Topological Protection of Majorana Qubits

TL;DR

This paper investigates the thermal stability of Majorana-based topological qubits, demonstrating their robustness against thermal fluctuations due to quantum non-locality and the bulk gap, with some impact on measurement visibility.

Contribution

It provides a detailed analysis of how thermal effects influence Majorana qubits, confirming their protection and identifying specific effects on measurement schemes and decoherence rates.

Findings

Thermal occupation of midgap states does not hinder adiabatic braiding.

Interferometry measurement visibility is reduced by thermal effects.

Qubit decoherence rate is exponentially suppressed at low temperatures.

Abstract

We study the stability of the topological quantum computation proposals involving Majorana fermions against thermal fluctuations. We use a minimal realistic model of a spinless px+ipy superconductor and consider effect of excited midgap states localized in the vortex core as well as of transitions above the bulk superconducting gap on the quasiparticle braiding, interferometry-based qubit read-out schemes, and quantum coherence of the topological qubits. We find that thermal occupation of the midgap states does not affect adiabatic braiding operations but leads to a reduction in the visibility of the interferometry measurements. We also consider quantum decoherence of topological qubits at finite temperatures and calculate their decay rate which is associated with the change of the fermion parity and, as such, is exponentially suppressed at temperatures well below the bulk excitation gap. Our conclusion is that the Majorana-based topological quantum computing schemes are indeed protected by the virtue of the quantum non-locality of the stored information and the presence of the bulk superconducting gap.