Anyon computers with smaller groups

2003/06/30 by Carlos Mochon · 2 citations
Computer Science · Physics and Astronomy · #Anyon #Computability, Logic, AI Algorithms #Computer science #Parallel Computing and Optimization Techniques #Physics #Quantum Computing Algorithms and Architecture #Quantum mechanics #Topological quantum computer #quant-ph

paper · pdf · doi:10.1103/physreva.69.032306

published as Phys. Rev. A 69, 032306 (2004) · 28 pages, REVTeX 4 (minor corrections in v2)

openalex publication_date 2004/03/11 · arxiv created 2004/03/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Anyons obtained from a finite gauge theory have a computational power that depends on the symmetry group. The relationship between group structure and computational power is discussed in this paper. In particular, it is shown that anyons based on finite groups that are solvable but not nilpotent are capable of universal quantum computation. This extends previously published results to groups that are smaller and therefore more practical. Additionally, a new universal gate set is built out of an operation called a probabilistic projection, and a quasiuniversal leakage correction scheme is discussed.

Citations

• Discrete non-Abelian gauge theories in Josephson-junction arrays and quantum computation
• Fault-tolerant quantum computation by anyons
• Anyons from nonsolvable finite groups are sufficient for universal quantum computation
• Topological quantum computation
• Discrete gauge theories
• Bounded-width polynomial-size branching programs recognize exactly those languages in NC1
• Fault-tolerant quantum computation

Cited by

• Reconstructing non-Abelian braiding and fusion without anyon transport
• Universal gates from braiding and fusing anyons on quantum hardware