Fusion of Majorana bound states with mini-gate control in two-dimensional systems

A hallmark of topological superconductivity is the non-Abelian statistics of Majorana bound states (MBS), its chargeless zero-energy emergent quasiparticles. The resulting fractionalization of a single electron, stored nonlocally as a two spatially-separated MBS, provides a powerful platform for implementing fault-tolerant topological quantum computing. However, despite intensive efforts, experimental support for MBS remains indirect and does not probe their non-Abelian statistics. Here we propose how to overcome this obstacle in mini-gate controlled planar Josephson junctions (JJs) and demonstrate non-Abelian statistics through MBS fusion, detected by charge sensing using a quantum point contact, based on dynamical simulations. The feasibility of preparing, manipulating, and fusing MBS in two-dimensional (2D) systems is supported in our experiments which demonstrate the gate control of topological transition and superconducting properties with five mini gates in InAs/Al-based JJs. While we focus on this well-established platform, where the topological superconductivity was already experimentally detected, our proposal to identify elusive non-Abelian statistics motivates also further MBS studies in other gate-controlled 2D systems. The current efforts to look for Majorana bound states (MBS) still cannot probe the hallmark property, the non-Abelian statistics. Here, the authors propose to realize non-Abelian statistics through MBS fusion in mini-gate controlled planar Josephson junctions.

Automated summary

This study proposes a method to realize the fusion of MBS and demonstrate their non-Abelian statistics in mini-gate controlled planar Josephson junctions. The feasibility of preparing, manipulating, and fusing MBS in 2D systems is supported by experimental results. This research provides insights into the understanding and further study of MBS.