Single-Shot Decoding and Fault-tolerant Gates with Trivariate Tricycle Codes
中文速览 本文介绍了一类名为“三变量三轮车”（Trivariate Tricycle, TT）码的新型量子低密度奇偶校验码（qLDPC）。该构造方法推广了现有的双变量双轮车码，通过使用基于三个三变量多项式的长度为3的链复形来定义CSS码。这种代数结构天然地赋予了TT码一系列优越特性：首先，它们存在“元校验”（meta-check），使得在Z基下能够实现单次解码（single-shot decoding），从而显著降低解码的时间开销。其次，数值搜索发现了参数远超三维环面码（3D Toric Code）的实例，在同等逻辑比特数和码距下，数据比特开销最多可减少48倍。此外，所有TT码都拥有一组丰富的容错逻辑门，包括码块内部的移位自同构和码块之间的横向CZ门。最重要的是，通过选择特定的多项式（如权重为2的多项式），该构造可以实现常数深度的逻辑CCZ门，这是实现通用容错量子计算的关键。总而言之，TT码提供了一个统一的框架，将高编码率、高效解码和丰富的逻辑门操作等多种理想特性结合在一起，为构建实用化的容错量子计算机提供了有力的候选方案。 English Research Briefing Research Briefing: Single-Shot Decoding and Fault-tolerant Gates with Trivariate Tricycle Codes 1. The Core Contribution This paper introduces Trivariate Tricycle (TT) codes, a new family of quantum Low-Density Parity Check (qLDPC) codes that systematically combine multiple highly desirable features for fault-tolerant quantum computing. The central thesis is that by generalizing the algebraic construction of previous qLDPC codes into a three-dimensional framework based on trivariate polynomials, it is possible to create codes that simultaneously possess high thresholds, partial single-shot decodability, a rich set of transversal Clifford gates, and, for certain sub-constructions, constant-depth non-Clifford CCZ gates. The primary conclusion is that this unified construction yields codes with significantly lower qubit overheads than established benchmarks like the 3D Toric Code, presenting a powerful new avenue for designing efficient and practical quantum computer architectures. ...