Pi}W\\Sigma_S W^\\dagger\\tilde{\\Pi}$. For example, if we let $S=[0,\\ell]$, $\\Pi_S$ projects out right singular vectors with singular value at most $\\ell$. These threshold projectors play a major role in quantum algorithms." ] }, { "cell_type": "markdown", "id": "6a5f11c2", "metadata": {}, "source": [ "## Polynomial approximation" ] }, { "cell_type": "markdown", "id": "653abb7b", "metadata": {}, "source": [ "For numerical demonstration, we let $\\ell = 0.5$. To implement $\\Pi_{[0,0.5]}$, we can implement the singular value transformation of $A$ for a rectangle function $f$. We can call `cvx_poly_coef` from `qsppack.utils` to find the best even polynomial approximating $f(x)$ on the interval $D_\\delta = [0, 0.5-\\delta] \\cup [0.5+\\delta,1]$, with $\\delta = 0.05$. This subroutine uses convex optimization to solve the problem." ] }, { "cell_type": "code", "execution_count": 1, "id": "e94bd673", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "norm error = 6.529647593817857e-08\n", "max of solution = 0.8999999998163493\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", "delta = 0.05\n", "opts = {\n", " 'intervals': [0, 0.5-delta, 0.5+delta, 1],\n", " 'objnorm': np.inf,\n", " 'epsil': 0.1,\n", " 'npts': 500,\n", " 'fscale': 0.9,\n", " 'maxiter': 100,\n", " 'useReal': False,\n", " 'targetPre': True,\n", " 'isplot': True,\n", " 'method': 'cvxpy'\n", "}\n", "targ = np.vectorize(lambda x: 1 if np.abs(x) < 0.5 else 0)\n", "deg = 250\n", "parity = deg % 2\n", "\n", "coef = cvx_poly_coef(targ, deg, opts)\n", "coef = coef[parity::2]" ] }, { "cell_type": "markdown", "id": "928680e6", "metadata": {}, "source": [ "## Solve for phase factors and verify" ] }, { "cell_type": "code", "execution_count": 2, "id": "24de1a27", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "iter err \n", " 1 +4.8372e-01\n", " 2 +1.9792e-01\n", " 3 +2.7183e-02\n", " 4 +3.0104e-04\n", " 5 +3.2273e-08\n", "Stop criteria satisfied.\n", "The residual error is\n", "1.942890293094024e-14\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Solve for phase factors\n", "from qsppack.solver import solve\n", "opts['method'] = 'Newton'\n", "phi_proc, out = solve(coef, parity, opts)\n", "\n", "# Verify result\n", "from qsppack.utils import chebyshev_to_func, get_entry\n", "xlist1 = np.linspace(0, 0.5 - delta, 500)\n", "xlist2 = np.linspace(0.5 + delta, 1, 500)\n", "xlist = np.concatenate((xlist1, xlist2))\n", "targ_value = targ(xlist)\n", "func_value = chebyshev_to_func(xlist, coef, parity, True)\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", "# Plot error\n", "import matplotlib.pyplot as plt\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 }