Topological Quantum Compiling

Abstract

A method for compiling quantum algorithms into specific braiding patterns for non-Abelian quasiparticles described by the so-called Fibonacci anyon model is developed. The method is based on the observation that a universal set of quantum gates acting on qubits encoded using triplets of these quasiparticles can be built entirely out of three-stranded braids (three-braids). These three-braids can then be efficiently compiled and improved to any required accuracy using the Solovay-Kitaev algorithm.

20 pages, 20 figures, published version

References in corpus (1)

• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State

Cited by in corpus (5)

• Interferometry of non-Abelian Anyons
• Topological Quantum Computing with Read-Rezayi States
• Constructing Functional Braids for Low-Leakage Topological Quantum Computing
• Skein Theory and Topological Quantum Registers: Braiding Matrices and Topological Entanglement Entropy of Non-Abelian Quantum Hall States
• Topological Entropy of Quantum Hall States in Rotating Bose Gases