How Small-World Interactions Can Lead to Improved Quantum Annealer Designs

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There are many factors that influence the design of quantum annealing processing units. Here we address the issue of improving quantum annealing processing unit designs from the point of view of the critical behavior of spin glasses. It has been argued [Phys. Rev. X 4, 021008 (2014)] that among the most difficult Ising spin-glass ground-state problems are those related to lattices which exhibit a finite-temperature spin-glass transition. Here, we show that adding small-world couplers between qubits (spins) to the native quasi-planar quantum processing unit graph results in a topology where a disordered Ising system can undergo a finite-temperature spin-glass transition, even when an Ising spin glass on the quasi-planar native graph does not display a transition into a glassy phase at any finite temperature. To ensure that these systems can be engineered with current fabrication techniques, using large-scale Monte Carlo simulations we demonstrate that highly-constrained systems restricted to a few fabrication layers and with fixed coupler angles can also exhibit a finite-temperature spin-glass transition. This indicates that these systems might be mean-field-like, which also means that embedding highly-nonplanar problems might be simplified when compared to the underlying native topology. Our results are illustrated using the quasi-planar Chimera topology currently used in the D-Wave Systems Inc. quantum annealing machines, as well as standard two-dimensional square lattices. The presented approach can be generalized to other topologies.