Control Flow Operators in PyTorch
Yidi Wu, Thomas Bohnstingl, et al.
ICML 2025
Recent progress in quantum chemistry has been accelerated by means of quantum computing. Within the framework of Quantum-Centric Supercomputing [1], hybrid quantum-classical algorithms efficiently compute properties of matter at a scale beyond brute-force classical methods, thus alleviating some limitations related to Variational Quantum Eigensolver methods.
Typically, quantum chemistry simulations with quantum computers are based on the second-quantized electronic Hamiltonian within the Born-Oppenheimer approximation. This means calculating the one-body and two-body integrals using an approximate (classical) method, such as Hartree-Fock, given the atomic positions within a crystal unit cell. In contrast, lattice Hamiltonians are rarely used in the context of chemistry and material science. However, they are promising for applications involving Artificial Intelligence methods, as they can effectively encode the entire electronic structure within a limited number of parameters.
In this work, we investigate the band gap of periodic materials in a lattice-Hamiltonian representation by means of a hybrid, quantum-classical computational workflow. Specifically, we employ the Extended Hubbard Model (EHM), frequently used to describe the phenomenological behavior of strongly correlated systems. The EHM parameterizes the electronic Hamiltonian using a set of {tij} hopping parameters, as well as {Ui} intra-site and {Vij} inter-site Coulomb interactions, to account for localization and hybridization effects. For each candidate material, we calculate the Hamiltonian parameters self-consistently within the Density Functional Theory (DFT), based on an atomic-level description of their unit cell. The electronic Hamiltonian is then solved using hybrid quantum-classical methods, by sampling the Local Unitary Cluster Jastrow (LUCJ) ansatz within the Sample-based Quantum Diagonalization (SQD) framework. By applying this approach to materials with metal-oxide bonds, we compute key electronic properties, such as band gaps [2]. In addition, we investigate the potential of EHM-derived parameters as feature vectors for AI-driven structure-property prediction models, harnessing machine learning to bridge the gap between quantum models and material property trends.
[1] Alexeev, Yuri, et al. "Quantum-centric supercomputing for materials science: A perspective on challenges and future directions." Future Generation Computer Systems 160 (2024): 666-710.
[2] Duriez, Alan, et al. "Computing band gaps of periodic materials via sample-based quantum diagonalization." arXiv preprint arXiv:2503.10901 (2025).
Yidi Wu, Thomas Bohnstingl, et al.
ICML 2025
Gosia Lazuka, Andreea Simona Anghel, et al.
SC 2024
Ben Fei, Jinbai Liu
IEEE Transactions on Neural Networks
Robert Farrell, Rajarshi Das, et al.
AAAI-SS 2010