A topological Josephson junction platform for realizing Majorana modes and Non-Abelian rotations

As part of the intense effort towards realizing Majorana mode platforms that perform qubit operations, we present a proposed topological Josephson junction architecture whose experimental implementation we are working towards in conjunction. The architecture consists of superconducting electrodes deposited on a topological insulator film to form networks of lateral Josephson junctions. Magnetic fields piercing the junction enable flux-controlled nucleation of multiple Majorana bound state modes localized in the junction at locations where the local phase difference is an odd multiple of p, i.e. attached to the cores of Josephson vortices. We describe protocols for i) tuning the coupling between the Majorana modes to affect non-Abelian rotations, and ii) measuring non-local parity correlations induced by such a rotation. The platform makes use of local magnetic fields and supercurrent pulses to manipulate the Majorana modes and enables the detection of their parity-based qubit states by Josephson current measurements and charge-sensitive single-electron transistors. We report our progress in the experimental realization of this architecture.