Validity of Born-Markov master equations for single and two-qubit systems

TL;DR

This paper evaluates the accuracy of common Born-Markov master equations, like Redfield and Lindblad, against exact results for single and two-qubit systems coupled to a bath, highlighting their limitations in certain parameter regimes.

Contribution

It provides a comprehensive comparison of weak-coupling master equations with exact solutions, establishing their validity range and guiding their use in quantum device modeling.

Findings

Master equations often fail at low temperatures.

Optimized parameters improve phenomenological modeling.

Guidelines for the validity range of Born-Markov equations.

Abstract

The urgent need for reliable simulation tools to match the extreme accuracy needed to control tailored quantum devices highlights the importance of understanding open quantum systems and their modeling. To this end, we compare here the commonly used Redfield and Lindblad master equations against numerically exact results in the case of one and two resonant qubits transversely coupled at a single point to a Drude-cut ohmic bath. All the relevant parameters are varied over a broad range which allows us to give detailed predictions about the validity and physically meaningful applicability of the weak-coupling approaches. We characterize the accuracy of the approximate approaches by comparing the maximum difference of their system evolution superoperators with numerically exact results. After optimizing the parameters of the approximate models to minimize the difference, we also explore if and to what extent the weak-coupling equations can be applied at least as phenomenological models. Optimization may lead to an accurate reproduction of experimental data, but yet our results are important to estimate the reliability of the extracted parameter values such as the bath temperature. Our findings set general guidelines for the range of validity of the usual Born-Markov master equations and indicate that they fail to accurately describe the physics in surprisingly broad range of parameters, in particular at low temperatures. Since quantum-technological devices operate there their accurate modeling calls for a careful choice of methods.