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arXiv · 2103.08381

Non-Abelian statistics with mixed-boundary punctures on the toric code

Asmae Benhemou·Jiannis K. Pachos·Dan E. Browne
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Abstract

The toric code is a simple and exactly solvable example of topological order realising Abelian anyons. However, it was shown to support non-local lattice defects, namely twists, which exhibit non-Abelian anyonic behaviour [1]. Motivated by this result, we investigated the potential of having non-Abelian statistics from puncture defects on the toric code. We demonstrate that an encoding with mixed-boundary punctures reproduces Ising fusion, and a logical Pauli-$X$ upon their braiding. Our construction paves the way for local lattice defects to exhibit non-Abelian properties that can be employed for quantum information tasks.

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Asmae Benhemou, Jiannis K. Pachos, Dan E. Browne. 2021-03-15. Non-Abelian statistics with mixed-boundary punctures on the toric code. https://doi.org/10.1103/physreva.105.042417

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