Probing the parity of Majorana bound states in lateral S-TI-S Josephson junctions via SET detectors and fusion operations*

We propose experiments designed to probe the parity of Majorana bound states (MBS) in S-TI-S (Superconductor-Topological Insulator-Superconductor) lateral Josephson junctions. These junctions are expected to host MBS at Josephson vortex cores where the phase difference across the junction is an odd multiple of π. Our approach is to integrate Al-AlO_x-Al single-electron transistors (SET), which are sensitive to the parity of the MBS pairs, with Nb-Bi₂Se₃-Nb Josephson junctions, in which the MBS can be created and manipulated to carry out braiding operations. We also present a modification to the experiment in which the MBS pairs are combined on an Au quantum dot to demonstrate fusion. We report progress toward implementing these schemes and incorporating them into circuits for quantum information processing.