Proposal for coherent coupling of Majorana zero modes and superconducting qubits using the 4π Josephson effect.

We propose to use an ancilla fluxonium qubit to interact with a Majorana qubit hosted by a topological one-dimensional wire. The coupling is obtained using the Majorana qubit-controlled 4π Josephson effect to flux bias the fluxonium qubit. We demonstrate how this coupling can be used to sensitively identify topological superconductivity, to measure the state of the Majorana qubit, to construct 2-qubit operations, and to implement quantum memories with topological protection.