Non-Abelian statistics with mixed-boundary punctures on the toric code
Quantum Physics
2022-04-19 v3
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- 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.
Cite
@article{arxiv.2103.08381,
title = {Non-Abelian statistics with mixed-boundary punctures on the toric code},
author = {Asmae Benhemou and Jiannis K. Pachos and Dan E. Browne},
journal= {arXiv preprint arXiv:2103.08381},
year = {2022}
}