Jun 2026· arXiv.org· Vol abs/2606.28911· 0 citations· 52 references
Computer SciencePhysics
TL;DR
MALOQ (Massively Accelerated Learning of Operators for Quantum Transport) is introduced, an application built to train on and predict electronic-structure matrices for systems made of few to 100k atoms, described by large basis sets, and covering a wide range of atomic elements.
Abstract
Machine-learned (ML) operator models can be trained to predict density functional theory (DFT) Hamiltonian/density matrices at significantly reduced computational cost, thus extending electronic-structure calculations to previously unfeasible scales. Here, we introduce MALOQ (Massively Accelerated Learning of Operators for Quantum Transport), an application built to train on and predict electronic-structure matrices for systems made of few to 100k atoms, described by large basis sets, and covering a wide range of atomic elements. Based on a state-of-the-art, SO(2)-equivariant backbone architecture, MALOQ provides (i) custom data-processing kernels to handle high-rank Hamiltonian matrix data and (ii) a scalable edge-wise distribution of atomic graph(s). Trained on the largest molecular Hamiltonian datasets available today, it reduces time-per-epoch by over 30% compared to a molecule-wise-distributed framework, and enables inference on material graphs of arbitrary size. We demonstrate scalable training and inference for 3,000-12,000 atoms on the Alps supercomputer, up to 192 GPUs and 256 GPUs, respectively.
While machine learning interatomic potentials (MLiPs) have matured to revolutionize material science, deep learning models for electronic structure are just beginning to emerge and restricted, almost exclusively, to non-orthogonal basis Hamiltonians. We introduce G(Wa)NN, the first deep-learning model capable of generating the electronic Hamiltonian of solid-state systems in an orthogonal Wannier basis. G(Wa)NN is trained on an unprecedented, diverse dataset of more than 111K Wannier Hamiltonians (150M+ hopping matrices) spanning 69 elements. The combination of optimized inference and linear-scaling methods for orthogonal Hamiltonians unlock transport simulations at massive scales (10K+ atoms). Crucially, the framework supports local finetuning, allowing users to adapt the base model to custom Wannier Hamiltonian datasets. To seamlessly translate these predictions into physical observables, we introduce Tailwater, a Python package providing an API interface to G(Wa)NN alongside a high performance post-processing library. Tailwater enables automated projection of the predicted Hamiltonian into an arbitrary low-energy subspace-directly mirroring familiar Wannier90 workflows-and includes a suite of Kernel Polynomial Method (KPM) functions that exploit the orthogonal basis to achieve strict linear scaling for spectral observables. The Tailwater ecosystem, with the G(Wa)NN model at its core, aims to help bridge the gap between deep learning and macro-scale quantum transport simulations.
This work examines when structured long-range connectivity provides a useful resource, focusing on sparse power-of-two (PWR2) coupling graphs, and identifies circuit geometry and qubit reconfigurability as task-dependent resources for variational algorithms.
Helene M. Losl, Aydin Deger, Andrew J. Daley· 0 citations
Results indicate that the topology-aligned inductive bias is the active ingredient driving parameter efficiency at QM9 scale, with implications for matched-baseline benchmarking in quantum machine learning.
This work presents spectral Born machines, a class of quantum generative models that results from viewing and generalizing the class of IQP Born machines through the lens of group Fourier analysis, and suggests that highly over-parameterized spectral Born machines may be immune to overfitting, even in strongly data-scarce regimes.
Austin L. Huang, William Maxwell, Vasilis Belis et al.· 3 citations
Mandala is a modular software framework for learning block-sparse electronic-structure matrices with E(3)-equivariant graph neural networks that connects electronic-structure learning and observable-guided modeling while retaining a representation tied to quantum-mechanical operators rather than only scalar or vector targets as in MLIPs.
B. Brzoza, Wiktoria Szopa, Z. Elabid et al.· 0 citations
This thesis investigates the application of machine-learning methods in the context of quantum computing and neutrino physics, with particular emphasis on the construction of effective representations for complex, high-dimensional data. The first part of the work is devoted to Quantum Extreme Learning Machines (QELMs), a hybrid quantum--classical framework in which classical data are encoded into quantum states and processed through fixed quantum dynamics, while learning is performed by a classical readout layer. Within this framework, we analyze the role of encoding strategies, feature-reduction methods, Hamiltonian structure, and measurement, with particular focus on the relationship between quantum dynamics, expressivity, entanglement, and classical simulability. The second part of the thesis concerns the application of deep learning to the analysis of images produced by water Cherenkov detectors in neutrino physics. Convolutional architectures, including residual networks, are developed for the classification of complex events in realistic simulated datasets, showing that such models can effectively extract relevant information from detector data. Taken together, these results highlight the potential of machine learning, in both its classical and quantum forms, as a powerful framework for the analysis of complex data in fundamental physics, while also outlining relevant challenges and directions for future research.
