设计率为1/5、物理量子比特数低于1000的高性能量子LDPC码
Quantum LDPC codes with design rate 1/5 and good performance below 1000 physical qubits
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中文总结 AI 辅助
本文提出设计率1/5的高性能量子LDPC码，结合特定译码算法与适配电路，提升了恒定码率量子LDPC码在近期容错量子计算机中的实用性。
中文摘要 AI 辅助
恒定码率量子低密度奇偶校验（LDPC）码在渐近极限下可实现具有恒定空间开销的容错量子计算，但发现具备优异实际性能的有限长度码实例仍具挑战性。本文提出一类新的量子LDPC码，其设计率为1/5、校验重为9，在0.1%强度的无空闲电路级噪声下，结合GPU加速的Relay置信传播（Relay-BP）译码（平均延迟约1-2 ms），在数百个物理量子比特时即可接近每量子比特周期的teraquop存储机制，该机制适用于囚禁离子和中性原子处理器。该构造涉及设计率为1/2的经典LDPC码的平衡积，二者共享非阿贝尔群对称性ℤ_ℓ ⋊ ℤ_m，这对经典纠错可能具有独立研究价值。我们采用简单贪心调度器构建适配可重构原子阵列的症候提取电路，根据当前硬件规格，单轮重排时间约为30-60 ms，未来仍有较大改进空间。我们还构建了对群对称等变的逻辑泡利基，可显著压缩码手术的设计空间。这些结果共同推动了恒定码率量子LDPC码在近期容错量子计算机中的实用性。
英文摘要
Constant-rate quantum low-density parity-check (LDPC) codes promise fault-tolerant quantum computation with constant spatial overhead in the asymptotic limit. Nonetheless, discovering finite-length code instances with good practical performance remains challenging. We introduce a new family of quantum LDPC codes with design rate $1/5$ and check weight $9$ that approaches the teraquop memory regime per qubit-round with several hundred physical qubits, under idling-free circuit-level noise of strength $0.1\%$ and GPU-accelerated Relay-belief-propagation (Relay-BP) decoding with average latencies around 1-2 ms, a regime relevant to trapped-ion and neutral-atom processors. The construction involves the balanced product of classical LDPC codes with design rate $1/2$ that share non-abelian $\mathbb{Z}_\ell \rtimes \mathbb{Z}_m$ group symmetries, which may be of independent interest for classical error correction. We build syndrome extraction circuits tailored to reconfigurable atom arrays using a simple greedy scheduler, with single-round rearrangement times around 30-60 ms using present hardware specifications, and substantial room for future improvements. We also construct logical Pauli bases that are equivariant with respect to the group symmetry, which can significantly compress the design space for code surgery. Together, these results further advance the practicality of constant-rate quantum LDPC codes for near-term, fault-tolerant quantum computers.
