Universal Quantum Computation with Metaplectic Anyons

Abstract

We show that braidings of the metaplectic anyons $X_{\epsilon }$ in $SO(3{)}_2=SU(2{)}_4$ with their total charge equal to the metaplectic mode $Y$ supplemented with measurements of the total charge of two metaplectic anyons are universal for quantum computation. We conjecture that similar universal computing models can be constructed for all metaplectic anyon systems $SO(p{)}_2$ for any odd prime $p\ge 5$. In order to prove universality, we find new conceptually appealing universal gate sets for qutrits and qupits.

To appear in Journal of Mathematical Physics

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• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Abelian and Non-Abelian States in $\nu =2/3$ Bilayer Fractional Quantum Hall Systems
• $SO(N{)}_2$ Braid group representations are Gaussian
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