  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.
