发表机构
Massachusetts Institute of Technology; Harvard University（麻省理工学院; 哈佛大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对超高码率量子LDPC码，利用群对称性和并行手术方法实现快速逻辑计算，通过链映射卷积降低开销，并展示在多个码上仅需2.5倍空间开销和3-4轮综合征提取，为高效容错量子架构提供新途径。
AI 中文摘要
量子低密度奇偶校验（qLDPC）码为减少容错量子计算的量子比特开销提供了一条有前景的途径，近期超高码率构造实现了高于二分之一的编码率。在这项工作中，我们为超高码率码开发了快速并行的逻辑计算方法。我们首先利用码的群对称性将逻辑量子比特划分为轨道，然后应用并行手术方法来实现群不变的逻辑泡利乘积测量集合。这些测量具有高度可编程性，因为只要每个测量在整个轨道（或多个轨道）上重复，我们就可以任意耦合逻辑轨道。为了减少空间和时间开销，我们开发了一种称为链映射卷积的技术，该技术利用群结构以高效方式提升我们协议的空间和时间距离。作为案例研究，我们为[[256, 68, 12]]和[[576, 148, 18]]对分区码以及一个[[1152, 580, 12]]的1/2码率码构建了保距离的并行测量装置，仅需约2.5倍空间开销和每次3-4轮综合征提取。相同方法还支持将培育的魔法态并行注入高码率码。最后，我们通过子群限制扩展了可编程性，揭示了逻辑控制与容错所需时空资源之间的权衡，并强调了结构化并行在减少开销中的关键作用。这些结果为设计低时空开销的qLDPC逻辑操作提供了新方法，为更高效的容错量子架构开辟了道路。
英文摘要
Quantum low-density parity-check (qLDPC) codes offer a promising route to reducing the qubit overhead of fault tolerance, with recent ultra-high-rate constructions achieving encoding rates above one half. In this work, we develop fast and parallel logical computation methods for ultra-high-rate codes. We first utilize the group symmetries of the codes to partition the logical qubits into orbits, and then apply parallel surgery methods to implement group-invariant collections of logical Pauli-product measurements. These measurements are highly programmable, as we may arbitrarily couple logical orbits as long as each measurement is repeated across the whole orbit(s). To reduce the space and time overheads, we develop a technique called chain-map convolution, which uses the group structure to boost both the spatial and temporal distances of our protocol in a highly efficient manner. As case studies, we construct distance-preserving parallel measurement gadgets for the [[256, 68, 12]], [[576, 148, 18]] pair-partition codes, and a [[1152, 580, 12]] rate-$1/2$ code, with only around $2.5\times$ space overhead and 3-4 rounds of syndrome extraction each. The same methods also enable parallel injection of cultivated magic states into high-rate codes. Finally, we extend programmability through subgroup restrictions, revealing a tradeoff between logical control and the spacetime resources required for fault tolerance and highlighting the crucial role structured parallelism plays in reducing overhead. These results provide new methods for designing qLDPC logical operations with low spacetime overhead, opening a route toward more efficient fault-tolerant quantum architectures.
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