From Majorana Fermions to Topological Order
Abstract
We consider a system consisting of a 2D network of links between Majorana fermions on superconducting islands. We show that the fermionic Hamiltonian modeling this system is topologically-ordered in a region of parameter space. In particular we show that Kitaev's toric code emerges in fourth-order perturbation theory. By using a Jordan-Wigner transformation we can map the model onto a family of signed 2D Ising models in a transverse field where the signs (FM or AFM) are determined by additional gauge bits. Our mapping allows an understanding of the non-perturbative regime and the phase transition to a non-topological phase. We discuss the physics behind a possible implementation of this model and argue how it can be used for topological quantum computation by adiabatic changes in the Hamiltonian.
Keywords
Cite
@article{arxiv.1201.3757,
title = {From Majorana Fermions to Topological Order},
author = {Barbara M. Terhal and Fabian Hassler and David P. DiVincenzo},
journal= {arXiv preprint arXiv:1201.3757},
year = {2012}
}
Comments
4+4 pages, 5 figures. v2 has a new reference and a few new comments. In v3: yet another new reference and Supplementary Material is renamed Appendix. In v4: several typos are corrected, to appear in Phys. Rev. Lett