Anyons from nonsolvable finite groups are sufficient for universal quantum computation

2002/06/30 by Carlos Mochon · 8 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum and electron transport phenomena #Quantum many-body systems #quant-ph

paper · pdf · doi:10.1103/physreva.67.022315

published as Phys. Rev. A 67, 022315 (2003) · 17 pages, REVTeX 4 (minor changes in v2, added motivation for leakage correction)

openalex publication_date 2003/02/28 · arxiv created 2003/03/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a constructive proof that anyonic magnetic charges with fluxes in a nonsolvable finite group can perform universal quantum computations. The gates are built out of the elementary operations of braiding, fusion, and vacuum pair creation, supplemented by a reservoir of ancillas of known flux. Procedures for building the ancilla reservoir and for correcting leakage are also described. Finally, a universal qudit gate set, which is ideally suited for anyons, is presented. The gate set consists of classical computation supplemented by measurements of the X operator.

Citations

• Both Toffoli and Controlled-NOT need little help to do universal quantum computation
• Fault-tolerant quantum computation by anyons
• Discrete gauge theories
• Quantum computation with abelian anyons

Cited by

• Towards Topological Quantum Computation? - Knotting and Fusing Flux\n Tubes
• Reconstructing non-Abelian braiding and fusion without anyon transport
• Non-Abelian Chern–Simons models with discrete gauge groups on a lattice
• Exact solution of Z₂ Chern-Simons model on a triangular lattice
• Measuring topological order
• Topological Quantum Computing with Only One Mobile Quasiparticle
• Anyon computers with smaller groups
• Universal gates from braiding and fusing anyons on quantum hardware