Single-shot preparation of hypergraph product codes via dimension jump
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914079266832384 |
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| author | Hong, Yifan |
| author_facet | Hong, Yifan |
| contents | Quantum error correction is a fundamental primitive of fault-tolerant quantum computing. But in order for error correction to proceed, one must first prepare the codespace of the underlying error-correcting code. A popular method for encoding quantum low-density parity-check codes is transversal initialization, where one begins in a product state and measures a set of stabilizer generators. In the presence of measurement errors however, this procedure is generically not fault-tolerant, and so one typically needs to repeat the measurements many times, resulting in a deep initialization circuit. We present a protocol that prepares the codespace of constant-rate hypergraph product codes in constant depth with $O(\sqrt{n})$ spatial overhead, and we show that the protocol is robust even in the presence of measurement errors. Our construction is inspired by dimension-jumping in topological codes and leverages two properties that arise from the homological product of codes. We provide some improvements to lower the spatial overhead and discuss applications to fault-tolerant architectures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05171 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Single-shot preparation of hypergraph product codes via dimension jump Hong, Yifan Quantum Physics Quantum error correction is a fundamental primitive of fault-tolerant quantum computing. But in order for error correction to proceed, one must first prepare the codespace of the underlying error-correcting code. A popular method for encoding quantum low-density parity-check codes is transversal initialization, where one begins in a product state and measures a set of stabilizer generators. In the presence of measurement errors however, this procedure is generically not fault-tolerant, and so one typically needs to repeat the measurements many times, resulting in a deep initialization circuit. We present a protocol that prepares the codespace of constant-rate hypergraph product codes in constant depth with $O(\sqrt{n})$ spatial overhead, and we show that the protocol is robust even in the presence of measurement errors. Our construction is inspired by dimension-jumping in topological codes and leverages two properties that arise from the homological product of codes. We provide some improvements to lower the spatial overhead and discuss applications to fault-tolerant architectures. |
| title | Single-shot preparation of hypergraph product codes via dimension jump |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2410.05171 |