  A recent theoretical proposal suggests that a simple circuit utilizing two
superinductors may produce a qubit with ground state degeneracy [P. Brooks et
al., Phys. Rev. A 87, 052306 (2013)]. We perform a full circuit analysis along
with exact diagonalization of the circuit Hamiltonian to elucidate the nature
of the spectrum and low-lying wave functions of this $0-\pi$ device. We show
that the ground state degeneracy is robust to disorder in charge, flux and
critical current as well as insensitive to modest variations in the circuit
parameters. Our treatment is non-perturbative, provides access to excited
states and matrix elements, and is immediately applicable also to intermediate
parameter regimes of experimental interest.
