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

TL;DR

This paper proposes a superconducting circuit-based circulator that enables controlled braiding of Majorana zero modes, facilitating scalable quantum operations through phase manipulation and external coupling.

Contribution

It introduces an exact Lagrangian derivation for a Josephson junction circuit that performs circulator functions and enables non-Abelian braiding of Majorana zero modes.

Findings

Exact effective potential derived for the circuit.

Selective current direction control in the circulator.

Implementation of Majorana braiding via phase manipulation.

Abstract

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.