Energy Gap of Quantum Spin Glasses: A Projection Quantum Monte Carlo Study
Year: 2026
Authors: Brodoloni L., Astrakharchik G.E., Giorgini S., Pilati S.
Autors Affiliation: Univ Camerino, Sch Sci & Technol, Phys Div, CQM Grp, I-62032 Camerino, Italy; INFN, Sez Perugia, I-06123 Perugia, Italy; Univ Politecn Cataluna, Dept Fis & Enginyeria Nucl, Campus Nord B4-B5, E-08034 Barcelona, Spain; Univ Trento, Pitaevskii BEC Ctr, INO CNR, I-38123 Trento, Italy; Univ Trento, Dipartimento Fis, I-38123 Trento, Italy.
Abstract: The performance of quantum annealing for combinatorial optimization is fundamentally limited by the minimum energy gap O encountered at quantum phase transitions. We investigate the scaling of O 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 superalgebraic scaling of O, recently reported for binary couplings [M. Bernaschi et al., The quantum transition of the two-dimensional Ising spin glass, Nature (London) 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 O proportional to N-1/3. This finding provides a promising outlook for the potential efficiency of quantum annealers for optimization problems with dense connectivity.
Journal/Review: PHYSICAL REVIEW LETTERS
Volume: 137 (6) Pages from: 60403-1 to: 60403-9
More Information: We thank M. Murdaca and E. Vitali for assistance on the LUMI supercomputer. Support from the following sources is acknowledged: PNRR MUR Project No. PE0000023-NQSTI; PRIN 2022 MUR Project Hybrid algorithms for quantum simulators, No. 2022H77XB7; PRIN-PNRR 2022 MUR Project UEFA, No. P2022NMBAJ; National Centre for HPC, Big Data and Quantum Computing (ICSC) , CN00000013 Spoke 7-Materials & Molecular Sciences; CINECA Award No. INF25_lincoln; and EuroHPC Joint Undertaking for awarding access to the EuroHPC supercomputer LUMI, hosted by CSC (Finland) , through EuroHPC Development and Regular Access calls.r Spoke 7-Materials & Molecular Sciences; CINECA Award No. INF25_lincoln; and EuroHPC Joint Undertaking for awarding access to the EuroHPC supercomputer LUMI, hosted by CSC (Finland) , through EuroHPC Development and Regular Access calls.KeyWords: Critical-behavior; ModelDOI: 10.1103/fm8m-kz13
