  We show that quantized superconducting circuits are non-integrable at the
classical level of description, adorned by nonlinear resonances amidst
stochastic sea. The spectral fluctuations of these quasi-integrable systems
exhibit intermediate behaviour between regularity and chaos. The distribution
function of ratios of adjacent spacings, and, nearest-neighbour spacing
distribution functions attest to the occurrence of "mild chaos". Based on these
features, we propose criteria for protection of qubits from decoherence which
amounts to choosing the parameters of the system in a way that the system
resides as close as possible to the elliptic point of the primary nonlinear
resonance of the corresponding classical system.
