Effects of non-equilibrium noise on a quantum memory encoded in Majorana zero modes

TL;DR

This paper investigates the impact of non-equilibrium noise on the coherence time of Majorana-based quantum memories, revealing that non-local encoding does not significantly extend coherence due to rapid quasi-particle propagation.

Contribution

The study demonstrates that non-local encoding in Majorana systems does not substantially improve coherence times because of fast quasi-particle propagation speeds.

Findings

Non-local encoding does not significantly enhance coherence time.

Quasi-particle propagation speed is approximately the Fermi velocity.

Local and non-local encodings have similar decay times.

Abstract

In order to increase the coherence time of topological quantum memories in systems with Majorana zero modes, it has recently been proposed to encode the logical qubit states in non-local Majorana operators which are immune to localized excitations involving the unpaired Majorana modes. In this encoding, a logical error only happens when the quasi-particles, subsequent to their excitation, travel a distance of the order of the spacing between the Majorana modes. Here, we study the decay time of a quantum memory encoded in a clean topological nanowire interacting with an environment with a particular emphasis on the propagation of the quasi-particles above the gap. We show that the non-local encoding does not provide a significantly longer coherence time than the local encoding. In particular, the characteristic speed of propagation is of the order of the Fermi velocity of the nanowire and not given by the much slower group velocity of quasi-particles which are excited just above the gap.