Quasi-locality and efficient simulation of Markovian quantum dynamics

TL;DR

This paper demonstrates that the evolution of open many-body quantum systems with short-range interactions can be efficiently approximated locally, enabling scalable classical and quantum simulations with rigorous error bounds.

Contribution

It establishes a generalized Lieb-Robinson bound for open quantum systems, showing quasi-locality and efficient simulation methods for such dynamics.

Findings

Evolution can be approximated locally with exponential accuracy.

Classical simulation cost is independent of system size.

Quantum simulation can be made efficient in time with error bounds.

Abstract

We consider open many-body systems governed by a time-dependent quantum master equation with short-range interactions. With a generalized Lieb-Robinson bound, we show that the evolution in this very generic framework is quasi-local, i.e., the evolution of observables can be approximated by implementing the dynamics only in a vicinity of the observables' support. The precision increases exponentially with the diameter of the considered subsystem. Hence, the time-evolution can be simulated on classical computers with a cost that is independent of the system size. Providing error bounds for Trotter decompositions, we conclude that the simulation on a quantum computer is additionally efficient in time. For experiments and simulations, our result can be used to rigorously bound finite-size effects.