Succinct Description and Efficient Simulation of Non-Markovian Open Quantum Systems

TL;DR

This paper introduces a succinct representation and an efficient quantum algorithm for simulating the complex dynamics of non-Markovian open quantum systems, addressing a significant gap in quantum simulation methods.

Contribution

It provides the first universal succinct description of non-Markovian dynamics with quantifiable error and develops an algorithm with polylogarithmic cost in simulation time and precision.

Findings

Succinct representation of non-Markovian dynamics with error bounds

Quantum algorithm with cost $O(t \, ext{polylog}(t/\epsilon))$ for simulation

Potential new approaches using stochastic Schrödinger equations

Abstract

Non-Markovian open quantum systems represent the most general dynamics when the quantum system is coupled with a bath environment. The quantum dynamics arising from many important applications are non-Markovian. Although for special cases, such as Hamiltonian evolution and Lindblad evolution, quantum simulation algorithms have been extensively studied, efficient quantum simulations for the dynamics of non-Markovian open quantum systems remain underexplored. The most immediate obstacle for studying such systems is the lack of a universal succinct description of their dynamics. In this work, we fulfill the gap of studying such dynamics by 1) providing a succinct representation of the dynamics of non-Markovian open quantum systems with quantifiable error, and 2) developing an efficient quantum algorithm for simulating such dynamics with cost $O(t\, \mathrm{polylog}(t/\epsilon))$ for evolution time $t$ and precision $\epsilon$. Our derivation of the succinct representation is based on stochastic Schr\"odinger equations, which could lead to new alternatives to deal with open quantum systems as well.