Exploring Quantum Annealing Architectures: A Spin Glass Perspective

• URL: http://arxiv.org/abs/2307.13065v1
• Date: Mon, 24 Jul 2023 18:37:10 GMT
• Title: Exploring Quantum Annealing Architectures: A Spin Glass Perspective
• Authors: Gabriel Jaum\`a, Juan Jos\'e Garc\'ia-Ripoll, and Manuel Pino
• Abstract summary: We study the spin-glass transition in several Ising models of relevance for quantum annealers. We find a spin-glass phase for some random lattices (random-regular and small-world graphs) in good agreement with previous results. Our results for the quasi-two-dimensional graphs implemented in the D-Wave annealers indicate only a zero-temperature spin-glass state.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the spin-glass transition in several Ising models of relevance for quantum annealers. We extract the spin-glass critical temperature by extrapolating the pseudo-critical properties obtained with Replica-Exchange Monte-Carlo for finite-size systems. We find a spin-glass phase for some random lattices (random-regular and small-world graphs) in good agreement with previous results. However, our results for the quasi-two-dimensional graphs implemented in the D-Wave annealers (Chimera, Zephyr, and Pegasus) indicate only a zero-temperature spin-glass state, as their pseudo-critical temperature drifts towards smaller values. This implies that the asymptotic runtime to find the low-energy configuration of those graphs is likely to be polynomial in system size, nevertheless, this scaling may only be reached for very large system sizes -- much larger than existing annealers -- as we observe an abrupt increase in the computational cost of the simulations around the pseudo-critical temperatures. Thus, two-dimensional systems with local crossings can display enough complexity to make unfeasible the search with classical methods of low-energy configurations.

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