Two Anderson impurities coupled through a superconducting island: charge stability diagrams and double impurity qubit

We present a model of two Anderson impurities coupled to and through a superconducting island. The model parametrizes the strength of the coupling between impurity sites, allowing it to represent a variable distance between the impurities. We systematically explore the effect of the model parameters in the subspaces with total even and odd occupancy, identifying unique features of the charge stability diagrams that distinguish the two parities. For total odd electron parity, we identify a device tuning, in which the splitting between the two lowest energy states is highly insensitive to changes of the chemical potentials. We investigate the degree to which a qubit based on such two states is tunable and discuss an optimal choice of parameters to maximize inhomogeneous dephasing time. Finally, we point out that the proposed qubit lacks a transition dipole moment, and outline some of the consequences on viable driving and readout mechanisms. The prototype qubits could be realized with the existing capabilities of coupling quantum dots to hard-gapped superconductors.