近日，美国加州大学圣芭芭拉分校Yimu Bao团队研究了局部退相干下Floquet码的相位。该项研究成果发表在2025年12月18日出版的《物理评论A》杂志上。

Floquet码是一种具有周期性演化逻辑空间的动态量子存储器。其核心特征在于，每个周期后该编码会呈现任意子自同构，从而引发每个逻辑态的非平凡演化。

研究组分析了局域退相干与完美测量条件下的Floquet码，并证明在低于退相干阈值时，该编码处于以任意子自同构为特征的鲁棒性相位中。他们首先推导了二维Floquet码在局域泡利退相干下最大似然译码器对应的三维统计力学模型。研究组识别出一类特殊的双量子比特泡利信道，在该信道作用下三维统计力学模型可解耦为二维模型，并获得了此类退相干通道的阈值。随后，研究组提出了一种在局域退相干存在时检测任意子自同构的方法。通过理论分析表明，该方法能有效区分重复综合征测量下的Floquet码与环面码，并在阈值处经历相变。

附：英文原文

Title: Phases of Floquet code under local decoherence

Author: Yuchen Tang, Yimu Bao

Issue&Volume: 2025/12/18

Abstract: Floquet code is a dynamical quantum memory with a periodically evolving logical space. As a defining feature, the code exhibits an anyon automorphism after each period, giving rise to a nontrivial evolution of each logical state. In this paper, we study the Floquet code under local decoherence and perfect measurements and demonstrate that, below the decoherence threshold, the code is in a robust phase characterized by the anyon automorphism. We first derive the three-dimensional (3D) statistical mechanics model for the maximum likelihood decoder of the two-dimensional (2D) Floquet code under local Pauli decoherence. We identify a class of two-qubit Pauli channels under which the 3D statistical mechanics model becomes decoupled 2D models and obtain the threshold for such decoherence channels. We then propose a diagnostic of the anyon automorphism in the presence of local decoherence. We analytically show that this diagnostic distinguishes the Floquet code from the toric code under repeated syndrome measurements and undergoes a phase transition at the threshold.

DOI: 10.1103/sylh-bb3w

Source: https://journals.aps.org/pra/abstract/10.1103/sylh-bb3w