  Minimal Kitaev chains composed of two semiconducting quantum dots coupled via
a grounded superconductor have emerged as a promising platform to realize and
study Majorana bound states (MBSs). We propose a hybrid qubit based on a
Josephson junction between two such double quantum dots (DQDs) embedded in a
superconducting qubit geometry. The qubit makes use of the $4{\pi}$-Josephson
effect in the Kitaev junction to create a subspace based on the even/odd
fermionic parities of the two DQD arrays hosting MBSs. Deep in the transmon
regime, we demonstrate that by performing circuit QED spectroscopy on such
hybrid Kitaev-Transmon "Kitmon" qubit one could observe distinct MBS features
in perfect agreement with precise analytical predictions in terms of DQD
parameters only. This agreement allows to extract the Majorana polarization in
the junction from the microwave response.
