Universal quantum computation with metaplectic anyons

2014/05/31 by Shawn X. Cui, Zhenghan Wang · 104 citations
Computer Science · Mathematics · Physics and Astronomy · #Anyon #Charge (physics) #Computation #Conjecture #Order (exchange) #Prime (order theory) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum computer #Quantum many-body systems #Topological quantum computer #cond-mat.other #math.QA #msc:57R56 #msc:81P68 #quant-ph

paper · pdf · doi:10.1063/1.4914941

published in Journal of Mathematical Physics 56(3) (American Institute of Physics) · To appear in Journal of Mathematical Physics

openalex publication_date 2015/03/01 · arxiv created 2015/03/15 · arxiv updated 2015/11/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We show that braidings of the metaplectic anyons Xϵ in SO(3)2 = SU(2)4 with their total charge equal to the metaplectic mode Y supplemented with projective measurements of the total charge of two metaplectic anyons are universal for quantum computation. We conjecture that similar universal anyonic computing models can be constructed for all metaplectic anyon systems SO(p)2 for any odd prime p ≥ 5. In order to prove universality, we find new conceptually appealing universal gate sets for qutrits and qupits.

Citations

• Interferometry versus projective measurement of anyons
• Quantum computations: algorithms and error correction
• A Modular Functor Which is Universal¶for Quantum Computation

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