Non-equilibrium quantum Monte Carlo algorithm for stabilizer Renyi entropy in spin systems

TL;DR

This paper introduces an efficient quantum Monte Carlo algorithm to compute stabilizer Renyi entropy, a measure of quantum magic, in spin systems, applicable across dimensions and temperatures, with demonstrated accuracy and polynomial computational cost.

Contribution

The paper presents a novel Monte Carlo algorithm for calculating stabilizer Renyi entropy in spin systems, extending applicability to all dimensions and temperatures with proven efficiency.

Findings

Algorithm accurately computes stabilizer Renyi entropy in 1D and 2D transverse field Ising models.

Results agree with tensor-network methods, validating the algorithm.

Computational cost is polynomial in system size, confirmed analytically and numerically.

Abstract

Quantum magic, or nonstabilizerness, provides a crucial characterization of quantum systems, regarding the classical simulability with stabilizer states. In this work, we propose a novel and efficient algorithm for computing stabilizer R\'enyi entropy, one of the measures for quantum magic, in spin systems with sign-problem free Hamiltonians. This algorithm is based on the quantum Monte Carlo simulation of the path integral of the work between two partition function ensembles and it applies to all spatial dimensions and temperatures. We demonstrate this algorithm on the one and two dimensional transverse field Ising model at both finite and zero temperatures and show the quantitative agreements with tensor-network based algorithms. Furthermore, we analyze the computational cost and provide both analytical and numerical evidences for it to be polynomial in system size.