Quantum computation and quantum coherence in mesoscopic Josephson junctions

Macroscopic quantum dynamics of Josephson junctions has attracted recently renewed interest in the context of quantum computation. Quantum coherence o f the charge states in a single-Cooper-pair box or the flux states in an rf SQUID can be used to create charge and flux: qubits for quantum computatio n. The aim of this paper is to give a brief introduction to the basic conce pts of quantum computation with Josephson junctions and to discuss the theo ry of quantum coherence in the rf-stimulated macroscopic resonant tunneling of flux in SQUID's. The results for resonant flux tunneling show that the quantum coherent flux oscillations should lead to splitting of resonant tun neling peaks, indicating that the resonant tunneling can be a convenient to ol for studying macroscopic quantum coherence of flux.