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Supplementary information files for: Validity of Born-Markov master equations for single- and two-qubit systems

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posted on 08.10.2021, 13:15 by Vasilii Vadimov, Jani Tuorila, Tuure Orell, Jürgen Stockburger, Tapio Ala-NissilaTapio Ala-Nissila, Joachim Ankerhold, Mikko Möttönen
Supplementary files for article: Validity of Born-Markov master equations for single- and two-qubit systems.
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.


European Research Council under Grant No. 681311 (QUESS)

Academy of Finland through its Centre of Excellence in Quantum Technology (QTF) (Grants No. 312298 and No. 312300)

Jane and Aatos Erkko Foundation

Technology Industries of Finland Centennial Foundation

German Science Foundation (Grants No. AN336/11-1 and No. AN336/12-1)

Centre for Integrated Quantum Science and Technology (IQST)

Zeiss Foundation under the grant TQuant



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  • Mathematical Sciences

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