Minimal circuit for a flux-controlled Majorana qubit in a quantum spin-Hall insulator

TL;DR

This paper proposes a minimal flux-controlled circuit using a top-transmon design to manipulate a Majorana qubit, enabling coherence characterization through microwave cavity oscillations without topological protection.

Contribution

It introduces a novel, minimal flux-controlled circuit for Majorana qubits that allows full coherence characterization without relying on topological protection.

Findings

Demonstrates flux-controlled qubit rotations via Josephson junctions.

Shows Rabi oscillations can be monitored through cavity resonance.

Provides a method to measure coherence times of Majorana qubits.

Abstract

We construct a minimal circuit, based on the top-transmon design, to rotate a qubit formed out of four Majorana zero-modes at the edge of a two-dimensional topological insulator. Unlike braiding operations, generic rotations have no topological protection, but they do allow for a full characterization of the coherence times of the Majorana qubit. The rotation is controlled by variation of the flux through a pair of split Josephson junctions in a Cooper pair box, without any need to adjust gate voltages. The Rabi oscillations of the Majorana qubit can be monitored via oscillations in the resonance frequency of the microwave cavity that encloses the Cooper pair box.