One of the most serious problem raised by attempts to build devices based
on qubits is the decoherence induced by the residual couplings between
these small systems and their environment. Instead of trying
to eliminate this quantum noise, an alternative strategy has been
proposed some years ago by Kitaev, namely to build quantum circuits which
would be to a large extent insensitive to external perturbations.
This is achieved by a deeply non-local coding of the information in
terms of many-body wave-functions.
 
I'll present two types of superconducting arrays which exhibit
degenerate ground-states relatively immune to local noisy perturbations.
The first type provides a way to implement physically a gauge
theory model with a discrete local symmetry group. The second one
simulates a quantum Ising-like model with a set of anticommuting non-local
symmetries attached to rows and columns of the lattice and is
beginning to be studied experimentally at Rutgers and Grenoble.