The paper presents a graph-theoretic framework for analyzing Heisenberg antiferromagnets, where the Hamiltonian in a fixed-magnetization sector is represented as a constant minus the weighted Laplacian of a Hilbert graph (HG). The ground-state energy is linked to the largest eigenvalue of this Laplacian, equivalent to a spectral relaxation of weighted Max‑Cut on the HG, while the phase-dependent part of the variational energy maps to an antiferromagnetic XY model on the same graph. Restricting to real variational states reduces the problem to an Ising model, and the optimal sign structure of the ground state can be recovered in polynomial time from the HG weights, with the bipartiteness of the HG determining whether a diagonal sign transformation can eliminate all positive off-diagonal elements.
By Mahmud Ashraf Shamim, Md Moshiur Rahman Raj, Mohamed Hibat-Allah, Ruy Fabila-Monroy, Nobuchika Okada, Paulo T. Araujo
arXiv:2609.07456v1 Announce Type: cross
Abstract: We study the use of graph neural networks (GNNs) for finding approximate ground states of Ising models. Efficiently finding these ground states is of...
By Joe Bacchus George, George T. Cantwell
arXiv:2602.09093v2 Announce Type: replace-cross
Abstract: Computational discovery of magnetic materials remains challenging because magnetism arises from the competition between kinetic energy and Co...
By Max Geier, Liang Fu
The paper presents a method for learning the mapping from combinatorial optimization problem instances to high‑quality variational angles for the Quantum Approximate Optimization Algorithm (QAOA). By training models that predict these angles, the authors replace the expensive per‑instance classical optimization with a single forward pass, achieving near‑identical solution quality while being several orders of magnitude faster. The learned models generalize to unseen graph topologies, and experiments on quantum hardware confirm that the sampled solutions are indistinguishable from those obtained with traditional solver‑derived angles.
By Johannes Jakubik, Isabelle Wittmann, Zaheed Gaffoor, Gciniwe Simphiwe Baloyi, Craig Mahlasi, Etienne Vos, Thomas Brunschwiler, Daniel J. Egger
arXiv:2606. 15983v1 Announce Type: cross Abstract: Recent theoretical progress has established conditions under which machine learning models can efficiently predict ground-state properties of gapped local Hamiltonians when trained on quantum-generated data.
By Ben Jaderberg, Freya Shah, Minjun Jeon, M. Emre Sahin, Christa Zoufal, Kunal Sharma
arXiv:2509.00341v3 Announce Type: replace-cross
Abstract: Conic programs arising in physics, quantum information, machine learning, and engineering are often defined over sparse graphs. Although such...
By Thinh Viet Le, Mark M. Wilde, Vassilis Kekatos
arXiv:2607. 10656v1 Announce Type: cross Abstract: Characterizing quantum topological phases requires measuring non-local string order parameters, demanding access to the full system, which is often experimentally unfeasible.
By Mehran Khosrojerdi, Sougato Bose, Alessandro Cuccoli, Paola Verrucchi, Abolfazl Bayat, Leonardo Banchi
arXiv:2606. 13912v1 Announce Type: cross Abstract: Neural-network quantum states (NQS) are a leading variational tool for quantum many-body physics, yet their optimization is fragile whenever the ground state carries a non-trivial sign or complex phase structure, a situation generic to gauge fields, broken time-reversal symmetry, and fermionic statistics.
By Yi-Ran Xue, Rui Wang, Baigeng Wang, Chenan Wei
arXiv:2407.11473v2 Announce Type: replace
Abstract: Maximum entropy inference and learning of graphical models are pivotal tasks in learning theory and optimization. This work extends algorithms for...
By Minbo Gao, Zhengfeng Ji, Fuchao Wei
arXiv:2606. 30358v1 Announce Type: cross Abstract: We design an algorithm for learning the coefficients of an $n$-qubit constant-local Lindbladian to $\varepsilon$ error with $O(g d^2 \log(n) / \varepsilon^2)$ total evolution time, where $g$ is the single-site energy and $d$ is the (approximate) degree of the interaction graph.
By Laura Lewis, Ewin Tang, John Wright
arXiv:2608. 11911v1 Announce Type: cross Abstract: A central promise of useful quantum advantage is the ability to compute ground states of Hamiltonian systems beyond the reach of classical simulation methods.
By Timothy Heightman, Elena Orlova, Philip Mantrov, Aleksei Ustimenko
The paper introduces a quantum method for extracting spectral features from the density of states (DOS) of a problem-dependent Hamiltonian, applied to signed graphs represented as Ising models. It demonstrates that standardized moments of the Ising DOS count signed closed walks, are switching‑invariant, and size‑free, enabling accurate learning of the frustration index with a mean error of 0.4 on 140,000 labeled graphs. The authors propose DOS‑QPE, a phase estimation technique that requires far fewer shots than traditional methods, and highlight potential applications in social network analysis, spin‑glass studies, correlation clustering, and protein‑interaction networks.