Importance Sampling Scheme for the Stochastic Simulation of Quantum Spin Dynamics

TL;DR

This paper introduces an importance sampling method for simulating quantum spin dynamics, reducing fluctuations and extending simulation capabilities by focusing on dominant classical trajectories.

Contribution

It develops a novel importance sampling scheme based on classical trajectories to improve stochastic simulation of quantum spin systems.

Findings

Reduces fluctuations in stochastic quantum simulations

Extends accessible simulation times and system sizes

Provides a framework for further methodological improvements

Abstract

The numerical simulation of dynamical phenomena in interacting quantum systems is a notoriously hard problem. Although a number of promising numerical methods exist, they often have limited applicability due to the growth of entanglement or the presence of the so-called sign problem. In this work, we develop an importance sampling scheme for the simulation of quantum spin dynamics, building on a recent approach mapping quantum spin systems to classical stochastic processes. The importance sampling scheme is based on identifying the classical trajectory that yields the largest contribution to a given quantum observable. An exact transformation is then carried out to preferentially sample trajectories that are close to the dominant one. We demonstrate that this approach is capable of reducing the temporal growth of fluctuations in the stochastic quantities, thus extending the range of accessible times and system sizes compared to direct sampling. We discuss advantages and limitations of the proposed approach, outlining directions for further developments.