  We discuss decoherence in charge qubits formed by multiple lateral quantum
dots in the framework of the spin-boson model and the Born-Markov
approximation. We consider the intrinsic decoherence caused by the coupling to
bulk phonon modes. Two distinct quantum dot configurations are studied: (i)
Three quantum dots in a ring geometry with one excess electron in total and
(ii) arrays of quantum dots where the computational basis states form multipole
charge configurations. For the three-dot qubit, we demonstrate the possibility
of performing one- and two-qubit operations by solely tuning gate voltages.
Compared to the proposal by DiVincenzo {\it et al.} involving a linear
three-dot spin qubit, the three-dot charge qubit allows for less overhead on
two-qubit operations. For small interdot tunnel amplitudes, the three-dot
qubits have $Q$ factors much higher than those obtained for double dot systems.
The high-multipole dot configurations also show a substantial decrease in
decoherence at low operation frequencies when compared to the double-dot qubit.
