Fusion rules and vortices in $p_x+ip_y$ superconductors

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.