Fault-tolerant mixed boundary punctures on the toric code

TL;DR

This paper explores fault-tolerant non-Abelian anyon properties in mixed boundary punctures on the toric code, demonstrating robustness against noise and proposing a quantum information masking scheme.

Contribution

It extends the mixed boundary puncture model to include antisymmetric subspaces, showing fault-tolerance and non-Abelian statistics in both symmetric and antisymmetric subspaces.

Findings

Non-Abelian statistics supported in antisymmetric subspace

Fault-tolerance against collective noise demonstrated

Quantum information masking scheme validated

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.