Exploiting Anyonic Behavior of Quasicrystals for Topological Quantum Computing

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.

References in corpus (8)

• Fractional statistics in anyon collisions
• Interacting anyons in topological quantum liquids: The golden chain
• A short introduction to Fibonacci anyon models
• Complete Band Gaps in 2D Photonic Quasicrystals
• Critical eigenstates and their properties in one and two dimensional quasicrystals
• Topological states in quasicrystals
• Majorana Zero-Energy Mode and Fractal Structure in Fibonacci-Kitaev Chain
• Character varieties and algebraic surfaces for the topology of quantum computing