Exploring Quantum Annealing Architectures: A Spin Glass Perspective

This work analyzes the spin-glass transition across various Ising models relevant to quantum annealers. By employing the parallel tempering method, the location of the spin-glass phase transition is extrapolated from the pseudo-critical temperature of finite-sized systems. The results confirm a spin-glass phase at finite temperature in random-regular and small-world graphs, in agreement with previous studies. However, strong evidence is obtained that this phase only occurs at zero temperature in the quasi-2D graphs of D-Wave, as their pseudo-critical temperature drifts toward zero. This implies that the asymptotic runtime to find the low-energy configuration of those graphs is likely to be polynomial in the size of the problem. Nevertheless, this scaling may only be reached for system sizes much larger than existing annealers, as the drift in the pseudo-critical temperature is slow. This slowness, together with an abrupt increase in thermalization times around the pseudo-critical temperature, may render the search for low-energy configurations with classical methods impractical. The search for quantum advantage with quantum annealers requires finding families of problems in which classical methods fail, leaving room for improvement. In search of these families and their characteristics, Ising problems with the topologies of D-Wave's annealers are studied and a dichotomy is reconciled: in theory, they should be easy, but in practice, they are hard. image