Fusion rules and vortices in $p_x+ip_y$ superconductors

TL;DR

This paper explores the fusion rules of vortices in $p_x+ip_y$ superconductors and discusses how these rules enable reading out topologically protected quantum information, with implications for quantum computing.

Contribution

It explains how vortex fusion in $p_x+ip_y$ superconductors can be used to access topologically protected quantum states, advancing understanding of their potential for quantum computation.

Findings

Fusion rules match Ising anyon model

Vortex-antivortex fusion encodes quantum information

Potential application to topological quantum computing

Abstract

The "half-quantum" vortices ($\sigma$) and quasiparticles ($\psi$) in a two-dimensional $p_x+ip_y$ superconductor obey the Ising-like fusion rules $\psi\times \psi=1$, $\sigma\times \psi=\sigma$, and $\sigma\times \sigma= 1+\psi$. We explain how the physical fusion of vortex-antivortex pairs allows us to use these rules to read out the information encoded in the topologically protected space of degenerate ground states. We comment on the potential applicability of this fact to quantum computation. Modified 11/30/05 to reflect manuscript as accepted for publication. Includes corrected last section.