Protected qubits and Chern-Simons theories in Josephson junction arrays
- 7 January 2005
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 71 (2), 024505
- https://doi.org/10.1103/physrevb.71.024505
Abstract
We present general symmetry arguments that show the appearance of doubly degenerate 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 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.
Keywords
This publication has 26 references indexed in Scilit:
- Superconducting Tetrahedral Quantum BitsPhysical Review Letters, 2004
- Topological Order in the Insulating Josephson Junction ArrayPhysical Review Letters, 2003
- Fault-tolerant quantum computation by anyonsAnnals of Physics, 2003
- Possible realization of an ideal quantum computer in Josephson junction arrayPhysical Review B, 2002
- Topological quantum memoryJournal of Mathematical Physics, 2002
- Topologically protected quantum bits using Josephson junction arraysNature, 2002
- Quantum computingReports on Progress in Physics, 1998
- Reliable quantum computersProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1998
- Quantum computation and Shor's factoring algorithmReviews of Modern Physics, 1996
- Scheme for reducing decoherence in quantum computer memoryPhysical Review A, 1995