发表机构
OptQC Corp.; RIKEN Center for Quantum Computing (RQC); Department of Applied Physics, Graduate School of Engineering, The University of Tokyo（OptQC公司; 理化学研究所量子计算中心; 东京大学工学研究科应用物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构造了一族恒定速率、稳定子权重亚对数增长的量子码，仅用横向和折叠横向门即可实现完整逻辑Clifford群，为低空间开销容错量子计算提供路径。
AI 中文摘要
低空间开销的容错量子计算不仅需要高码率的量子纠错码，还需要逻辑操作的空间高效实现。横向门和折叠横向门因其能限制错误传播且无需额外量子比特而颇具前景。然而，它们所支持的逻辑操作通常受限，核心挑战在于构造能够将完整的逻辑Clifford门集与优良码参数相结合的量子码。在本工作中，我们引入一族量子码，其具有渐近恒定的编码速率和亚对数增长的稳定子权重，同时仅通过横向门和折叠横向门即可支持整个逻辑Clifford群。我们的构造基于经典码，其码空间是其Tanner图自同构群的绝对不可约Steinberg模。取这些经典码的超图积，可得到量子码，其中所有逻辑Clifford操作均可由固定的横向门和折叠横向门集合合成。此外，稳定子权重的缓慢增长使得小规模实例具有较高的纠错性能。这些结果为利用横向门和折叠横向门实现低空间开销的容错量子计算提供了路径。
英文摘要
Low-space-overhead fault-tolerant quantum computation requires not only high-rate quantum error-correcting codes but also space-efficient implementations of logical operations. Transversal and fold-transversal gates are promising since they limit error propagation and require no additional qubits. However, the logical operations they enable are typically restricted, and a central challenge is to construct codes that combine a complete set of logical Clifford gates with favorable code parameters. In this work, we introduce a family of quantum codes with an asymptotically constant encoding rate and sublogarithmically growing stabilizer weight, while supporting the entire logical Clifford group using only transversal and fold-transversal gates. Our construction is based on classical codes whose code spaces are absolutely irreducible Steinberg modules of their Tanner-graph automorphism groups. Taking hypergraph products of these classical codes yields quantum codes for which all logical Clifford operations can be synthesized from a fixed set of transversal and fold-transversal gates. Moreover, the slow growth of the stabilizer weight enables a high error-correcting performance in small instances. These results provide a path toward fault-tolerant quantum computation with low space overhead using transversal and fold-transversal gates.
Comments27 pages including appendices, 2 figures
