  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.
