Proposal for a flux qubit in a dc SQUID with the $4\pi$ period Josephson effect

TL;DR

This paper proposes a superconducting flux qubit based on a dc SQUID with a topological nanowire junction exhibiting a $4\\pi$ Josephson effect, offering enhanced stability, noise tolerance, and scalability for quantum computing.

Contribution

It introduces a novel flux qubit design utilizing Majorana bound states and the $4\\pi$ Josephson effect, enabling improved stability and controllability in quantum circuits.

Findings

The flux qubit exhibits a double-well potential energy landscape.

The two lowest energy levels are isolated and show opposite supercurrents.

The proposed system can be coupled and manipulated for quantum information processing.

Abstract

Constructing qubits which are suitable for quantum computation remains a notable challenge. Here, we propose a superconducting flux qubit in a dc SQUID structure, formed by a conventional insulator Josephson junction and a topological nanowire Josephson junction with Majorana bound states. The zero energy Majorana bound states transport $4\pi$ period Josephson currents in the nanowire junction. The interplay between this $4\pi$ period Josephson effect and the convectional $2\pi$ period Josephson effect in the insulator junction induces a double-well potential energy landscape in the SQUID. As a result, the two lowest energy levels of the SQUID are isolated from other levels. These two levels show contradicting circulating supercurrents, thus can be used as a flux qubit. We reveal that this flux qubit has the merits of stability to external noises, tolerance to the deviation of system parameters, and scalability to large numbers. Furthermore, we demonstrate how to couple this flux qubit with the Majorana qubit by tuning the junction parameters, and how to use this coupling to manipulate the Majorana qubit.