四维Chamon码
The four-dimensional Chamon code
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中文总结 AI 辅助
本研究针对四维Chamon码，建立其代数结构与晶格的对应关系，明确其受限移动激发类型，揭示超平面对称性等结构特性，开发两层解码策略，解码精度优于BP-OSD。
中文摘要 AI 辅助
分形子模型因具有非常规基态简并度（GSD）和受限移动激发，作为量子存储器候选方案已受到广泛关注。本研究前期工作中提出的四维（4D）Chamon码，通过两个二维（2D）环面码的4D XYZ乘积构造而成，其GSD随系统尺寸指数增长，与三维（3D）Chamon码类似，表明它可视为3D Chamon码的4D推广。然而，4D Chamon码的激发特性尚未被深入研究，且仍缺乏高性能解码策略。本研究首先建立4D Chamon码的代数结构与4D晶格的对应关系，从而刻画量子比特和稳定子的几何分布；其次，证明4D Chamon码支持三类与3D Chamon码类似的受限移动激发，进一步支持其作为3D Chamon码4D推广的解释；最后，揭示两个与解码相关的结构特性：超平面对称性和投影诱导的2D环面码结构。通过利用这些特性，本研究开发了两层解码策略，将原始解码问题分解为多个独立且可并行的子问题。数值模拟显示，所提解码器的解码精度显著优于BP-OSD，证明将码的固有几何和代数结构融入解码器设计的益处。
英文摘要
Fracton models have attracted considerable interest as candidates for quantum memories because of their unconventional ground-state degeneracy (GSD) and restricted-mobility excitations. The four-dimensional (4D) Chamon code introduced in our previous work is constructed via the 4D XYZ product of two two-dimensional (2D) toric codes. Its GSD grows exponentially with the system size, similar to that of the three-dimensional (3D) Chamon code, suggesting that it may be regarded as a 4D generalization of the 3D Chamon code. However, the excitation properties of the 4D Chamon code have not been studied in depth, and a high-performance decoding strategy is still lacking. In this work, we first establish the correspondence between the algebraic structure of the 4D Chamon code and the 4D lattice, thereby characterizing the geometric distributions of qubits and stabilizers. Second, we show that the 4D Chamon code supports three types of restricted-mobility excitations analogous to those of the 3D Chamon code, further supporting its interpretation as a 4D generalization of the 3D Chamon code. Finally, we uncover two structural properties relevant to decoding: a hyperplane symmetry and a projection-induced 2D toric-code structure. By exploiting these properties, we develop a two-layer decoding strategy that decomposes the original decoding problem into multiple independent and parallelizable subproblems. Numerical simulations show that the proposed decoder substantially outperforms BP-OSD in decoding accuracy, demonstrating the benefit of incorporating the intrinsic geometric and algebraic structures of the code into decoder design.
