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Time optimal control based on classification of quantum gates

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Abstract

We study the minimum time to implement an arbitrary two-qubit gate in two heteronuclear spins systems. We give a systematic characterization of two-qubit gates based on the invariants of local equivalence. The quantum gates are classified into four classes, and for each class the analytical formula of the minimum time to implement the quantum gates is explicitly presented. For given quantum gates, by calculating the corresponding invariants one easily obtains the classes to which the quantum gates belong. In particular, we analyze the effect of global phases on the minimum time to implement the gate. Our results present complete solutions to the optimal time problem in implementing an arbitrary two-qubit gate in two heteronuclear spins systems. Detailed examples are given to typical two-qubit gates with or without global phases.

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Acknowledgements

This work is supported by the NSF of China under Grant Nos. 11531004, 11675113, 11701320, Shandong provincial NSF of China Grant No. ZR2016AM04, Simons Foundation Grant No. 523868, Beijing Municipal Commission of Education under Grant No. KZ201810028042, and Beijing Natural Science Foundation (Z190005).

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Authors and Affiliations

  1. School of Mathematical Sciences, Qufu Normal University, Shandong, 273165, China

    Bao-Zhi Sun

  2. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    Shao-Ming Fei

  3. Max-Planck-Institute for Mathematics in the Sciences, 04103, Leipzig, Germany

    Shao-Ming Fei & Xianqing Li-Jost

  4. Department of Mathematics, North Carolina State University, Raleigh, NC, USA

    Naihuan Jing

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  1. Bao-Zhi Sun
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  2. Shao-Ming Fei
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  3. Naihuan Jing
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  4. Xianqing Li-Jost
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Correspondence to Bao-Zhi Sun.

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Sun, BZ., Fei, SM., Jing, N. et al. Time optimal control based on classification of quantum gates. Quantum Inf Process 19, 103 (2020). https://doi.org/10.1007/s11128-020-2602-1

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