  High fidelity quantum information processing requires a combination of fast
gates and long-lived quantum memories. In this work, we propose a hybrid
architecture, where a parity-protected superconducting qubit is directly
coupled to a Majorana qubit, which plays the role of a quantum memory. The
superconducting qubit is based upon a $\pi$-periodic Josephson junction
realized with gate-tunable semiconducting wires, where the tunneling of
individual Cooper pairs is suppressed. One of the wires additionally contains
four Majorana zero modes that define a qubit. We demonstrate that this enables
the implementation of a SWAP gate, allowing for the transduction of quantum
information between the topological and conventional qubit. This architecture
combines fast gates, which can be realized with the superconducting qubit, with
a topologically protected Majorana memory.
