  We propose a scheme for the circulator function in a superconducting circuit
consisting of a three-Josephson junction loop and a trijunction. In this study
we obtain the exact Lagrangian of the system by deriving the effective
potential from the fundamental boundary conditions. We subsequently show that
we can selectively choose the direction of current flowing through the branches
connected at the trijunction, which performs a circulator function. Further, we
use 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 interact
with each other through the phases of trijunction. The circulator function
determines the phases of the trijunction and thus the coupling between the MZMs
to gives rise to the braiding operation. We modify the system so that MZMs
might be coupled to the external ones to perform qubit operations in a scalable
design.
