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

A small-world search for quantum speedup: How small-world interactions can lead to improved quantum annealer designs