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We propose a scheme for the circulator function in a superconducting circuitconsisting of a three-Josephson junction loop and a trijunction. In this studywe obtain the exact Lagrangian of the system by deriving the effectivepotential from the fundamental boundary conditions. We subsequently show thatwe can selectively choose the direction of current flowing through the branchesconnected at the trijunction, which performs a circulator function. Further, weuse this circulator function for a non-Abelian braiding of Majorana zero modes(MZMs). In the branches of the system we introduce pairs of MZMs which interactwith each other through the phases of trijunction. The circulator functiondetermines the phases of the trijunction and thus the coupling between the MZMsto gives rise to the braiding operation. We modify the system so that MZMsmight be coupled to the external ones to perform qubit operations in a scalabledesign.

Circulator function in a Josephson junction circuit and braiding of Majorana zero modes