Quantum error correction codes play a central role in the realisation of fault-tolerant quantum computing. Chamon model is a 3D generalization of the toric code. The error correction computation on this model has not been explored so far. In this work, the Chamon model is turned to a non-CSS error correction code. Logical qubits are built by the construct of logical Pauli operators. The property of logical operators reveals the expressions of code distance. According to the topological properties of Chamon models, an error elimination algorithm is proposed. Based on the error elimination algorithm, we propose a global randomized error correction algorithm to decode Chamon models in every single-qubit depolarized channel. This decoding algorithm is improved by adding the pretreatment process, termed the probabilistic greedy local algorithm, which adapts to different kinds of high-dimensional models. The estimated threshold error rate for numerical experiment can be raised to $4.92\%$.

翻译：量子纠错码在实现容错量子计算中起着核心作用。Chamon模型是toric码的三维推广，目前尚未有研究探讨该模型上的纠错计算。本文将Chamon模型转化为非CSS纠错码，通过构造逻辑泡利算子构建逻辑量子比特，逻辑算子的性质揭示了码距离的表达式。根据Chamon模型的拓扑特性，提出了一种错误消除算法。基于该算法，我们提出了一种全局随机化纠错算法，用于在单量子比特退极化信道中对Chamon模型进行译码。通过添加预处理过程（称为概率贪婪局部算法）改进该译码算法，该预处理算法可适应不同类型的高维模型。数值实验估计的阈值错误率可提升至$4.92\%$。