Solovay–Kitaev Approximations of Special Orthogonal Matrices
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 theo...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/2530609 |
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| _version_ | 1832560132907597824 |
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| author | Anuradha Mahasinghe Sachiththa Bandaranayake Kaushika De Silva |
| author_facet | Anuradha Mahasinghe Sachiththa Bandaranayake Kaushika De Silva |
| author_sort | Anuradha Mahasinghe |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b0dfe1d107064acca8659001839b215e |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-b0dfe1d107064acca8659001839b215e2025-02-03T01:28:21ZengWileyAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/25306092530609Solovay–Kitaev Approximations of Special Orthogonal MatricesAnuradha Mahasinghe0Sachiththa Bandaranayake1Kaushika De Silva2Department of Mathematics, University of Colombo, Colombo 03, Sri LankaDepartment of Mathematics, University of Colombo, Colombo 03, Sri LankaDepartment of Mathematics, University of Sri Jayewardenepura, Nugegoda, Sri LankaThe 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.http://dx.doi.org/10.1155/2020/2530609 |
| spellingShingle | Anuradha Mahasinghe Sachiththa Bandaranayake Kaushika De Silva Solovay–Kitaev Approximations of Special Orthogonal Matrices Advances in Mathematical Physics |
| title | Solovay–Kitaev Approximations of Special Orthogonal Matrices |
| title_full | Solovay–Kitaev Approximations of Special Orthogonal Matrices |
| title_fullStr | Solovay–Kitaev Approximations of Special Orthogonal Matrices |
| title_full_unstemmed | Solovay–Kitaev Approximations of Special Orthogonal Matrices |
| title_short | Solovay–Kitaev Approximations of Special Orthogonal Matrices |
| title_sort | solovay kitaev approximations of special orthogonal matrices |
| url | http://dx.doi.org/10.1155/2020/2530609 |
| work_keys_str_mv | AT anuradhamahasinghe solovaykitaevapproximationsofspecialorthogonalmatrices AT sachiththabandaranayake solovaykitaevapproximationsofspecialorthogonalmatrices AT kaushikadesilva solovaykitaevapproximationsofspecialorthogonalmatrices |