Adaptive Resummation of Markovian Quantum Dynamics

TL;DR

This paper presents a novel resummation technique for Markovian quantum dynamics that provides highly accurate analytical approximations, outperforming traditional methods especially when no small parameters are available.

Contribution

It introduces a generalized Dyson series resummation method that ensures optimal convergence for Markovian open quantum systems without relying on small parameters.

Findings

Accurately approximates quantum evolution with errors on the per mil level

Demonstrates effectiveness on spatial detection and Landau-Zener problems

Approximations are asymptotically exact across parameter ranges

Abstract

We introduce a method for obtaining analytic approximations to the evolution of Markovian open quantum systems. It is based on resumming a generalized Dyson series in a way that ensures optimal convergence even in the absence of a small parameter. The power of this approach is demonstrated by two benchmark examples: the spatial detection of a free particle and the Landau-Zener problem in the presence of dephasing. The derived approximations are asymptotically exact and exhibit errors on the per mil level over the entire parameter range.