最优时空代价下的单次纠错
Single-Shot Error Correction at Optimal Spacetime Cost
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中文总结 AI 辅助
本文提出一种显式含噪纠错电路，利用量子Tanner码在最优时空代价下实现单次纠错，仅增加对数开销，适用于一般电路噪声，并扩展到恒定深度逻辑Clifford操作。
中文摘要 AI 辅助
近期工作表明，对于独立擦除，存储 $K$ 个逻辑量子比特 $S$ 个时间步长且误差至多 $\u03b5$ 需要 $\Omega(S(K+\log(S/\u03b5)))$ 的时空代价。相应的构造也已给出，但假设理想纠错。本文表明，在硬件支持长程量子比特连接和快速可靠的经典处理的前提下，通过显式的含噪纠错电路和高效解码，并计入所有态制备、门、测量和等待位置，可实现相同的缩放。因此，可靠性仅增加所有存储量子比特共享的对数开销。该构造适用于足够弱但一般的电路噪声，包括综合征提取期间的故障和相关故障，对于独立擦除，其与已知最佳下界在常数因子内匹配。我们利用量子 Tanner 码实现此缩放，每个存储步包含一轮综合征提取，随后进行固定数量的并行经典解码器步骤，以将残余误差降低到足以使后续故障可纠正，无论存储器大小、存储时间或目标精度如何。这共同实现了每步指数级小的失败概率，同时保持每个存储步的代价与码大小成线性。同样的分析也扩展到某些恒定深度的逻辑 Clifford 操作。
英文摘要
Recent work established that, for independent erasures, storing $K$ logical qubits for $S$ time steps with error at most $\varepsilon$ requires a spacetime cost of $Ω(S(K+\log(S/\varepsilon)))$. A matching construction was also given, but assumes ideal error correction. Here we show that the same scaling can be achieved with an explicit noisy error-correction circuit and efficient decoding, counting all state-preparation, gate, measurement, and wait locations, provided that the hardware supports long-range qubit connectivity and fast, reliable classical processing. Thus, reliability adds only a logarithmic overhead shared by all stored qubits. The construction works for sufficiently weak but otherwise general circuit noise, including faults during syndrome extraction and correlated faults, and for independent erasures it matches the best known lower bound up to constant factors. We attain this scaling using quantum Tanner codes, with each memory step consisting of one round of syndrome extraction followed by a fixed number of parallel classical decoder steps that reduce the residual error enough to keep later faults correctable, regardless of memory size, storage time, or target accuracy. Together, this gives exponentially small failure probability per step while keeping the cost of each memory step linear in the code size. The same analysis also extends to certain constant-depth logical Clifford operations.
发表机构
- QuICS, NIST/University of Maryland（量子信息与计算科学研究所，美国国家标准与技术研究院/马里兰大学）
- UMIACS, University of Maryland（计算机与信息系统联合学院，马里兰大学）
- IonQ Inc.（IonQ公司）
- Quantum Research Center, Technology Innovation Institute（量子研究中心，技术创新研究所）
- Institute of Advanced Intelligence and Computing, A*STAR（先进智能与计算研究所，新加坡科技研究局）
- Centre for Quantum Technologies, National University of Singapore（量子技术中心，新加坡国立大学）
- Nanyang Quantum Hub, Nanyang Technological University（南洋量子枢纽，南洋理工大学）
机构由 AI 辅助整理，请以论文原文为准。
