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A Geometric Characterization of Quantum Gates

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Abstract

Quantum gates are unitary operators and pure states are denoted by unit vectors in state spaces. A quantum gate (i.e., unitary operator) maps convex combinations of vectors in the closed unit ball of the state space to themselves. On the contrary, whether or not some kinds of convex combinations preserving maps on the closed unit ball of the state space are unitary. In the paper, we devote to giving an answer to the inverse problem.

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Acknowledgements

Thanks for comments. The authors declare that there is no conflict of interest regarding the publication of this paper. The work is supported by National Science Foundation of China under Grant No. 11771011 and Natural Science Foundation of Shanxi Province under Grant No. 201701D221011, 201601D021009.

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Authors and Affiliations

  1. College of Software, Taiyuan University of Technology, Taiyuan, Shanxi, 030024, People’s Republic of China

    Yi-Bin He

  2. College of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi, 030024, People’s Republic of China

    Li Wang

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  1. Yi-Bin He
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  2. Li Wang
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Correspondence to Li Wang.

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He, YB., Wang, L. A Geometric Characterization of Quantum Gates. Int J Theor Phys 58, 2218–2227 (2019). https://doi.org/10.1007/s10773-019-04112-9

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  • DOI: https://doi.org/10.1007/s10773-019-04112-9

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