Topological Quantum Computing with Read-Rezayi States

Abstract

Read-Rezayi fractional quantum Hall states are among the prime candidates for realizing non-Abelian anyons which in principle can be used for topological quantum computation. We present a prescription for efficiently finding braids which can be used to carry out a universal set of quantum gates on encoded qubits based on anyons of the Read-Rezayi states with $k>2$, $k\ne 4$. This work extends previous results which only applied to the case $k=3$ (Fibonacci) and clarifies why in that case gate constructions are simpler than for a generic Read-Rezayi state.

5 pages, 3 figures

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