University of Oulu

Vadimov, V., Tuorila, J., Orell, T., Stockburger, J., Ala-Nissila, T., Ankerhold, J., & Möttönen, M. (2021). Validity of Born-Markov master equations for single- and two-qubit systems. Physical Review B, 103(21).

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

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Author: Vadimov, Vasilii1,2,3; Tuorila, Jani1,2,4; Orell, Tuure5;
Organizations: 1QCD Labs, QTF Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 13500, FI-00076 Aalto, Espoo, Finland
2MSP Group, QTF Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Espoo, Finland
3Institute for Physics of Microstructures, Russian Academy of Sciences, 603950 Nizhny Novgorod, GSP-105, Russia
4IQM, Keilaranta 19, FI-02150 Espoo, Finland
5Nano and Molecular Materials Research Unit, University of Oulu, P.O. Box 3000, FI-90014, Finland
6Institute for Complex Quantum Systems and IQST, University of Ulm, 89069 Ulm, Germany
7Interdisciplinary Centre for Mathematical Modelling, Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, United Kingdom
8VTT Technical Research Centre of Finland Ltd., QTF Center of Excellence, P.O. Box 1000, FI-02044 VTT, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 1.1 MB)
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Language: English
Published: American Physical Society, 2021
Publish Date: 2021-08-27


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.

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Series: Physical review. B
ISSN: 2469-9950
ISSN-E: 2469-9969
ISSN-L: 2469-9950
Volume: 103
Article number: 214308
DOI: 10.1103/PhysRevB.103.214308
Type of Publication: A1 Journal article – refereed
Field of Science: 114 Physical sciences
Funding: 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 (IQST), and the Zeiss Foundation under the grant TQuant. The authors wish to acknowledge CSC – IT Center for Science, Finland, for computational resources.
Copyright information: © 2021 American Physical Society,