# Braiding errors in interacting Majorana quantum wires

## TL;DR

This paper investigates braiding errors in Majorana bound states within Kitaev wires, highlighting how non-adiabaticity, hybridization, and interactions influence the fidelity and phase accuracy of braiding operations.

## Contribution

It provides a detailed numerical analysis of braiding errors considering the full quasi-particle background and interaction effects, advancing understanding of topological quantum computation.

## Key findings

- Fidelity loss mainly due to incomplete adiabaticity and MBS hybridization.
- Explicit braiding phase extraction reveals breakdown of independent-particle picture.
- Nearest-neighbor interactions can improve or impair braiding depending on their sign and strength.

## Abstract

Avenues of Majorana bound states (MBSs) have become one of the primary directions towards a possible realization of topological quantum computation. For a Y-junction of Kitaev quantum wires, we numerically investigate the braiding of MBSs while considering the full quasi-particle background. The two central sources of braiding errors are found to be the fidelity loss due to the incomplete adiabaticity of the braiding operation as well as the hybridization of the MBS. The explicit extraction of the braiding phase in the low-energy Majorana sector from the full many-particle Hilbert space allows us to analyze the breakdown of the independent-particle picture of Majorana braiding. Furthermore, we find nearest-neighbor interactions to significantly affect the braiding performance to the better or worse, depending on the sign and magnitude of the coupling.