Universal Quantum Computation with Metaplectic Anyons

TL;DR

This paper demonstrates that braiding and measuring metaplectic anyons in certain quantum systems can perform universal quantum computation, introducing new gate sets for qutrits and qupits.

Contribution

It establishes universality of braiding metaplectic anyons in $SO(3)_2$ and proposes similar models for all $SO(p)_2$ systems with odd primes.

Findings

Braiding of metaplectic anyons is universal for quantum computation.

New universal gate sets for qutrits and qupits are introduced.

Conjecture that all $SO(p)_2$ systems are similarly universal.

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 $p\geq 5$. In order to prove universality, we find new conceptually appealing universal gate sets for qutrits and qupits.