Reaching states below the threshold energy in spin glasses via quantum annealing

• URL: http://arxiv.org/abs/2603.23602v1
• Date: Tue, 24 Mar 2026 18:00:04 GMT
• Title: Reaching states below the threshold energy in spin glasses via quantum annealing
• Abstract summary: We investigate the behavior of quantum annealing at approximate optimization in the canonical mean-field spin-glass models.<n>We demonstrate that quantum annealing is also capable of exploiting this effect to locate sub-threshold states in $O(1)$ time.<n>By deriving and numerically solving closed integro-differential equations that hold in the thermodynamic limit, our results are free from finite-size effects.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Although quantum annealing is usually considered as a method for locating the ground states of difficult spin-glass and optimization problems, its use in approximate optimization -- finding low- but not zero-energy states in a reasonably short amount of time -- is no less important. Here we investigate the behavior of quantum annealing at approximate optimization in the canonical mean-field spin-glass models, the spherical $p$-spin models, and find that it performs surprisingly well. Whereas it had long been assumed that infinite-range spin glasses have a unique ``threshold'' energy at which all quench and annealing dynamics become trapped until exponential timescales, recent work has shown that two-stage quenches can in fact reach states below the naive threshold in more generic situations. We demonstrate that quantum annealing is also capable of exploiting this effect to locate sub-threshold states in $O(1)$ time. Not only can it attain energies as far below the threshold as classical annealing algorithms, but it can do so significantly faster: for an annealing schedule taking time $τ$, the residual energy under quantum annealing decays as $τ^{-α}$ with an exponent up to twice as large as that of simulated annealing in the cases considered. Importantly, by deriving and numerically solving closed integro-differential equations that hold in the thermodynamic limit, our results are free from finite-size effects and hold for annealing times that are unambiguously independent of system size.

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