Quantum computers, if available, could perform certain tasks much more efficiently than classical computers by exploiting different physical principles(1-3). A quantum computer would be comprised of coupled, two-state quantum systems or qubits, whose coherent time evolution must be controlled in a computation. Experimentally, trapped ions(4,5), nuclear magnetic resonance(6-8) in molecules, and quantum optical systems(9) have been investigated for embodying quantum computation. But solid-state implementations(10-14) would be more practical, particularly nanometre-scale electronic devices: these could be easily embedded in electronic circuitry and scaled up to provide the large numbers of qubits required for useful computations. Here we present a proposal for solid-state qubits that utilizes controllable, low-capacitance Josephson junctions. The design exploits coherent tunnelling of Cooper pairs in the superconducting state, while employing the control mechanisms of single-charge devices: single- and two-bit operations can be controlled by gate voltages. The advantages of using tunable Josephson couplings include the simplification of the operation and the reduction of errors associated with permanent couplings.