arXiv AI
Graph-Theoretic Analysis of Phase Optimization Complexity in Variational Wave Functions for Heisenberg Antiferromagnets
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arXiv AI
Oct 22
Graph-Theoretic Formulation of Hamiltonian and Ground-State Sign Structures in Heisenberg Antiferromagnets
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.
arXiv Machine Learning
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Graph neural networks and the energetic cavity method for combinatorial optimization
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...
arXiv Machine Learning
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Predicting magnetism with first-principles AI
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...
arXiv Machine Learning
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Learning angles for quantum approximate optimization
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.
arXiv Machine Learning
Jun 16
Learning ground state observables from quantum computing experiments
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.
arXiv Machine Learning
Sep 17
Solving Conic Programs over Sparse Graphs using a Variational Quantum Approach: The Case of the AC Optimal Power Flow
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...