  Several physical realizations of quantum bits have been proposed. Of those,
nano-electronic devices appear most suitable for large-scale integration and
potential applications. We suggest to use low-capacitance Josephson junctions,
exploiting the coherence of tunneling in the superconducting state combined
with the possibility to control individual charges by Coulomb blockade effects
(cond-mat/9706016,cond-mat/9808067). These systems constitute quantum bits,
with logical states differing by one Cooper-pair charge. Single- and two-bit
operations can be performed by applying a sequence of gate voltages. The phase
coherence time is sufficiently long to allow a series of these steps. In
addition to the manipulation of qubits the resulting quantum state has to be
read out. This can be accomplished by coupling a single-electron transistor
capacitively to the qubit (cond-mat/9801125). To describe this quantum
measurement process we study the time evolution of the density matrix of the
coupled system. Only when a transport voltage is turned on, the transistor
destroys the phase coherence of the qubit; in this case within a short time.
The measurement is accomplished after a longer time scale, when the signal
resolves the different quantum states. At still longer times the measurement
process itself destroys the information about the initial state. We present a
suitable set of system parameters, which can be realized by present-day
technology.
