Quantum Frustration as a Protection Mechanism in Non-Topological Majorana Qubits

TL;DR

This paper investigates how quantum frustration can protect non-topological Majorana qubits from decoherence caused by environmental noise, highlighting its limitations against certain noise types.

Contribution

It introduces the concept of quantum frustration as a decoherence mitigation mechanism for Majorana qubits and analyzes its effectiveness against different noise spectra.

Findings

Frustration protects against Ohmic noise ($s=1$) and some sub-Ohmic noise ($0.76<s<1$).

Frustration is ineffective against $1/f$ noise ($s o0$), leading to decoherence.

The qubit's stability depends on the nature of the local environment experienced by Majorana modes.

Abstract

I analyze the decoherence of a $\pi$-junction qubit encoded by two co-located Majorana modes. Although not topologically protected, the qubit leverages distinct spatial profiles to couple to two independent environmental baths, realizing the phenomenon of quantum frustration. This mechanism is tested against the threat of quasiparticle poisoning (QP). I show that frustration is effective against Ohmic noise ($s=1$) and has some protection for $0.76<s<1$ sub-Ohmic noise. However, the experimentally prevalent $1/f$ noise ($s\to0$) falls deep within the model's localized phase, where frustration is insufficient. This causes spontaneous symmetry breaking and catastrophic decoherence. The qubit's viability depends on what the effective environment is that these local Majorana wave functions experience.