Universal quantum computing with parafermions assisted by a half fluxon

TL;DR

This paper introduces a robust method for implementing non-Clifford gates in parafermionic quantum computing using the Aharonov-Casher effect, enabling universal quantum computation without magic state distillation.

Contribution

It proposes a novel scheme to perform non-Clifford gates via braiding a half fluxon around parafermionic zero modes, enhancing the capabilities of parafermion-based quantum computing.

Findings

The scheme enables universal quantum computing with parafermions.

A practical setup using existing proposals for realization.

The method avoids the need for magic state distillation.

Abstract

Braiding of anyons such as Majoranas or parafermions provides only Clifford gates which do not form a universal set of quantum gates. We propose a robust and resource-efficient scheme to perform a non-Clifford gate on a logical qudit encoded in parafermionic zero modes via the Aharonov-Casher effect. This gate can be implemented by moving a half flux quantum around the pair of parafermionic zero modes. The parafermion modes can be realized in a two-dimensional set-up using existing proposals and a half fluxon carrying half flux quantum can be created as a part of a half fluxon/anti-half fluxon pair in a spin-triplet Josephson junction with a dipole defect. With an appropriate bias current pulse, the half fluxon can be braided around the parafermions. Supplementing this gate with the braiding of parafermions provides the avenue for universal quantum computing with parafermions without magic state distillation.