Coupling of SET to lateral S-TI-S Josephson junction for parity readout and fusion of Majorana bound states

Current developments toward topologically protected quantum computing rely heavily on the verification of the existence of Majorana bound states (MBS). A measurement of the parity of MBS is necessary for their implementation in topological qubit operations. We propose experiments for probing parity of MBS in Superconductor-Topological Insulator-Superconductor (S-TI-S) lateral Josephson junctions, in which MBS are nucleated at Josephson vortex cores where the phase difference across the junction is an odd multiple of π. We design two types of single-electron transistors (SETs) for parity experiments: the Al/AlO_x/Al SET which is sensitive to the parity of MBS pairs, and a SET with an Au quantum dot for demonstrating fusion of MBS. We report progress toward implementing these devices with S-TI-S junctions for the purpose of incorporation into circuits for qubit braiding operations.