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Nonadiabatic holonomic quantum computation and its optimal control

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Abstract

The geometric phase has the intrinsic property of being resistant to some types of local noises as it only depends on global properties of the evolution path. Meanwhile, the non-Abelian geometric phase is in the matrix form, and thus can naturally be used to implement high performance quantum gates, i.e., the so-called holonomic quantum computation. This article reviews recent advances in nonadiabatic holonomic quantum computation, and focuses on various optimal control approaches that can improve the gate performance, in terms of gate fidelity and robustness. Besides, we also pay special attention to its possible physical realizations and some concrete examples of experimental realizations. Finally, with all these efforts, within state-of-the-art technology, the performance of the implemented holonomic quantum gates can outperform the conventional dynamical ones, under certain conditions.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 12275090), Guangdong Provincial Key Laboratory (Grant No. 2020B1212060066), and Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0302300).

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Authors and Affiliations

  1. Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), School of Physics, South China Normal University, Guangzhou, 510006, China

    Yan Liang, Pu Shen, Tao Chen & Zheng-Yuan Xue

  2. Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou, 510006, China

    Tao Chen & Zheng-Yuan Xue

  3. Hefei National Laboratory, Hefei, 230088, China

    Zheng-Yuan Xue

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  1. Yan Liang
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  2. Pu Shen
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  3. Tao Chen
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  4. Zheng-Yuan Xue
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Correspondence to Zheng-Yuan Xue.

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Liang, Y., Shen, P., Chen, T. et al. Nonadiabatic holonomic quantum computation and its optimal control. Sci. China Inf. Sci. 66, 180502 (2023). https://doi.org/10.1007/s11432-023-3824-0

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  • DOI: https://doi.org/10.1007/s11432-023-3824-0

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