无泄漏检测单元的稳定子码量子比特丢失推断
Qubit Loss Inference with Stabilizer Codes without Leakage Detection Units
AI总结：
本文针对稳定子码量子比特丢失问题，提出无需泄漏检测单元的推断方法，通过推导可检测条件构建最小集合覆盖模型，经模拟验证其可降低逻辑错误率并减少时空开销。
AI中文摘要：
量子比特丢失是指量子比特的物理载体离开计算系统却未直接暴露该事件位置的情况，这类错误是光子、中性原子和囚禁离子等平台上容错量子计算的主要障碍。通常需借助泄漏检测单元（LDU）等额外硬件操作识别丢失位置，这会引入时空开销且自身可能成为错误源。本文研究是否可通过标准重复稳定子测量得到的校正子数据推断稳定子码上的量子比特丢失。在涉及丢失量子比特的门采用非纠缠模型的条件下，本文推导了一般稳定子码中丢失可检测的充分条件，该条件基于丢失量子比特的支撑被移除后稳定子校验之间反交换关系的出现。利用该条件，本文用观测到的非确定性校验集合构建了精确的丢失推断问题及其最大似然形式，随后将该问题松弛为最小集合覆盖问题并采用贪心启发式算法求解。本文通过囚禁离子和中性原子平台的电路级噪声模拟，在旋转表面码上评估了所得的推断和丢失校正协议：在近期硬件相关的低至中等丢失率区域，与带噪声LDU的基线相比，基于推断的自适应协议可降低逻辑错误率，同时需要更少的时空开销。
英文摘要：
Qubit loss occurs when the physical carrier of a qubit leaves the computational system without directly revealing the event's location. Such errors are a major obstacle to fault-tolerant quantum computation on platforms including photonic, neutral-atom, and trapped-ion systems. Loss locations are commonly identified using additional hardware operations such as leakage-detection units (LDUs), which introduce space-time overhead and may themselves become a source of error. We investigate whether qubit loss on stabilizer codes can instead be inferred from syndrome data obtained through standard repeated stabilizer measurements. Under a non-entangling model for gates involving a lost qubit, we derive a sufficient condition for loss detectability in general stabilizer codes. The condition is based on the emergence of anticommutation between stabilizer checks after their support on the lost qubits is removed. By using that condition, we formulate the exact loss-inference problem using the observed set of non-deterministic checks together with its maximum-likelihood formulation. We then relax the problem to the minimum set cover problem with a greedy heuristic algorithm. We evaluate the resulting inference and loss-correction protocols on the rotated surface code via circuit-level noise simulations for trapped-ion and neutral-atom platforms. On both platforms, inference-based and adaptive protocols reduce the logical error rate relative to a noisy-LDU baseline in the low-to-moderate loss-rate regime relevant to near-term hardware, while requiring fewer space-time overheads.
