Fault-tolerant mixed boundary punctures on the toric code

Yao Shen; Fu-Lin Zhang

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arXiv · 2508.11230

Fault-tolerant mixed boundary punctures on the toric code

Yao Shen·Fu-Lin Zhang

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Abstract

Defects on the toric code, a well-known exactly solvable Abelian anyon model, can exhibit non-Abelian statistical properties, which can be classified into punctures and twists. Benhemou et al.[Phys. Rev. A. 105, 042417 (2022)] introduced a mixed boundary puncture model that integrates the advantages of both punctures and twists. They proposed that non-Abelian properties could be realized in the symmetric subspace {$|++\rangle$, $|--\rangle$}. This work demonstrates that the nontrivial antisymmetric subspace{$|+-\rangle$, $|-+\rangle$} also supports non-Abelian statistics. The mixed boundary puncture model is shown to be fault-tolerant in both subspaces, offering resistance to collective dephasing noise and collective rotation noise. In addition, we propose and validate a quantum information masking scheme within the three-partite mixed boundary puncture model.

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Yao Shen, Fu-Lin Zhang. 2025-08-15. Fault-tolerant mixed boundary punctures on the toric code. https://arxiv.org/abs/2508.11230

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