Lindblad evolution without the sign problem

TL;DR

This paper introduces a method to simulate real-time evolution in open fermion systems using quantum Monte Carlo without encountering the usual sign problem, by mapping to non-Hermitian quantum systems.

Contribution

It proposes a novel mapping technique that enables sign-problem-free quantum Monte Carlo simulations for certain real-time open quantum systems.

Findings

Successfully computed real-time fidelities in open fermion systems

Demonstrated sign-problem-free simulations in specific cases

Showed potential for broader applications in open quantum systems

Abstract

Quantum Monte Carlo is one of the most powerful numerical tools for studying nonpeturbative properties of quantum many-body systems. However, its application to real-time problems is limited since the complex and highly-oscillating path-integral weight of the real-time evolution harms the important sampling. % , which is the notorious sign problem. In this Letter, we show that some real-time problems in open fermion systems can be simulated using the quantum Monte Carlo. To this end, we prescribe a mapping between a real-time problem in open quantum systems and a statistical problem in non-Hermitian quantum systems; for some cases, the latter can be solved without suffering from the complex measure problem. To explain our idea and demonstrate how it works, we compute the real-time evolution of fidelities in open fermion systems under dissipation.