Abstract
In this paper, we present a least squares approach to identifying an unknown damping rate function in a time-convolution-less master equation describing the non-Markovian dynamics of a probing single qubit. For the purpose of identification, we measure two kinds of time trace observables \(\langle \sigma _z\rangle \) and \(\langle \sigma _x\rangle \) with which the identification problem can be solved via our least squares approach. In the case of measuring the time trace observable \(\langle \sigma _x\rangle \), a data-driven method is also developed to estimate the unmeasured \(\langle \sigma _y\rangle \) such that the identification problem fits into the least squares framework. A physical example is given to show the effectiveness of our method.
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Acknowledgements
This work was supported in part by the National Natural Science Foundation of China under Grants 61873162 and 61473199, in part by the Shanghai Pujiang Program under Grant 18PJ1405500, in part by the Suzhou Key Industry Technology Innovation Project SYG201808, in part by the Key Laboratory of System Control and Information Processing in Ministry of Education of China Scip201804. This work is also supported by the Open Research Project of the State Key Laboratory of Industrial Control Technology, Zhejiang University, China (No. ICT1900304).
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Xue, S., Tan, L., Jiang, M. et al. A least squares identifier for a quantum non-Markovian environment model. Quantum Inf Process 18, 310 (2019). https://doi.org/10.1007/s11128-019-2425-0
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DOI: https://doi.org/10.1007/s11128-019-2425-0