发表机构
School of Engineering and Applied Sciences, Harvard University; Department of Physics, Harvard University（哈佛大学工程与应用科学学院; 哈佛大学物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究建立自校准量子容错理论框架，利用错码测量实现高效在线优化，其收敛率与量子LDPC码的码距无关，经模拟证实该范式可同时保护逻辑信息并稳定硬件。
AI 中文摘要
量子纠错仅当所有物理操作均低于容错阈值时才能保护逻辑信息，该条件必须持续维持而非仅在初始校准时满足。然而实际中，模拟控制参数会因环境波动不可避免地发生漂移。由于未来容错量子计算预计将运行数天甚至数月，中断计算进行重复校准在根本上是不切实际的。一个有前景的替代方案是将校准直接整合到计算中，将错码测量重新用作校准信号（Sivak等人，《自然》2026年），但这种自校准能否以可证明的效率实现仍是一个悬而未决的问题。在此，我们建立了自校准量子容错的理论框架。我们证明，对于一大类由控制引起的误差，检测率以高概率构成模拟校准的局部强凸代理目标。该几何特性仅利用正常纠错期间收集的错码测量即可实现高效在线优化。我们证明，对于与时间无关的漂移，在O(1/ε²)个周期内可收敛至ε检测率，同时也为与时间相关的漂移建立了保证。我们进一步表明，对于量子低密度奇偶校验（LDPC）码，收敛率与码距无关。中性原子阵列的脉冲级模拟以及大规模电路级Clifford模拟均证实了这些理论预测。我们的结果确立了自校准容错作为一种可证明高效的范式，其中相同的错码测量同时保护逻辑信息并稳定底层硬件。
英文摘要
Quantum error correction protects logical information only when every physical operation remains below the fault-tolerance threshold, a condition that must be maintained continuously rather than only at the initial calibration. In practice, however, analog control parameters inevitably drift because of environmental fluctuations. As future fault-tolerant quantum computations are expected to run for days or even months, interrupting computation for repeated recalibration becomes fundamentally impractical. A promising alternative is to integrate calibration directly into computation by repurposing syndrome measurements as a calibration signal (Sivak et al, Nature 2026), but whether such self-calibration can be achieved with provable efficiency remains an open question. Here we establish a theoretical framework for such self-calibrating quantum fault tolerance. We prove that, for a broad class of control-induced errors, the detection rate defines a locally strongly convex surrogate objective for analog calibration with high probability. This geometric property enables a simple and efficient online optimization algorithm using only syndrome measurements collected during normal error correction. We prove convergence to an $\varepsilon$ detection rate within $O(1/\varepsilon^2)$ epochs for time-independent drifts and also establish guarantees for time-dependent drifts. We further show that the convergence rate is independent of the code distance for quantum low-density parity-check (LDPC) codes. Pulse-level simulations of neutral-atom arrays and large-scale circuit-level Clifford simulations confirm these theoretical predictions. Our results establish self-calibrating fault tolerance as a provably efficient paradigm in which the same syndrome measurements simultaneously protect logical information and stabilize the underlying hardware.
Comments65 pages, 12 figures
