High-rate qLDPC processors

Aditya Bhardwaj et al. · 2026 · arXiv (Cornell University)

| 编号 QE148 | 主题 qLDPC 码 | 链接 arXiv:2607.28795 |

摘要

摘要保留原文（英文）

摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。

Despite significant progress on quantum low-density parity-check (qLDPC) codes, building qLDPC processors that are high-rate, high-throughput, hardware-friendly, and fast-to-decode remains a challenge. We introduce mitten codes, a family of qLDPC processor codes of encoding rate $20%$ and check weight $9$, based on non-abelian groups. Their non-abelian structure evades distance bounds constraining abelian counterparts, allowing mitten codes to reach distance $18$ and beyond with just a few hundred data qubits. The logical operators of a mitten code are related by the group action, yielding a modular, low-overhead logical toolkit: full Clifford operations follow from bridging two reusable seed surgery gadgets or from a single fixed extractor. Furthermore, qLDPC processors based on mitten codes support high-rate surgery that executes many logical measurements in parallel, and parallel magic-state injection into all logical qubits at once. Under circuit-level noise, with our fast decoder, the $[![300,60,14]!]$ mitten code achieves, without extrapolation, a block logical error rate of ${\sim}10^{-11}$ per round at $0.1%$ physical error rate (PER), while the $[![ 975,195,\leq 24 ]\

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