We review recent results on a new class of Josephson arrays which have non-trivial topologyudand exhibit a novel quantum states at low temperatures. One of these states is characterized byudlong range order in a two Cooper pair condensate and by a discrete topological order parameter.udThe second state is insulating and can be considered as a result of evolution of the former state dueudto Bose-condensation of usual superconductive vortices with a flux quantum 0. Quantum phaseudtransition between these two states is controlled by variation of external magnetic field. Both theudsuperconductive and insulating states are characterized by the presence of 2K-degenerate groundudstates, with K being the number of topologically different cycles existing in the plane of the array.udThis degeneracy is «protected» from the external perturbations (and noise) by the topological orderudparameter and spectral gap. We show that in ideal conditions the low order effect of the externaludperturbations on this degeneracy is exactly zero and that deviations from ideality lead to onlyudexponentially small effects of perturbations. We argue that this system provides a physical implementationudof an ideal quantum computer with a built in error correction. A number of relativelyudsimple «echo-like» experiments possible on small-size arrays are discussed.
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