Machine-Learned Representations of Basis Sets and Their Application in Quantum Computational Chemistry

Abstract

Quantum simulations of electronic structure promise to deliver significant speedups over classical methods, but remain limited by the number of qubits on near-term devices. A key strategy to reduce quantum resource requirements is to truncate the molecular Hilbert space via compact and efficient basis sets. However, most optimized basis sets either rely on predefined heuristics or require expensive classical computations, such as CASSCF orbital optimization or ℓ1-norm minimization of the Hamiltonian. In this work, we introduce a general machine learning framework for fast basis set prediction in quantum computational chemistry. Our method employs an equivariant graph neural network that outputs a Hermitian matrix encoding optimized molecular orbitals. The eigenvectors of this matrix define a transferable and efficient basis set, trained on orbitals obtained via CASSCF and Hamiltonian ℓ1 norm optimization. We evaluate our model on hydrogen chains and demonstrate that the predicted bases achieve energy accuracy and Hamiltonian sparsity comparable to orbital-optimized methods, while reducing classical preprocessing time. In addition, the predicted orbitals can be directly used as high-quality initial guesses for CASSCF calculations, further accelerating their convergence.