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This study introduces an improved estimation technique within continuous-time projection quantum Monte Carlo to analyze energy gaps in 2D Edwards-Anderson and Sherrington-Kirkpatrick spin glass models. By clarifying how these minimum energy gaps scale with system size, the research provides critical theoretical insights into the fundamental performance limits of quantum annealing for combinatorial optimization problems.
Projection Monte Carlo Estimates Quantum Spin Glass Gaps
The minimum energy gap Δ, encountered at quantum phase transitions, fundamentally limits the performance of quantum annealing for combinatorial optimization. Researchers investigated the scaling of Δ with system size N for the two-dimensional Edwards-Anderson and the all-to-all Sherrington-Kirkpatrick models, utilizing a new estimator for continuous-time projection quantum Monte Carlo simulations.
Researchers have discovered a surprising persistence in the limitations facing quantum annealing, a technique for solving complex optimization problems. A study led by L. Brodoloni, G.E. Astrakharchik, S. Giorgini, and S. Pilati of Università di Camerino and colleagues reveals that the inverse-gap distribution in two-dimensional quantum spin glasses develops a "fat tail with infinite variance" as system size increases. This finding indicates that unfavorable super-algebraic scaling of the minimum energy gap, previously reported in Nature 631, 749 (2024) for binary couplings, extends to systems with Gaussian disorder, suggesting a universal characteristic of 2D spin glasses. The team also found the all-to-all Sherrington-Kirkpatrick model exhibits a finite-variance distribution, offering a…
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