No ((n, k, d < 127)) code can violate the quantum Hamming bound
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866913194676584448 |
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| author | Dallas, Emanuel Andreadakis, Faidon Lidar, Daniel |
| author_facet | Dallas, Emanuel Andreadakis, Faidon Lidar, Daniel |
| contents | It is well-known that pure quantum error correcting codes (QECCs) are constrained by a quantum version of the Hamming bound. Whether impure codes also obey such a bound, however, remains a long-standing question with practical implications for the efficacy of QECCs. We employ a combination of previously derived bounds on QECCs to demonstrate that a subset of all codes must obey the quantum Hamming bound. Specifically, we combine an analytical bound due to Rains with a numerical bound due to Li and Xing to show that no ((n,k,d < 127)) code can violate the quantum Hamming bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_11800 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | No ((n, k, d < 127)) code can violate the quantum Hamming bound Dallas, Emanuel Andreadakis, Faidon Lidar, Daniel Quantum Physics It is well-known that pure quantum error correcting codes (QECCs) are constrained by a quantum version of the Hamming bound. Whether impure codes also obey such a bound, however, remains a long-standing question with practical implications for the efficacy of QECCs. We employ a combination of previously derived bounds on QECCs to demonstrate that a subset of all codes must obey the quantum Hamming bound. Specifically, we combine an analytical bound due to Rains with a numerical bound due to Li and Xing to show that no ((n,k,d < 127)) code can violate the quantum Hamming bound. |
| title | No ((n, k, d < 127)) code can violate the quantum Hamming bound |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2208.11800 |