Demonstration of magic state power of $\mathbf{D}(\mathbf{S}_{3})$ anyons with two qudits

TL;DR

This paper demonstrates that $ ext{D}(S_3)$ non-Abelian anyons in a 6-level qudit lattice can generate universal quantum gates through braiding and fusion, using minimal control and encoding in just two qudits.

Contribution

It introduces a minimal, scalable protocol for realizing universal quantum computation with $ ext{D}(S_3)$ anyons using only creation and measurement operators.

Findings

$ ext{D}(S_3)$ anyons can produce magic states for universal quantum computation.

The scheme is encoded in just two qudits, making it scalable and practical.

The protocol requires no additional dynamical control beyond creation and measurement.

Abstract

We consider a lattice of $d=6$ qudits that supports $\mathbf{D}(\mathbf{S}_3)$ non-Abelian anyons. We present a method for implementing both braiding and fusion evolutions using only the operators that create and measure anyons, without requiring additional dynamical control. This provides a minimal protocol demonstrating that $\mathbf{D}(\mathbf{S}_3)$ anyons can generate magic states, thereby establishing their universality for quantum computation. Furthermore, we show that the entire scheme can be encoded in just two qudits, offering a compact blueprint that is inherently scalable and readily implementable in current quantum platforms.