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

TL;DR

This work addresses decoherence in a pi-junction qubit formed by two Majorana modes that are not strictly topologically protected. It develops a two-bath noise framework, modeling independent Dynes baths coupling to each Majorana, and analyzes decoherence using pure-dephasing theory and quantum frustration of decoherence. The main finding is that quantum frustration protects against Ohmic noise (s=1) and partially protects against sub-Ohmic noise in the range 0.76 < s < 1, but fails for 1/f noise (s → 0) where a localized, symmetry-broken phase leads to catastrophic decoherence. Practically, the qubit’s viability depends on the effective environment; eliminating zero-energy states or using specific junction geometries can enable robust coherence, while 1/f noise remains a major challenge.

Abstract

I analyze the decoherence of a $π$-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 is the effective environment that these local Majorana wave functions experience.

Figures (4)

• Figure 1: Two s-wave superconductors (gray) with a ferromagnetic layer between them (blue). On top is the semiconductor wire (green). The $\pi$-junction in the superconductors induces a $\pi$-junction in the wire by the proximity effect.
• Figure 2: Semiconductor wire (green) on top of an s-wave superconductor (gray) with nano-ferromagnets (blue) producing a magnetic domain wall. Figure adapted from Ref. gangadharaiah2011majorana.
• Figure 3: A semiconductor wire is cleaved and one of the segments is reoriented, the two different green tones represent the two wires creating a junction. Both a placed on top of an s-wave superconductor (gray).
• Figure 4: A simple 1D wire bands with Rashba spin orbit interaction. The blue/red lines correspond to the two spin bands that are dislocated by the spin-orbit vector $\left|\vec{k}_{so}\right|=m\alpha/\hbar^{2}$. After introducing the superconducting paring the two band hybridize creating the green and brown bands. At $k=0$ the gap between the hybridize bands is $\left|\Delta\right|$.