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The urgent need for reliable simulation tools to match the extreme accuracyneeded to control tailored quantum devices highlights the importance ofunderstanding open quantum systems and their modeling. To this end, we comparehere the commonly used Redfield and Lindblad master equations againstnumerically exact results in the case of one and two resonant qubitstransversely coupled at a single point to a Drude-cut ohmic bath. All therelevant parameters are varied over a broad range which allows us to givedetailed predictions about the validity and physically meaningful applicabilityof the weak-coupling approaches. We characterize the accuracy of theapproximate approaches by comparing the maximum difference of their systemevolution superoperators with numerically exact results. After optimizing theparameters of the approximate models to minimize the difference, we alsoexplore if and to what extent the weak-coupling equations can be applied atleast as phenomenological models. Optimization may lead to an accuratereproduction of experimental data, but yet our results are important toestimate the reliability of the extracted parameter values such as the bathtemperature. Our findings set general guidelines for the range of validity ofthe usual Born-Markov master equations and indicate that they fail toaccurately describe the physics in surprisingly broad range of parameters, inparticular at low temperatures. Since quantum-technological devices operatethere their accurate modeling calls for a careful choice of methods.

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