Physical implementation of protected qubits.
We review the general notion of topological protection of quantum states in spin models and its relation with the ideas of quantum error correction. We show that topological protection can be viewed as a Hamiltonian realization of error correction: for a quantum code for which the minimal number of errors that remain undetected is N, the corresponding Hamiltonian model of the effects of the environment noise appears only in the Nth order of the perturbation theory.We discuss the simplest model Hamiltonians that realize topological protection and their implementation in superconducting arrays. We focus on two dual realizations: in one the protected state is stored in the parity of the Cooper pair number, in the other, in the parity of the flux number. In both cases the superconducting arrays allow a number of fault-tolerant operations that should make the universal quantum computation possible.
Laboratoire de Physique Théorique et Hautes Énergies, CNRS UMR 7589 et Université Paris 6, Boîte 126, 4 place Jussieu, 75252 Paris Cedex 05, France.
B
B
Douçot
L B
LB
Ioffe
D003198:Computer Simulation; D039301:Computers, Molecular; D008956:Models, Chemical; D011789:Quantum Theory