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Hamilton-Zero: A Neural Tensor-Network Foundation Model for Ground States of Arbitrary Quadratic Qubit Hamiltonians — arXiv:2608.11911

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.11911
License (as archived): CC0-1.0
Archived: 2026-10-19T05:16:17.748Z
SHA-256 of the archived text: e0f47955e87619b774b24ee2f6f2e57708dea7477e12cd3a7b846163232fe774
Stable URL of this page: https://metraipolis.com/documento/dc_4d09faea72ff

How to cite

Hamilton-Zero: A Neural Tensor-Network Foundation Model for Ground States of Arbitrary Quadratic Qubit Hamiltonians — arXiv:2608.11911 — arXiv (en), https://arxiv.org/abs/2608.11911 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_4d09faea72ff (Metraipolis archive dc_4d09faea72ff, sha256 e0f47955e87619b774b24ee2f6f2e57708dea7477e12cd3a7b846163232fe774)

BibTeX

@misc{dc4d09faea72ff,
  title = {Hamilton-Zero: A Neural Tensor-Network Foundation Model for Ground States of Arbitrary Quadratic Qubit Hamiltonians — arXiv:2608.11911},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.11911},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_4d09faea72ff; sha256 e0f47955e87619b774b24ee2f6f2e57708dea7477e12cd3a7b846163232fe774},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.11911. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

A central promise of useful quantum advantage is the ability to compute ground states of Hamiltonian systems beyond the reach of classical simulation methods. Here we demonstrate that this problem can be effectively amortized across an arbitrary and universal set of Hamiltonians by a foundation model with $\sim0.5$B variational parameters, trained with contemporary techniques from large language models and deep reinforcement learning. To do this, we formulate $\text{spin-}1/2$ quantum ground-state learning as manifold variational optimisation over centrally odd scalar functions on $\mathrm{SU}(2)^N$. This replaces explicit Hilbert-space vector amplitudes with manifold functions on which the Hamiltonian acts through Lie derivatives, evaluated by custom automatic differentiation primitives. We prove that the resulting variational principle on this manifold preserves the $\text{spin-}1/2$ sector's ground-state upper bound using the Peter-Weyl theorem and justify the choice of such a representation with a no-go theorem for pure state foundation NQS. We then pre-train our foundation model on a dataset of hundreds of thousands of different Hamiltonian systems, varying the connection topology, system size, interaction types and strengths, bringing together a century of many-body literature. Using a novel $\mathrm{SU}(2)$ replica-exchange Langevin sampler and sharded natural-gradient optimisation, we train our model with our own extension of the Kronecker-Factored Approximate Curvature (KFAC) optimiser on system sizes up to 64 qubits. On a held-out generalisation dataset, we fine-tune our model on system sizes of up to 1024 qubits, and evaluate on systems up to 8100 qubits.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-08-13 in cs.AI).
Categorie arXiv: Quantum Physics (quant-ph) ; Disordered Systems and Neural Networks (cond-mat.dis-nn); Strongly Correlated Electrons (cond-mat.str-el); Artificial Intelligence (cs.AI).
Pagina del lavoro: https://arxiv.org/abs/2608.11911 — 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 2026-10-19T05:08:46.743Z dalla pagina https://arxiv.org/catchup/cs.AI/2026-08-13?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).