  We perform a theoretical study of composite superconducting qubit systems for
the case of a coupled qubit configuration based on a hybrid qubit circuit made
of both charge and phase qubits, which are coupled via a sigma(x)xsigma(z)
interaction. We compute the system's eigen-energies in terms of the qubit
transition frequencies and the strength of the inter-qubit coupling, and
describe the sensitivity of the energy crossing/anti-crossing features to such
coupling. We compute the hybrid system's dissipative dynamics for the cases of
i) collective and ii) independent decoherence, whereby the system interacts
with one common and two different baths of harmonic oscillators, respectively.
The calculations have been performed within the Bloch-Redfield formalism and we
report the solutions for the populations and the coherences of the system's
reduced density matrix. The dephasing and relaxation rates are explicitly
calculated as a function of the heat bath temperature.
