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Solovay–Kitaev Approximations of Special Orthogonal Matrices

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  • Anuradha Mahasinghe
  • Sachiththa Bandaranayake
  • Kaushika De Silva

Abstract

The circuit-gate framework of quantum computing relies on the fact that an arbitrary quantum gate in the form of a unitary matrix of unit determinant can be approximated to a desired accuracy by a fairly short sequence of basic gates, of which the exact bounds are provided by the Solovay–Kitaev theorem. In this work, we show that a version of this theorem is applicable to orthogonal matrices with unit determinant as well, indicating the possibility of using orthogonal matrices for efficient computation. We further develop a version of the Solovay–Kitaev algorithm and discuss the computational experience.

Suggested Citation

  • Anuradha Mahasinghe & Sachiththa Bandaranayake & Kaushika De Silva, 2020. "Solovay–Kitaev Approximations of Special Orthogonal Matrices," Advances in Mathematical Physics, Hindawi, vol. 2020, pages 1-7, June.
    • Handle: RePEc:hin:jnlamp:2530609
    DOI: 10.1155/2020/2530609
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