Inductively shunted transmon qubit with tunable transverse and longitudinal coupling

We present the design of an inductively shunted transmon qubit with flux-tunable coupling to an embedded harmonic mode. This circuit construction offers the possibility to flux-choose between pure transverse and pure longitudinal coupling, that is coupling to the $\sigma_x$ or $\sigma_z$ degree of freedom of the qubit. While transverse coupling is the coupling type that is most commonly used for superconducting qubits, the inherently different longitudinal coupling has some remarkable advantages both for readout and for the scalability of a circuit. Being able to choose between both kinds of coupling in the same circuit provides the flexibility to use one for coupling to the next qubit and one for readout, or vice versa. We provide a detailed analysis of the system's behavior using realistic parameters, along with a proposal for the physical implementation of a prototype device.