  We introduce a new hybrid qubit consisting of a Majorana qubit interacting
with a transmon longitudinally coupled to a resonator. To do so, we equip the
longitudinal transmon qubit with topological quasiparticles, supported by an
array of heterostructure nanowires, and derive charge- and phase-based
interactions between the Majorana qubit and the resonator and transmon degrees
of freedom. Inspecting the charge coupling, we demonstrate that the Majorana
self-charging can be eliminated by a judicious choice of charge offset, thereby
maintaining the Majorana degeneracy regardless of the quasiparticles spatial
arrangement and parity configuration. We perform analytic and numerical
calculations to derive the effective qubit-qubit interaction elements and
discuss their potential utility for state readout and quantum error correction.
Further, we find that select interactions depend strongly on the overall
superconducting parity, which may provide a direct mechanism to characterize
deleterious quasiparticle poisoning processes.
