Algorithmic quantum simulation of memory effects

TL;DR

This paper introduces a method for simulating memory effects in quantum systems using a Markovian quantum simulator and perturbation theory, enabling efficient simulation of complex dynamics with polynomial resources.

Contribution

It presents a novel algorithmic approach for simulating non-Markovian quantum dynamics without engineering specific environments, using perturbation techniques and Markovian simulators.

Findings

Achieves small error bounds with polynomial resource scaling

Can simulate both positive and nonpositive dynamics

Does not require engineering non-Markovian environments

Abstract

We propose a method for the algorithmic quantum simulation of memory effects described by integrodifferential evolution equations. It consists in the systematic use of perturbation theory techniques and a Markovian quantum simulator. Our method aims to efficiently simulate both completely positive and nonpositive dynamics without the requirement of engineering non-Markovian environments. Finally, we find that small error bounds can be reached with polynomially scaling resources, evaluated as the time required for the simulation.