Topological quantum compiling

2006/10/31 by Layla Hormozi, L. Hormozi, G. Zikos +4 · 4 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum and electron transport phenomena #cond-mat.mes-hall #quant-ph

paper · pdf · doi:10.1103/physrevb.75.165310

published as Phys. Rev. B 75, 165310 (2007) · 20 pages, 20 figures, published version

openalex publication_date 2007/04/11 · arxiv created 2007/04/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• String-net condensation: A physical mechanism for topological phases
• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Nonabelions in the fractional quantum hall effect
• Classical and quantum conformal field theory

Cited by

• Skein theory and topological quantum registers: Braiding matrices and topological entanglement entropy of non-Abelian quantum Hall states
• Topological Quantum Computing with Read-Rezayi States
• From Luttinger liquid to non-Abelian quantum Hall states
• Systematically generated two-qubit anyon braids