Capacitive coupling of persistent current qubits

Persistent current qubits are usually coupled to other elements via magnetic interactions. However, those interactions alone are only able to reproduce a small family of stoquastic models. To enlarge this family, we have analyzed the capacitive coupling between persistent current devices. First, we present a general theory to find the effective interaction in the computational subspace, which works even in the ultra-strong coupling regime. Then, we investigate several superconducting circuit designs with persistent current qubits (flux and fluxonium qubits) that, thanks to the capacitive coupling, can emulate relevant low-energy physics when coupled between them, to a waveguide or an LC mode. For instances, we will show cricuits parameters that allow to obtain an ultra-strong capacitive coupling between photons and qubit or the design of a long lived qutrit state coupled to a continuum of excitations.