Protected qubits and Chern-Simons theories in Josephson junction arrays

We present general symmetry arguments that show the appearance of doubly denerate states protected from external perturbations in a wide class of Hamiltonians. We construct the simplest spin Hamiltonian belonging to this class and study its properties both analytically and numerically. We find that...

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Bibliographic Details
Published in:Physical review. B, Condensed matter and materials physics Condensed matter and materials physics, 2005-01, Vol.71 (2), Article 024505
Main Authors: Douçot, B., Feigel’man, M. V., Ioffe, L. B., Ioselevich, A. S.
Format: Article
Language:English
Subjects:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Condensed Matter
CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
EXCITATION
HAMILTONIANS
INFORMATION THEORY
JOSEPHSON JUNCTIONS
Other
Physics
QUANTUM MECHANICS
SPIN
SYMMETRY
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Summary:We present general symmetry arguments that show the appearance of doubly denerate states protected from external perturbations in a wide class of Hamiltonians. We construct the simplest spin Hamiltonian belonging to this class and study its properties both analytically and numerically. We find that this model generally has a number of low energy modes which might destroy the protection in the thermodynamic limit. These modes are qualitatively different from the usual gapless excitations as their number scales as the linear size (instead of volume) of the system. We show that the Hamiltonians with this symmetry can be physically implemented in Josephson junction arrays and that in these arrays one can eliminate the low energy modes with a proper boundary condition. We argue that these arrays provide fault tolerant quantum bits. Further we show that the simplest spin model with this symmetry can be mapped to a very special Z_2 Chern-Simons model on the square lattice. We argue that appearance of the low energy modes and the protected degeneracy is a natural property of lattice Chern-Simons theories. Finally, we discuss a general formalism for the construction of discrete Chern-Simons theories on a lattice.
ISSN:1098-0121
1550-235X
DOI:10.1103/PhysRevB.71.024505