We propose a Josephson junction array which can be tuned into an unconventional insulating state by varying external magnetic field. This insulating state retains a gap to half vortices; as a consequence, such array with non-trivial global geometry e
xhibits a ground state degeneracy. This degeneracy is protected from the effects of external noise. We compute the gaps separating higher energy states from the degenerate ground state and we discuss experiments probing the unusual properties of this insulator.
We introduce a new class of Josephson arrays which have non-trivial topology and exhibit a novel state at low temperatures. This state is characterized by long range order in a two Cooper pair condensate and by a discrete topological order parameter.
These arrays have degenerate ground states with this degeneracy protected from the external perturbations (and noise) by the topological order parameter. We show that in ideal conditions the low order effect of the external perturbations on this degeneracy is exactly zero and that deviations from ideality lead to only exponentially small effects of perturbations. We argue that this system provides a physical implementation of an ideal quantum computer with a built in error correction and show that even a small array exhibits interesting physical properties such as superconductivity with double charge, 4e, and extremely long decoherence times.
