Capturing exponential variance using polynomial resources: applying tensor networks to non-equilibrium stochastic processes

TL;DR

This paper demonstrates that tensor network compression can efficiently estimate high-variance observables in non-equilibrium stochastic processes without sampling, outperforming traditional methods in systems with exponential variance scaling.

Contribution

It introduces a tensor network approach to capture high-variance observables efficiently, avoiding exponential sampling costs in complex stochastic systems.

Findings

Tensor networks accurately capture high-variance observables.

The method reduces computational complexity from exponential to polynomial.

Application to Jarzynski's equality demonstrates practical effectiveness.

Abstract

Estimating the expected value of an observable appearing in a non-equilibrium stochastic process usually involves sampling. If the observable's variance is high, many samples are required. In contrast, we show that performing the same task without sampling, using tensor network compression, efficiently captures high variances in systems of various geometries and dimensions. We provide examples for which matching the accuracy of our efficient method would require a sample size scaling exponentially with system size. In particular, the high variance observable $\mathrm{e}^{-\beta W}$, motivated by Jarzynski's equality, with $W$ the work done quenching from equilibrium at inverse temperature $\beta$, is exactly and efficiently captured by tensor networks.