Possible implementation of topologically protected qubits by a novel class of Josephson junction arrays

I review the conditions that need to be satisfied by a physical system implemeting a macroscopic quantum computer, focussing on the degree of protection of individual qubits from the noise of the environment. I argue that such degree of protection is possible in a macroscopic systems only if the information is stored very non-locally in the individual bits. I show that this 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. I begin with a warm-up toy model which explains the essence of the topological protection and non-local character of information storage in such systems. I then proceed with a formulation of very general mathematical requirements on a model that ensure 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.