Stability of Floquet Majorana box qubits

TL;DR

This paper studies the stability of Floquet Majorana box qubits in periodically driven topological superconductors, revealing how adiabatic protocols can maintain stability against interactions that generate quasiparticles.

Contribution

It introduces a protocol for stabilizing Floquet Majorana modes in Majorana box qubits by slowly increasing oscillation frequency, avoiding instability from interactions.

Findings

Adiabatic increase of oscillation amplitude causes instability due to quasiparticle creation.

Slowly increasing oscillation frequency can stabilize Floquet Majorana modes.

System can encode 3 qubits with fixed electron parity in a stable regime.

Abstract

In one-dimensional topological superconductors driven periodically with the frequency $\omega$, two types of topological edge modes may appear, the well-known Majorana zero mode and a Floquet Majorana mode located at the quasi-energy $\hbar \omega/2$. We investigate two Josephson-coupled topological quantum wires in the presence of Coulomb interactions, forming a so-called Majorana box qubit. An oscillating gate voltage can induce Floquet Majorana modes in both wires. This allows encoding 3 qubits in a sector with fixed electron parity. If such a system is prepared by increasing the amplitude of oscillations adiabatically, it is inherently unstable as interactions resonantly create quasi particles. This can be avoided by using instead a protocol where the oscillation frequency is increased slowly. In this case, one can find a parameter regime where the system remains stable.