Simulation of stochastic quantum systems using polynomial chaos expansions

TL;DR

This paper introduces a polynomial chaos expansion method for simulating stochastic quantum systems, offering a computationally efficient alternative to Monte Carlo methods by representing the density matrix as a series of orthogonal polynomials.

Contribution

The paper develops a novel polynomial chaos expansion approach for quantum system simulation driven by stochastic processes, improving computational efficiency.

Findings

More efficient than Monte Carlo simulation in numerical examples

Provides practical heuristics for truncating the expansion

Demonstrates effectiveness on a one-qubit system

Abstract

We present an approach to the simulation of quantum systems driven by classical stochastic processes that is based on the polynomial chaos expansion, a well-known technique in the field of uncertainty quantification. The polynomial chaos expansion represents the system density matrix as a series of orthogonal polynomials in the principle components of the stochastic process and yields a sparsely coupled hierarchy of linear differential equations. We provide practical heuristics for truncating this expansion based on results from time-dependent perturbation theory and demonstrate, via an experimentally relevant one-qubit numerical example, that our technique can be significantly more computationally efficient than Monte Carlo simulation.