  Low-capacitance Josephson junction systems as well as coupled quantum dots,
in a parameter range where single charges can be controlled, provide physical
realizations of quantum bits, discussed in connection with quantum computing.
The necessary manipulation of the quantum states can be controlled by applied
gate voltages. In addition, the state of the system has to be read out. Here we
suggest to measure the quantum state by coupling a single-electron transistor
to the q-bit. As long as no transport voltage is applied, the transistor
influences the quantum dynamics of the q-bit only weakly. We have analyzed the
time evolution of the density matrix of the transistor and q-bit when a voltage
is turned on. For values of the capacitances and temperatures which can be
realized by modern nano-techniques the process constitutes a quantum
measurement process.
