# Quantum walk on a chimera graph

## TL;DR

This paper investigates continuous-time quantum walks on chimera graphs, revealing localization phenomena and analyzing symmetries to understand quantum behavior relevant for quantum annealer design.

## Contribution

It introduces a symmetry-based framework to analyze quantum walks on chimera graphs and their variants, providing new insights into their spectral properties and localization effects.

## Key findings

- Quantum walks exhibit localization on chimera graphs.
- Symmetry operators classify the spectrum and stationary states.
- Enhanced and diminished chimera graphs show distinct quantum behaviors.

## 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.