AI 中文总结
本文提出一种无需预先知晓结构、利用随机单量子比特测量学习稳定子码生成元的算法，推导了所需态数下界与成功概率界，该方法在qLDPC码上的态数随量子比特数呈多项式对数级缩放。
AI 中文摘要
高效表征量子纠错码是容错量子计算道路上的关键挑战，稳定子码作为这类码的核心类别，由一组稳定子生成元定义。本文提出一种算法，该算法利用随机单量子比特测量，从其码空间内N个稳定子态副本中学习任意稳定子码的稳定子生成元，无需预先知晓该码的结构，这也可用于验证设备是否实现了预期的码。我们推导了高概率恢复稳定子生成元所需N的下界，以及算法整体成功概率的界。当将该方法应用于量子低密度奇偶校验（qLDPC）码（实用容错架构的主要候选方案）时，所需的态数量随量子比特数n呈多项式对数级缩放。
英文摘要
Efficiently characterizing quantum error correcting codes is a key challenge on the path to fault-tolerant quantum computation. Stabilizer codes, a central class of such codes, are defined by a set of stabilizer generators. Here, we present an algorithm that uses random single-qubit measurements to learn the stabilizer generators of any stabilizer code from $N$ copies of stabilizer states in its codespace, requiring no prior knowledge of the code's structure. This also enables verification that a device implements its intended code. We derive a lower bound on $N$ needed to recover the stabilizer generators with high probability, together with a bound on the algorithm's overall probability of success. When applied to quantum low-density parity-check (qLDPC) codes, a leading candidate for practical fault-tolerant architectures, our approach requires a number of states that scales polylogarithmically with $n$, the number of qubits.
