Single-shot preparation of hypergraph product codes via dimension jump
- URL: http://arxiv.org/abs/2410.05171v1
- Date: Mon, 7 Oct 2024 16:29:13 GMT
- Title: Single-shot preparation of hypergraph product codes via dimension jump
- Authors: Yifan Hong,
- Abstract summary: We present a protocol that prepares the codespace of constant-rate hypergraph product codes in constant depth with $O(sqrtn)$ spatial overhead.
We show that the protocol is robust even in the presence of measurement errors.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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.
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