稳定子码中通过单量子比特测量实现逻辑信息定位
Logical information localisation in stabiliser codes via single-qubit measurements
- QuSoft and CWI（QuSoft和CWI）
- QuTech, TU Delft（QuTech，代尔夫特理工大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文提出稳定子路径寻找（SPF）及其推广$g$-SPF，用于在稳定子码中通过单量子比特测量定位逻辑信息，证明表面码存在定位阈值，并给出精确与启发式两种高效算法，显著降低求解时间，支持容错通信应用。
中文摘要 AI 辅助
稳定子路径寻找（SPF）此前已被引入作为一种方法，用于在经历丢失的稳定子码中，通过仅一轮单量子比特测量，将逻辑信息定位到单个预先指定的目标量子比特上。当使用有限资源和飞行量子比特时，这种逻辑信息的快速读出是容错通信的有用工具。在本工作中，我们提供了通过SPF进行定位的广泛分析和计算研究。我们引入了$g$-SPF，其任务是将逻辑信息定位到至多$g$个未指定目标量子比特的集合上。通过基于渗流理论和稳定子码不相交性的分析论证，我们证明对于独立同分布（i.i.d.）的量子比特丢失，丢失概率$p<1/2$且平面表面码足够大时，对于常数$g$，通过$g$-SPF进行定位的成功概率趋近于1，这确立了定位阈值。此外，我们提出并实现了两种求解SPF的算法。第一种是精确的，将SPF表述为整数线性规划；第二种是启发式的，将SPF表述为解码问题。我们通过数值重现表面码的定位阈值来验证这两种算法，并证明启发式算法明显更快。与当前最先进的算法相比，我们的工作显著减少了求解SPF所需的时间，使我们能够研究比文献中先前考虑的更大的稳定子码中的定位。这些理论和计算结果共同为各种应用打开了大门，例如容错隐形传态和高效逻辑融合。
英文摘要
Stabiliser path finding (SPF) has previously been introduced as a method to localise logical information in a stabiliser code undergoing loss onto a single pre-specified target qubit, using only one round of single-qubit measurements. When working with limited resources and flying qubits, this fast read-out of logical information is a helpful tool for fault-tolerant communication. In this work, we provide a broad analytical and computational study of localisation via SPF. We introduce $g$-SPF, where the task is to localise the logical information onto a set of at most $g$ unspecified target qubits. Through analytical arguments based on percolation theory and the disjointness of stabiliser codes, we prove that for i.i.d. qubit loss with probability $p<1/2$ and sufficiently large planar surface codes, localisation via $g$-SPF for constant $g$ succeeds with a probability converging to one, which establishes a localisation threshold. Furthermore, we propose and implement two algorithms to solve SPF. The first is exact and formulates SPF as an integer linear program, whereas the second is heuristic and formulates SPF as a decoding problem. We validate both algorithms by numerically reproducing the localisation threshold for the surface code and demonstrate that the heuristic algorithm is considerably faster. Our work significantly reduces the time required to solve SPF compared to current state-of-the-art algorithms, allowing us to study localisation in substantially larger stabiliser codes than previously considered in the literature. Together, these theoretical and computational results open the door to various applications, such as fault-tolerant teleportation and efficient logical fusion.
