Quantum memory error correction computation based on Chamon model

TL;DR

This paper develops a novel error correction algorithm for the 3D Chamon quantum model, achieving a high threshold error rate of 4.92% for fault-tolerant quantum computing.

Contribution

It introduces a non-CSS error correction code based on the Chamon model and proposes a global randomized decoding algorithm with improvements for high-dimensional quantum error correction.

Findings

Achieved an estimated threshold error rate of 4.92%.

Developed a probabilistic greedy local decoding algorithm.

Extended error correction techniques to non-CSS codes in 3D models.

Abstract

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 $4.92\%$.