Engineering complex topological memories from simple Abelian models

TL;DR

This paper demonstrates how complex topological quantum memories inspired by non-Abelian anyons can be engineered using simpler Abelian models, facilitating experimental realization for quantum computation.

Contribution

It introduces methods to create complex topological memories from Abelian models, bridging the gap between theoretical non-Abelian anyon systems and practical Abelian implementations.

Findings

Control procedures for encoding quantum information are explicitly demonstrated.

Lattice models suitable for laboratory implementation are identified.

The approach enhances the feasibility of topological quantum computation.

Abstract

In three spatial dimensions, particles are limited to either bosonic or fermionic statistics. Two-dimensional systems, on the other hand, can support anyonic quasiparticles exhibiting richer statistical behaviours. An exciting proposal for quantum computation is to employ anyonic statistics to manipulate information. Since such statistical evolutions depend only on topological characteristics, the resulting computation is intrinsically resilient to errors. So-called non-Abelian anyons are most promising for quantum computation, but their physical realization may prove to be complex. Abelian anyons, however, are easier to understand theoretically and realize experimentally. Here we show that complex topological memories inspired by non-Abelian anyons can be engineered in Abelian models. We explicitly demonstrate the control procedures for the encoding and manipulation of quantum information in specific lattice models that can be implemented in the laboratory. This bridges the gap between requirements for anyonic quantum computation and the potential of state-of-the-art technology.