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

Vasilii Vadimov, Jani Tuorila, Tuure Orell, Jürgen Stockburger, Tapio Ala-Nissila, Joachim Ankerhold, Mikko Möttönen

Research output: Contribution to journalArticleScientificpeer-review

8 Citations (Scopus)


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 a 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.

Original languageEnglish
Article number214308
Number of pages14
JournalPhysical Review B
Issue number21
Early online date2 Jun 2021
Publication statusPublished - 17 Jun 2021
MoE publication typeA1 Journal article-refereed


This research was financially supported by the European Research Council under Grant No. 681311 (QUESS), by the Academy of Finland through its Centre of Excellence in Quantum Technology (QTF) (Grants No. 312298 and No. 312300), by the Jane and Aatos Erkko Foundation, and by the Technology Industries of Finland Centennial Foundation. It was also supported by the German Science Foundation (Grants No. AN336/11-1 and No. AN336/12-1), the Centre for Integrated Quantum Science and Technology, and the Zeiss Foundation under the grant TQuant.


Dive into the research topics of 'Validity of Born-Markov master equations for single- And two-qubit systems'. Together they form a unique fingerprint.

Cite this