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...

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Bibliographic Details
Published in:Reports on progress in physics 2012-07, Vol.75 (7), p.072001-072001
Main Authors: Douçot, B, Ioffe, L B
Format: Article
Language:English
Subjects:
Arrays
Computer Simulation
Computers, Molecular
Error correction
Fault tolerance
Flux
Models, Chemical
Parity
Quantum Theory
Qubits (quantum computing)
Superconductivity
Topology
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Summary: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.
ISSN:0034-4885
1361-6633
DOI:10.1088/0034-4885/75/7/072001