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 nanotechniques, the process constitutes a quantum measurement process.
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.
We have developed a fabrication process for nanoscale tunnel junctions which includes focused-ion-beam etching from different directions. By applying the process to a Nb/(Al–)Al2O3/Nb trilayer, we have fabricated a Nb single-electron transistor (SET), and characterized the SET at low temperatures, T=0.04–40 K. The superconducting gap energy and the transition temperature of the Nb SET agree with the bulk values, which suggests high quality Nb junctions. The single-electron charging energy of the SET is estimated to be larger than 1 K.