Approximating open quantum system dynamics in a controlled and efficient way: A microscopic approach to decoherence

TL;DR

This paper presents a method to efficiently approximate open quantum system dynamics by leveraging local interactions and the Lieb-Robinson bound, enabling polynomial scaling simulations of decoherence.

Contribution

It introduces a microscopic approach using a dynamical renormalization group to derive effective Hamiltonians within the light cone, improving simulation efficiency.

Findings

Efficient simulation with predefined error bounds.

Applicable to environments with discrete or continuous degrees of freedom.

Polynomial scaling in interaction time and environment size.

Abstract

We demonstrate that the dynamics of an open quantum system can be calculated efficiently and with predefined error, provided a basis exists in which the system-environment interactions are local and hence obey the Lieb-Robinson bound. We show that this assumption can generally be made. Defining a dynamical renormalization group transformation, we obtain an effective Hamiltonian for the full system plus environment that comprises only those environmental degrees of freedom that are within the effective light cone of the system. The reduced system dynamics can therefore be simulated with a computational effort that scales at most polynomially in the interaction time and the size of the effective light cone. Our results hold for generic environments consisting of either discrete or continuous degrees of freedom.