Energy gap of quantum spin glasses: a projection quantum Monte Carlo study
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arXiv
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| Format: | Preprint |
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2026
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| author | Brodoloni, L. Astrakharchik, G. E. Giorgini, S. Pilati, S. |
| author_facet | Brodoloni, L. Astrakharchik, G. E. Giorgini, S. Pilati, S. |
| contents | The performance of quantum annealing for combinatorial optimization is fundamentally limited by the minimum energy gap $Δ$ encountered at quantum phase transitions. We investigate the scaling of $Δ$ with system size $N$ for two paradigmatic quantum spin-glass models: the two-dimensional Edwards-Anderson (2D-EA) and the all-to-all Sherrington-Kirkpatrick (SK) models. Utilizing a newly proposed unbiased energy-gap estimator for continuous-time projection quantum Monte Carlo simulations, complemented by high-performance sparse eigenvalue solvers, we characterize the gap distributions across disorder realizations. It is found that, in the 2D-EA case, the inverse-gap distribution develops a fat tail with infinite variance as $N$ increases. This indicates that the unfavorable super-algebraic scaling of $Δ$, recently reported for binary couplings [Nature 631, 749 (2024)], persists for the Gaussian disorder considered here, pointing to a universal feature of 2D spin glasses. Conversely, the SK model retains a finite-variance distribution, with the disorder-averaged gap following a rather slow power law, close to $Δ\propto N^{-1/3}$. This finding provides a promising outlook for the potential efficiency of quantum annealers for optimization problems with dense connectivity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20108 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Energy gap of quantum spin glasses: a projection quantum Monte Carlo study Brodoloni, L. Astrakharchik, G. E. Giorgini, S. Pilati, S. Disordered Systems and Neural Networks Statistical Mechanics Computational Physics Quantum Physics The performance of quantum annealing for combinatorial optimization is fundamentally limited by the minimum energy gap $Δ$ encountered at quantum phase transitions. We investigate the scaling of $Δ$ with system size $N$ for two paradigmatic quantum spin-glass models: the two-dimensional Edwards-Anderson (2D-EA) and the all-to-all Sherrington-Kirkpatrick (SK) models. Utilizing a newly proposed unbiased energy-gap estimator for continuous-time projection quantum Monte Carlo simulations, complemented by high-performance sparse eigenvalue solvers, we characterize the gap distributions across disorder realizations. It is found that, in the 2D-EA case, the inverse-gap distribution develops a fat tail with infinite variance as $N$ increases. This indicates that the unfavorable super-algebraic scaling of $Δ$, recently reported for binary couplings [Nature 631, 749 (2024)], persists for the Gaussian disorder considered here, pointing to a universal feature of 2D spin glasses. Conversely, the SK model retains a finite-variance distribution, with the disorder-averaged gap following a rather slow power law, close to $Δ\propto N^{-1/3}$. This finding provides a promising outlook for the potential efficiency of quantum annealers for optimization problems with dense connectivity. |
| title | Energy gap of quantum spin glasses: a projection quantum Monte Carlo study |
| topic | Disordered Systems and Neural Networks Statistical Mechanics Computational Physics Quantum Physics |
| url | https://arxiv.org/abs/2602.20108 |