  There exists a large number of experimental and theoretical results
supporting the picture of macroscopic qubits implemented by nanoscopic
Josephson junctions of three different types -- charge qubit, flux qubit and
phase qubit. The standard unified description of such systems is based on the
formal quantization of the phenomenological Kirchhoff equations for the
corresponding circuits. In this paper a simplified version of the BCS theory
for superconductors is used to derive microscopic models for all types of small
Josephson junctions. For these models the state-dependent individual tunneling
of Cooper pairs couples ground pair states with excited pair states what leads
to a more complicated structure of the lowest lying energy levels. In
particular, the highly degenerate levels emerge, which act as probability sinks
for the qubit. These models allow also for the coupling to phonons as an
efficient mechanism of relaxation for all types of junctions. The alternative
formulas concerning basic spectral parameters of superconducting qubits are
presented and compared with the experimental data. Finally, the question
whether small Josephson junctions can be treated as macroscopic quantum systems
is briefly discussed.
