Stability of Floquet Majorana box qubits

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 $\hslash \omega /2$. 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.

5 pages main text and 4 pages supplementary material, 6 figures

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• Decay rates of almost strong modes in Floquet spin chains beyond Fermi's Golden Rule
• Robust spectral $\pi$ pairing in the random-field Floquet quantum Ising model
• Topological $\pi$ modes and beyond
• Almost Strong Zero Modes at Finite Temperature
• Topological excitations at time vortices in periodically driven systems
• Floquet Product Mode
• Generalized Majorana edge modes in a number-conserving periodically driven $p$-wave superconductor
• Quantum-vacuum-protected topological edge polaritons
• Linear differential equation approach to the Loschmidt amplitude