发表机构
Joint Center for Quantum Information and Computer Science, University of Maryland; Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS); Yau Mathematical Sciences Center, Tsinghua University（量子信息与计算机科学联合中心，马里兰大学; 上海数学与交叉学科研究院; 清华大学丘成桐数学科学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出统一代数理论，通过时空链复形统一多种量子容错表述，连接时空距离与小工具正确性，并涵盖多种故障模型及已知容错构造。
AI 中文摘要
我们提出了Clifford时空量子容错的一个统一代数理论，该理论支撑通用容错量子计算。我们从电路的张量网络表示构造了一个时空链复形，该复形通过相关的规范与稳定子结构编码了故障传播、探测器综合征和逻辑操作。我们证明该理论（1）统一了量子容错的各种表述，包括时空码、Gottesman的小工具框架、故障复形和ZX演算；（2）将时空距离与Gottesman形式体系中小工具级别的正确性属性联系起来；（3）自然地容纳一系列故障模型，特别是现象学和电路级模型，通过不同的张量分解和故障分配将这些通常分别表述的描述带入一个共同的代数框架；（4）将许多已知的容错构造和结果作为特例恢复，包括重复综合征提取、横向和折叠横向门的关联探测器、Steane型和Knill型综合征提取小工具以及单发纠错。
英文摘要
We present a unified algebraic theory of Clifford spacetime quantum fault tolerance, which underpins universal fault-tolerant quantum computation. We construct a spacetime chain complex from a tensor network representation of a circuit that encodes fault propagation, detector syndromes, and logical actions through the associated gauge and stabilizer structure. We show that this theory (1) unifies various formulations of quantum fault tolerance including spacetime codes, Gottesman's gadget framework, fault complexes, and ZX calculus; (2) connects spacetime distances to the gadget-level correctness properties in Gottesman's formalism; (3) naturally accommodates a range of fault models, in particular phenomenological and circuit-level models, bringing these often separately formulated descriptions into a common algebraic framework through different tensor decompositions and fault assignments; and (4) recovers many known fault tolerance constructions and results as special cases, including repeated syndrome extraction, correlated detectors for transversal and fold-transversal gates, Steane- and Knill-type syndrome extraction gadgets, and single-shot error correction.
Comments30 pages, 8 figures
