The rational approximations of the unitary groups

Authors:
Ming-Xing Luo;Yun Deng;Xiu-Bo Chen;Yi-Xian Yang
Affiliations:
Information Security and National Computing Grid Laboratory, Southwest Jiaotong University, Chengdu, China 610031 and State Key Laboratory of Information Security, Institute of Information Enginee ...;Institute of Computer Science, Sichuan University of Science Engineering, Zigong, China 64300;State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China 100093 and Information Security Center, Beijing University of Posts ...;Information Security Center, Beijing University of Posts and Telecommunications, Beijing, China 100876
Venue:
Quantum Information Processing
Year:
2013

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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.