Quantum walk on a chimera graph
Abstract
We analyze a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum-walk features such as localization that starkly distinguishes classical from quantum behavior. Motivated by technological thrusts, we study continuous-time quantum walks on enhanced variants of the chimera graph and on a diminished chimera graph with a random removal of sites. We explain the quantum walk by constructing a generating set for a suitable subgroup of graph isomorphisms and corresponding symmetry operators that commute with the quantum-walk Hamiltonian; the Hamiltonian and these symmetry operators provide a complete set of labels for the spectrum and the stationary states. Our quantum-walk characterization of the chimera graph and its variants yields valuable insights into graphs used for designing quantum-annealers.
Cite
@article{arxiv.1705.11036,
title = {Quantum walk on a chimera graph},
author = {Shu Xu and Xiangxiang Sun and Jizhou Wu and Wei-Wei Zhang and Nigum Arshed and Barry C. Sanders},
journal= {arXiv preprint arXiv:1705.11036},
year = {2018}
}