Nonequilibrium quantum Monte Carlo algorithm for stabilizer Rényi entropy in spin systems

Quantum magic, or nonstabilizerness, provides a crucial characterization of quantum systems, regarding the classical simulability with stabilizer states. In this work, we propose an alternative and efficient algorithm for computing stabilizer Rényi 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. We analyze the computational cost and provide analytical and numerical evidences for it to be polynomial in system size. This work also suggests a unifying framework for calculating various types of entropy quantities including entanglement Rényi entropy and entanglement Rényi negativity.