Topological Quantum Computing with Read-Rezayi States

TL;DR

This paper develops an efficient method for constructing braids to perform universal quantum gates using Read-Rezayi fractional quantum Hall states, advancing topological quantum computing with non-Abelian anyons.

Contribution

It introduces a new prescription for braiding in Read-Rezayi states with k>2, extending previous work limited to k=3, and explains the complexity differences.

Findings

Provides a systematic way to find braids for universal gates

Extends previous results from Fibonacci to general Read-Rezayi states

Clarifies why certain states have simpler gate constructions

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 $k>2$, $k\neq4$. 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.