Fast Algorithms of Bath Calculations in Simulations of Quantum System-Bath Dynamics

TL;DR

This paper introduces fast algorithms for bath calculations in quantum system-bath dynamics simulations, significantly reducing computational costs by reusing influence functionals, and verified through numerical experiments.

Contribution

The paper develops and proves the efficiency of algorithms that reuse bath influence functionals, reducing computational complexity in quantum simulations.

Findings

Reduction of calculations by a factor of O(N)

Numerical verification of algorithm efficiency

Improved simulation speed for quantum system-bath models

Abstract

We present fast algorithms for the summation of Dyson series and the inchworm Monte Carlo method for quantum systems that are coupled with harmonic baths. The algorithms are based on evolving the integro-differential equations where the most expensive part comes from the computation of bath influence functionals. To accelerate the computation, we design fast algorithms based on reusing the bath influence functionals computed in the previous time steps to reduce the number of calculations. It is proven that the proposed fast algorithms reduce the number of such calculations by a factor of $O(N)$, where $N$ is the total number of time steps. Numerical experiments are carried out to show the efficiency of the method and to verify the theoretical results.