Novel class of Josephson junction arrays with protected ground states and their application for quantum computing

A realistic implemetation of the macroscopic quantum computer requires that individual qubits are realized as quantum systems with degenerate ground states which are well protected from the effects of the environment. I show how this protection can be achieved in the new class of Josephson arrays with non-trivial symmetry or topology. For such "topologically protected" arrays the effect of noise is exponentially small in the array size which allows one in principle to get extremely small error rates and extremely long dephasing times in these systems. In this review I present a simple physical picture of the topological protection and explain why it is related to the presence of the topological order parameter in these systems. I formulate a set of general mathematical requirements on a model that ensures the appearance of the protected degenerate states and show how these conditions can be satisfied in a simple spin model. Finally I present Josephson junction array that is described by the mathematical model which satisfy these conditions and discuss its physical properties and how one can test these predictions experimentally.