Accelerated Inchworm Method with Tensor-Train Bath Influence Functional

TL;DR

This paper introduces a tensor-train-based algorithm that accelerates the inchworm method for simulating open quantum systems by efficiently approximating the bath influence functional, enabling long-time, high-dimensional simulations.

Contribution

The paper presents a novel tensor train approximation of the bath influence functional within the inchworm method, reducing computational complexity and improving simulation efficiency.

Findings

Tensor train approximation enables linear scaling with dimensions.

Deterministic quadrature replaces Monte Carlo for integral evaluation.

Method allows long-time simulations of open quantum system dynamics.

Abstract

We propose an efficient tensor-train-based algorithm for simulating open quantum systems with the inchworm method, where the reduced dynamics of the open quantum system is expressed as a perturbative series of high-dimensional integrals. Instead of evaluating the integrals with Monte Carlo methods, we approximate the costly bath influence functional (BIF) in the integrand as a tensor train, allowing accurate deterministic numerical quadrature schemes implemented in an iterative manner. Thanks to the low-rank structure of the tensor train, our proposed method has a complexity that scales linearly with the number of dimensions. Our method couples seamlessly with the tensor transfer method, allowing long-time simulations of the dynamics.