  Based on a network graph analysis of the underlying circuit, a quantum theory
of arbitrary superconducting charge qubits is derived. Describing the
dissipative elements of the circuit with a Caldeira-Leggett model, we calculate
the decoherence and leakage rates of a charge qubit. The analysis includes
decoherence due to a dissipative circuit element such as a voltage source or
the quasiparticle resistances of the Josephson junctions in the circuit. The
theory presented here is dual to the quantum circuit theory for superconducting
flux qubits. In contrast to spin-boson models, the full Hilbert space structure
of the qubit and its coupling to the dissipative environment is taken into
account. Moreover, both self and mutual inductances of the circuit are fully
included.
