Self-dual bivariate bicycle codes with transversal Clifford gates
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917193619341312 |
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| author | Liang, Zijian Chen, Yu-An |
| author_facet | Liang, Zijian Chen, Yu-An |
| contents | Bivariate bicycle codes are promising candidates for high-threshold, low-overhead fault-tolerant quantum memories. Meanwhile, color codes are the most prominent self-dual CSS codes, supporting transversal Clifford gates that have been demonstrated experimentally. In this work, we combine these advantages and introduce a broad family of self-dual bivariate bicycle codes. These codes achieve higher encoding rates than surface and color codes while admitting transversal CNOT, Hadamard, and $S$ gates. In particular, we enumerate weight-8 self-dual bivariate bicycle codes with up to $n \leq 200$ physical qubits, realized on twisted tori that enhance code distance and improve stabilizer locality. Representative examples include codes with parameters $[[n,k,d]]$: $[[16,4,4]]$, $[[40,6,6]]$, $[[56,6,8]]$, $[[64,8,8]]$, $[[120,8,12]]$, $[[152,6,16]]$, and $[[160,8,16]]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05211 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Self-dual bivariate bicycle codes with transversal Clifford gates Liang, Zijian Chen, Yu-An Quantum Physics Strongly Correlated Electrons Mathematical Physics Quantum Algebra Bivariate bicycle codes are promising candidates for high-threshold, low-overhead fault-tolerant quantum memories. Meanwhile, color codes are the most prominent self-dual CSS codes, supporting transversal Clifford gates that have been demonstrated experimentally. In this work, we combine these advantages and introduce a broad family of self-dual bivariate bicycle codes. These codes achieve higher encoding rates than surface and color codes while admitting transversal CNOT, Hadamard, and $S$ gates. In particular, we enumerate weight-8 self-dual bivariate bicycle codes with up to $n \leq 200$ physical qubits, realized on twisted tori that enhance code distance and improve stabilizer locality. Representative examples include codes with parameters $[[n,k,d]]$: $[[16,4,4]]$, $[[40,6,6]]$, $[[56,6,8]]$, $[[64,8,8]]$, $[[120,8,12]]$, $[[152,6,16]]$, and $[[160,8,16]]$. |
| title | Self-dual bivariate bicycle codes with transversal Clifford gates |
| topic | Quantum Physics Strongly Correlated Electrons Mathematical Physics Quantum Algebra |
| url | https://arxiv.org/abs/2510.05211 |