Quantum computing and quantum measurement with mesoscopic Josephson junctions

Recent experimental demonstrations of quantum coherence of the charge and f lux states of Josephson junctions show that the quantum Josephson dynamics can be used to develop scalable quantum logic circuits. In this work, I rev iew the basic concepts of Josephson tunneling and Josephson-junction qubits , and discuss two problems of this tunneling motivated by quantum computing applications. One is the theory of photon-assisted resonant flux tunneling in SQUID systems used to demonstrate quantum coherence of flux. Another is the problem of quantum measurement of charge with the SET electrometer. It is shown that the SET electrometer at the Coulomb blockade threshold is th e quantum-limited detector with energy sensitivity reaching (h) over bar/ro ot3 in the resonant-tunneling regime.