Low-capacitance Josephson junction arrays in the parameter range where
single charges can be controlled are suggested as possible physical r
ealizations of the elements which have been considered in the context
of quantum computers. We discuss single and multiple quantum-bit syste
ms. The systems an controlled by applied gate voltages, which also all
ow the necessary manipulation of the quantum states. We estimate that
the phase-coherence time is sufficiently long for experimental demonst
ration of the principles of quantum computation.