I argue that any realization of macroscopic quantum computer requires that individual logical qubits are realized as quantum systems with degenerate ground states which are protected from the effects of the environment. This protection can be achieved by a highly redundant system, similarly to a classical error correction in the noisy environment in which one checks for errors comparing values of different bits at regular intervals and correct the erroneous ones. Alternatively, the protection can be achieved by the proper choice of the Hamiltonian that automatically projects the quantum state of a large many body system into the error-free subspace. Because the quantum errors can happen both in phase and in amplitude the quantum error correction of the first type requires a huge overhead that makes it rather unrealistic for the existing physical implementations of logical qubits. In contrast, the Hamiltonian approach is not too difficult to realize in a broad class of models. The real challenge is to find the feasible implementation of these models. I will show that the novel class of Josephson array with non-trivial symmetry or topology satisfies these requirements. For these “topologically protected” arrays the effect of noise is exponentially small in array size.

Rutgers