  We describe a superconducting circuit consisting of a Josephson junction in
parallel with a quantum phase slip wire, which implements a Hamiltonian that is
periodic in both charge and flux. This Hamiltonian is exactly diagonalisable in
a double-Bloch band, and the eigenstates are shown to be code states of the
Gottesman-Kitaev-Preskill quantum error correcting code. The eigenspectrum has
several critical points, where the linear sensitivity to external charge and
flux noise vanishes. The states at these critical points thus hold promise as
qubit states that are insensitive to external noise sources.
