Almost-linear time decoding algorithm for topological codes

Nicolas Delfosse, Naomi H. Nickerson · 2017 · Quantum 5, 595 (2021)

| 编号 QE250 | 主题 译码算法 | 链接 arXiv:1709.06218 |

摘要

摘要保留原文（英文）

摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。

We design a fast decoding algorithm for topological codes to correct for Pauli errors and erasure and combination of both errors and erasure. Our algorithm has a worst case complexity of O(n α(n)), where n is the number of physical qubits and α is the inverse of Ackermann’s function. We prove that our algorithm performs optimally for errors of weight up to (d-1)/2 and for loss of up to d-1 qubits. Numerically, we obtain a threshold of 9.9% for the 2d-toric code with perfect syndrome measurements and 2.6% with faulty measurements.

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