Haar random codes attain the quantum Hamming bound, approximately
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915539551518720 |
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| author | Ma, Fermi Tan, Xinyu Wright, John |
| author_facet | Ma, Fermi Tan, Xinyu Wright, John |
| contents | We study the error correcting properties of Haar random codes, in which a $K$-dimensional code space $\boldsymbol{C} \subseteq \mathbb{C}^N$ is chosen at random from the Haar distribution. Our main result is that Haar random codes can approximately correct errors up to the quantum Hamming bound, meaning that a set of $m$ Pauli errors can be approximately corrected so long as $mK \ll N$. This is the strongest bound known for any family of quantum error correcting codes (QECs), and continues a line of work showing that approximate QECs can significantly outperform exact QECs [LNCY97, CGS05, BGG24]. Our proof relies on a recent matrix concentration result of Bandeira, Boedihardjo, and van Handel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07158 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Haar random codes attain the quantum Hamming bound, approximately Ma, Fermi Tan, Xinyu Wright, John Quantum Physics Information Theory We study the error correcting properties of Haar random codes, in which a $K$-dimensional code space $\boldsymbol{C} \subseteq \mathbb{C}^N$ is chosen at random from the Haar distribution. Our main result is that Haar random codes can approximately correct errors up to the quantum Hamming bound, meaning that a set of $m$ Pauli errors can be approximately corrected so long as $mK \ll N$. This is the strongest bound known for any family of quantum error correcting codes (QECs), and continues a line of work showing that approximate QECs can significantly outperform exact QECs [LNCY97, CGS05, BGG24]. Our proof relies on a recent matrix concentration result of Bandeira, Boedihardjo, and van Handel. |
| title | Haar random codes attain the quantum Hamming bound, approximately |
| topic | Quantum Physics Information Theory |
| url | https://arxiv.org/abs/2510.07158 |