Bath-induced decoherence in finite-size Majorana wires at non-zero temperature

TL;DR

This paper investigates the optimal speed for braiding Majorana zero-modes in finite-size superconducting wires, considering environmental decoherence effects, to guide experimental implementations of topological quantum computing.

Contribution

It calculates the intermediate braiding time scale in finite systems coupled to a bosonic bath, balancing adiabaticity and decoherence effects, providing practical speed boundaries.

Findings

Identifies the optimal braiding time scale balancing adiabaticity and decoherence.

Provides bounds for braiding speed with specific gate fidelity.

Highlights susceptibility of Majorana systems to environmental noise.

Abstract

Braiding Majorana zero-modes around each other is a promising route towards topological quantum computing. Yet, two competing maxims emerge when implementing Majorana braiding in real systems: On the one hand, perfect braiding should be conducted adiabatically slowly to avoid non-topological errors. On the other hand, braiding must be conducted fast such that decoherence effects introduced by the environment are negligible, which are generally unavoidable in finite-size systems. This competition results in an intermediate time scale for Majorana braiding that is optimal, but generally not error-free. Here, we calculate this intermediate time scale for a T-junction of short one-dimensional topological superconductors coupled to a bosonic bath that generates fluctuations in the local electric potential, which stem from, e.g., environmental photons or phonons of the substrate. We thereby obtain boundaries for the speed of Majorana braiding with a predetermined gate fidelity. Our results emphasize the general susceptibility of Majorana-based information storage in finite-size systems and can serve as a guide for determining the optimal braiding times in future experiments.