Exploiting Anyonic Behavior of Quasicrystals for Topological Quantum Computing

TL;DR

This paper demonstrates that quasicrystals exhibit anyonic behaviors suitable for topological quantum computing, establishing a link between Fibonacci anyons and quasicrystal tiling spaces for quantum information encoding.

Contribution

It introduces a novel correspondence between Fibonacci anyons and quasicrystal tiling spaces, proposing a new approach for topological quantum information processing.

Findings

Quasicrystals can host anyonic excitations relevant for quantum computing.

A correspondence between Fibonacci anyons and quasicrystal tilings is established.

Potential encoding schemes for topological quantum information are discussed.

Abstract

We show that quasicrystals exhibit anyonic behavior that can be used for topological quantum computing. In particular, we study a correspondence between the fusion Hilbert spaces of the simplest non-abelian anyon, the Fibonacci anyons, and the tiling spaces of a class of quasicrystals, which includes the one dimensional Fibonacci chain and the two dimensional Penrose tiling. A possible encoding on tiling spaces of topological quantum information processing is also discussed.