A universal circuit set using the S3 quantum double

Abstract

One potential route toward fault-tolerant universal quantum computation is to use non-Abelian topological codes. In this work, we investigate how to achieve this goal with the quantum double model \({\mathcal{D}}({S}_{3})\). By embedding each on-site Hilbert space into a qubit-qutrit pair, we explicitly construct circuits for creating, moving, and locally measuring all non-trivial anyons. We also design a specialized anyon interferometer to remotely measure the total charge of well-separated anyons; this avoids fusion, which compromises fault tolerance. These protocols enable the implementation of a universal gate set proposed by Cui et al. and active correction of the circuit-level noise during computation. To further suppress errors, we encode each physical degree of freedom of \({\mathcal{D}}({S}_{3})\) into a novel error-correcting code, enabling fault-tolerant realization, at the logical level, of all gates in the anyon manipulation circuits. Our proposal offers a promising path to realize robust universal topological quantum computation in the NISQ era.