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arXiv · 1705.11036

Quantum walk on a chimera graph

Shu Xu·Xiangxiang Sun·Jizhou Wu·Wei-Wei Zhang·Nigum Arshed·Barry C. Sanders
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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.

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Shu Xu, Xiangxiang Sun, Jizhou Wu, Wei-Wei Zhang, Nigum Arshed, Barry C. Sanders. 2018-03-19. Quantum walk on a chimera graph. https://doi.org/10.1088/1367-2630%2Faab701

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