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Generalized Mean-Field Ising Model as a Benchmark Family with Exact Solutions — arXiv:2610.38803

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.38803
License (as archived): CC0-1.0
Archived: 2026-11-01T02:50:07.564Z
SHA-256 of the archived text: 55ce26381fd0cd141aef85e32a53ef0744fd273ca99bd7e90cace94ad1c6ee54
Stable URL of this page: https://metraipolis.com/documento/dc_4bd2f9512e77

How to cite

Generalized Mean-Field Ising Model as a Benchmark Family with Exact Solutions — arXiv:2610.38803 — arXiv (en), https://arxiv.org/abs/2610.38803 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_4bd2f9512e77 (Metraipolis archive dc_4bd2f9512e77, sha256 55ce26381fd0cd141aef85e32a53ef0744fd273ca99bd7e90cace94ad1c6ee54)

BibTeX

@misc{dc4bd2f9512e77,
  title = {Generalized Mean-Field Ising Model as a Benchmark Family with Exact Solutions — arXiv:2610.38803},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.38803},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_4bd2f9512e77; sha256 55ce26381fd0cd141aef85e32a53ef0744fd273ca99bd7e90cace94ad1c6ee54},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.38803. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Exactly solvable models provide opportunities to understand complex optimization problems while offering controlled benchmarks for computational methods. However, nontrivial models that combine analytical tractability with challenging optimization structure remain scarce. Here, we introduce the Generalized Mean-Field Ising (GMFI) family, a densely connected and inhomogeneous class of Ising Hamiltonians whose ground states can nevertheless be obtained exactly. This exact solution reveals a hidden low-dimensional structure and enables a complete number-theoretic classification of different system sizes and degenerate ground states. Uniquely, the GMFI family can be used to benchmark both quantum and classical optimization methods over system sizes far beyond exact diagonalization. We investigate the GMFI family using several approaches, including theoretical analysis of quantum annealing, experiments on a D-Wave quantum processor, the quantum approximate optimization algorithm (QAOA), imaginary-time evolution (ITE), greedy algorithm, simulated annealing, and a quantum-inspired greedy algorithm. Despite the GMFI model's exact solvability, it exhibits nontrivial algorithmic behavior: although the quantum-annealing gap is expected to decrease with increasing system size, it shows pronounced and unexpected system-size-dependent oscillatory signatures. These results establish GMFI models as a rare bridge between exact many-body theory, number theory, optimization, and quantum hardware, providing a scalable benchmark for identifying and understanding algorithmic limitations in classical and quantum computing.

Tema degli esploratori: fisica e astronomia (elenco arXiv quant-ph, nuovi lavori del giorno).
Categorie arXiv: Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2610.38803 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-01T02:19:43.466Z dalla pagina https://arxiv.org/list/quant-ph/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).