Fusion and parity readout of Majorana bound states in lateral S-TI-S Josephson junctions*

We propose experiments designed to demonstrate the fusion of Majorana bound states (MBS) and to measure their parity 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, 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 fusion and braiding operations. We report progress toward implementing these schemes and incorporating them into circuits for quantum information processing.