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.