Decay rates for topological memories encoded with Majorana fermions

TL;DR

This paper demonstrates that Majorana-based qubits are vulnerable to dynamic perturbations, with information decoherence occurring over time, challenging the assumption of their inherent protection against decoherence.

Contribution

The authors develop a generic method to analyze how external perturbations affect Majorana modes, revealing that dynamic disturbances cause long-term decoherence.

Findings

Static perturbations cause saturation of information loss.

Dynamic perturbations lead to complete decoherence over time.

Dephasing and energy fluctuations harm Majorana memory stability.

Abstract

Recently there have been numerous proposals to create Majorana zero modes in solid state heterojunctions, superconducting wires and optical lattices. Putatively the information stored in qubits constructed from these modes is protected from various forms of decoherence. Here we show that this is not the case. We present a generic method to study the effect of external perturbations on these modes. We focus on the case where there are no interactions between different Majorana modes either directly or through intermediary fermions. To quantify the rate of loss of the information stored in the Majorana modes we study the two-time correlators for qubits built from them. We analyze a generic gapped fermionic environment (bath) interacting via tunneling with different components of the qubit (different Majorana modes). We find that static (time-independent) perturbations are not harmful, and just lead to a depletion of the information stored that saturates in the long-time limit. On the other hand we find markedly different results for dynamic (time dependent) systems, with no coherence surviving in the long time limit. In particular we find that dephasing and energy fluctuations of the modes in the fermionic bath have adverse effects on the Majorana memories.