Majorana phase-gate based on the geometric phase

TL;DR

This paper explores how to implement a phase-gate in a Majorana-based qubit system using braiding of overlapping modes, highlighting the role of geometric phases and particle-hole symmetry in the process.

Contribution

It introduces a method for efficient phase-gate implementation via braiding in a Kitaev model with interactions, emphasizing the control of dynamical phases through symmetry.

Findings

Braiding of overlapping Majorana modes can realize phase-gates.

Particle-hole symmetry can eliminate dynamical phases during braiding.

The approach is applicable to systems described by the extended Kitaev model.

Abstract

We study dynamics of a single qubit encoded in two pairs of Majorana modes, whereby each pair is hosted on a trijunction described by the Kitaev model extended by many-body interactions. We demonstrated that the challenging phase-gate may be efficiently implemented via braiding of partially overlapping modes. Although such qubit acquires both geometric and dynamical phases during the braiding protocol, the latter phase may be eliminated if the Majorana modes are hosted by systems with appropriate particle-hole symmetry.