On quantum computing with macroscopic Josephson qubits

The achievements of quantum computation theory, e.g. Shor's factoring algorithm, motivate efforts to realize quantum computers. Among systems proposed for quantum computing, macroscopic superconducting circuits of Josephson junctions appear promising for integration in electronic circuits and large-scale applications. Recently, a superconducting tunnel junction circuit was designed and a sufficiently high quality factor of quantum coherence has been obtained. This indicates that decoherence need not be among the obstacles in building quantum computers with macroscopic Josephson circuits. In this paper we present the setup of some elementary quantum logic with macroscopic Josephson qubits, strengthened by some simulation work, and then study the feasibility of implementing Shor's quantum factoring algorithm on them. It is shown that it would be eventually possible to build a 2-dimensional Josephson qubit array, possibly accompanied by classical computing components, capable of performing useful quantum computations.