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

• URL: http://arxiv.org/abs/2103.08381v3
• Date: Wed, 1 Dec 2021 10:24:10 GMT
• Title: Non-Abelian statistics with mixed-boundary punctures on the toric code
• Authors: Asmae Benhemou, Jiannis K. Pachos, Dan E. Browne
• Abstract summary: We investigate the potential of having non-Abelian statistics from puncture defects on the toric code. An encoding with mixed-boundary punctures reproduces Ising fusion, and a logical Pauli-$X$ upon their braiding.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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