一类基于码级联的渐近好量子码

拓扑容错量子纠错的级联方案

Concatenation Schemes for Topological Fault-tolerant Quantum Error Correction

本研究提出基于小型纠错/检错码与三维cluster态级联的拓扑容错量子纠错方案，通过容错态制备与解码将电路级错误转为擦除错误，最优经典码级联方案显著提升阈值、降低时空开销。

Partially Concatenated Calderbank-Shor-Steane Codes Achieving the Quantum Gilbert-Varshamov Bound Asymptotically

In this paper, we utilize a concatenation scheme to construct new families of quantum error correction codes achieving the quantum Gilbert-Varshamov (GV) bound asymptotically. We concatenate alternant codes with any linear code achieving the classical GV bound to construct Calderbank-Shor-Steane (CSS) codes. We show that the concatenated code can achieve the quantum GV bound asymptotically and can approach the Hashing bound for asymmetric Pauli channels. By combing Steane's enlargement construction of CSS codes, we derive a family of enlarged stabilizer codes achieving the quantum GV bound for…

带有横向非Clifford门的渐近优质量子码

Asymptotically Good Quantum Codes with Transversal Non-Clifford Gates

本研究构造了恒定素数幂维度下支持横向CCZ门、码维与码距随分组长度线性增长的渐近优质量子码，解决了此前需增大字母表规模的难题，推导出开销指数趋于0的魔态蒸馏协议，并给出两种参数不同的构造方案。

广义级联量子码

Generalized Concatenated Quantum Codes

我们引入了广义级联量子码的概念。这种推广的级联方法为构造好的量子码，包括稳定子码和非加性码提供了一种系统的方法。利用这种方法，我们构造了新的单错误校正非加性量子码的家庭，在二进制和非二进制的情况下，它不仅优于任何稳定剂码有限块长度，但也渐近实现量子汉明界限大块长度。

Good and asymptotically good quantum codes derived from algebraic geometry codes

In this paper we construct several new families of quantum codes with good and asymptotically good parameters. These new quantum codes are derived from (classical) algebraic geometry (AG) codes by applying the Calderbank-Shor-Steane (CSS) construction. Many of these codes have large minimum distances when compared with its code length and they have relatively small Singleton defect. For example, we construct a family [[46; 2(t_2 - t1); d]]_25 of quantum codes, where t_1, t_2 are positive integers such that 1 < t_1 < t_2 < 23 and d >= min {46 - 2t_2, 2t_1-2}, of length n = 46, with minimum dist…

渐近良好的二元三正交码与高层横向门

Asymptotically good binary triorthogonal codes and higher-level transversal gates

本文构造了从第三层起每层Clifford层级中支持对角横向门的渐近良好二元CSS码，首次得到渐近良好的二元三正交码族，并实现恒定开销的T态蒸馏。