  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 noncompact variables. The
periodic Josephson potential gives rise to a Bloch band structure,
characterised by the Bloch quasicharge. We analyse the possibility of creating
superpositions of different quasicharge 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.
