Manipulation of decoupled Majorana zero modes (MZMs) could enable
topologically-protected quantum computing. However, the practical realization
of a large number of perfectly decoupled MZMs needed to perform nontrivial
quantum computation has proven to be challenging so far. Fortunately, even a
small number of imperfect MZMs can be used to qualitatively extend the behavior
of standard superconducting qubits, allowing for new approaches for noise
suppression, qubit manipulation and read-out. Such hybrid devices take
advantage of interplay of Cooper pair tunneling, coherent single electron
tunneling, and Majorana hybridization. Here we provide a qualitative
understanding of this system, give analytical results for its ground state
energy spanning full parameter range, and describe potential sensing
applications enabled by the interplay between Majorana and Cooper pair
tunneling.Comment: 13 page