Three-Majorana Cotunneling Interferometer for Non-Abelian Braiding and Topological Quantum Gate Implementation

TL;DR

This paper introduces a minimal three-Majorana zero mode interferometer that enables non-Abelian braiding, implementing Clifford and non-Clifford gates for topological quantum computing through cotunneling interference and magnetic flux control.

Contribution

It presents a novel, minimal three-Majorana setup for braiding and quantum gate implementation, including non-Clifford gates, using cotunneling interference and flux tuning.

Findings

Demonstrates tunable coupling between MZMs via interference

Enables implementation of Clifford and non-Clifford gates

Provides a pathway for universal topological quantum computation

Abstract

We propose a novel scheme for performing Majorana zero mode (MZM) braiding utilizing cotunneling processes in a three-MZM system incorporating reference arms. This approach relies on the interference between cotunneling paths through the MZMs and reference arms, establishing an effective, tunable coupling between the MZMs. The strength and sign of this coupling can be manipulated via the reference arms and applied magnetic flux. Notably, the introduction of a half quantum flux reverses the coupling sign, enabling an echo-like protocol to eliminate dynamic phases during braiding. Our setup, requiring only three MZMs, represents a minimal platform for demonstrating non-Abelian braiding statistics. We demonstrate that this system facilitates the implementation of Clifford gates via braiding and, significantly, permits the realization of non-Clifford gates, such as the $T$ gate, by geometric phase, thereby offering a potential pathway towards universal topological quantum computation.