Building a bigger Hilbert space for superconducting devices, one Bloch state at a time

Superconducting circuits for quantum information processing are often described theoretically in terms of a discrete charge, or equivalently, a compact phase/flux, at each node in the circuit. Here we revisit the consequences of lifting this assumption for transmon and Cooper-pair-box circuits, which are constituted from a Josephson junction and a capacitor, treating both the superconducting phase and charge as non-compact variables. The periodic Josephson potential gives rise to a Bloch band structure, characterised by the Bloch quasi-charge. We analyse the possibility of creating superpositions of different quasi-charge states by transiently shunting inductive elements across the circuit, and suggest a choice of eigenstates in the lowest Bloch band of the spectrum that may support an inherently robust qubit encoding.