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The rational approximations of the unitary groups

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Abstract

This paper is to investigate the rational approximation of the unitary groups. Specially, based on the Household decomposition we prove that the rational unitary subgroup is dense in the complex unitary group. Moreover, its random approximate property is characterized by the natural Harr measure, which can be used to obtain random unitary matrix. Our simulation shows that these results may be applied to approximate quantum computations.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (Nos. 11226336, 61003287, 61170272, 61272514), the Fundamental Research Funds for the Central Universities (Nos. SWJTU11BR174, BUPT2012RC0221), the Specialized Research Fund for the Doctoral Program of Higher Education (20100005120002), the Fok Ying Tong Education Foundation (No. 131067).

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Authors and Affiliations

  1. Information Security and National Computing Grid Laboratory, Southwest Jiaotong University, Chengdu, 610031, China

    Ming-Xing Luo

  2. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Ming-Xing Luo & Xiu-Bo Chen

  3. Institute of Computer Science, Sichuan University of Science Engineering, Zigong, 64300, China

    Yun Deng

  4. Information Security Center, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Xiu-Bo Chen & Yi-Xian Yang

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  1. Ming-Xing Luo
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  2. Yun Deng
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  3. Xiu-Bo Chen
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  4. Yi-Xian Yang
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Correspondence to Ming-Xing Luo.

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Luo, MX., Deng, Y., Chen, XB. et al. The rational approximations of the unitary groups. Quantum Inf Process 12, 3149–3166 (2013). https://doi.org/10.1007/s11128-013-0588-7

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