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We study the spin-glass transition in several Ising models of relevance forquantum annealers. We extract the spin-glass critical temperature byextrapolating the pseudo-critical properties obtained with Replica-ExchangeMonte-Carlo for finite-size systems. We find a spin-glass phase for some randomlattices (random-regular and small-world graphs) in good agreement withprevious results. However, our results for the quasi-two-dimensional graphsimplemented in the D-Wave annealers (Chimera, Zephyr, and Pegasus) indicateonly a zero-temperature spin-glass state, as their pseudo-critical temperaturedrifts towards smaller values. This implies that the asymptotic runtime to findthe low-energy configuration of those graphs is likely to be polynomial insystem size, nevertheless, this scaling may only be reached for very largesystem sizes -- much larger than existing annealers -- as we observe an abruptincrease in the computational cost of the simulations around thepseudo-critical temperatures. Thus, two-dimensional systems with localcrossings can display enough complexity to make unfeasible the search withclassical methods of low-energy configurations.

Exploring Quantum Annealing Architectures: A Spin Glass Perspective