Manipulation of Phases and Supercurrents in S-TI-S Lateral Josephson Junction Networks*

Quantum computing using topological Q-bits composed of Majorana Fermions (MF) shows promise for its robustness against disorder and its scalability with existing lithography infrastructure. In lateral Josephson junction networks, the MFs are localized to points in the junction where the phase difference of the superconducting order parameter across the junction is equal to an odd multiple of π. Quantum computations are performed by physically moving MFs pinned to odd π crossings around one another, encoding the quantum state of the system in the historical locations of the MFs relative to each other. Understanding the phase distributions around multi-junction nodes in the network is one key hurdle that needs to be overcome before the implementation of this architecture is a reality. Measurements and modeling of Nb-BiSe-Nb lateral Josephson junctions in three and four junction geometries will be presented. The results will be discussed with their implication for the realization of a topological quantum architecture.