A Transferable Machine Learning Approach to Predict Optimized Orbitals for Electronic Structure Problems

TL;DR

This paper introduces a graph neural network that predicts optimized molecular orbitals directly from geometry, enabling scalable, accurate, and transferable orbital predictions to accelerate quantum chemistry computations.

Contribution

The authors develop a GNN framework that generalizes orbital predictions to larger systems without retraining, reducing classical preprocessing in quantum algorithms.

Findings

Model achieves mean absolute energy errors of ~100 and 10 milli-Hartrees for different configurations.

Predicts orbitals that serve as effective warm-starts, reducing optimizer iterations.

Demonstrates transferability to larger, unseen hydrogenic systems without retraining.

Abstract

Variational quantum eigensolver ans\"atze hold considerable promise for ground-state energy calculations on near-term quantum hardware, yet most promising ansatz designs currently strongly depend on how well the molecular orbital basis captures the electronic correlation of the system. Computing optimized orbital coefficients via classical routines is computationally expensive and must be performed independently for each molecular geometry -- a bottleneck that limits scalability across chemical space. We present a graph neural network framework that predicts optimized orbital coefficients directly from molecular geometry and pair-wise bonding structure. Trained on hydrogenic systems of modest size ($H_4$ and $H_6$) across tens of thousands of geometries, our model transfers to larger, unseen systems ($H_8$, $H_{10}$ and $H_{12}$) without retraining -- demonstrating strong out-of-distribution generalization with respect to system size. When evaluating on structured and random configurations, and comparing against energies obtained with full classical optimization, our model reaches mean absolute energy errors $\mathcal{O}(10^2)$ and $\mathcal{O}(10)$ milli-Hartrees, respectively. Beyond energy estimation, the predicted orbitals serve as high-quality warm-start initializations that substantially reduce optimizer iterations to ground-state energy convergence. These results establish graph neural networks as an effective and scalable strategy for accelerating orbital optimization in hybrid quantum-classical workflows, directly reducing the classical pre-processing overhead that currently limits the practical deployment of variational quantum eigensolver on near-term quantum hardware.