Digital quantum simulation of many-body non-Markovian dynamics

TL;DR

This paper introduces a digital quantum simulation algorithm for complex many-body non-Markovian open quantum systems, combining Suzuki-Lie-Trotter decomposition with unitary operations and measurements, supported by rigorous error analysis.

Contribution

It develops a novel algorithmic approach for simulating non-Markovian dynamics on quantum computers, including error bounds and efficiency analysis.

Findings

Rigorous error bounds for Suzuki-Lie-Trotter decomposition

Efficient simulation of non-Markovian systems with local indivisibility

Potential for experimental implementation

Abstract

We present an algorithmic method for the digital quantum simulation of many-body locally indivisible non-Markovian open quantum systems. It consists of two parts: firstly, a Suzuki-Lie-Trotter decomposition of the global system propagator into the product of subsystem propagators, which may not be quantum channels, and secondly, an algorithmic procedure for the implementation of the subsystem propagators through unitary operations and measurements on a dilated space. By providing rigorous error bounds for the relevant Suzuki-Lie-Trotter decomposition, we are able to analyze the efficiency of the method, and connect it with an appropriate measure of the local indivisibility of the system. In light of our analysis, the proposed method is expected to be experimentally achievable for a variety of interesting cases.