We introduce the generative quantum eigensolver (GQE), a new quantum computational framework that operates outside the variational quantum algorithm paradigm by applying classical generative models to quantum simulation. The GQE algorithm optimizes a classical generative model to produce quantum circuits with desired properties. Here, we develop a transformer-based implementation, which we name the generative pre-trained transformer-based (GPT) quantum eigensolver (GPT-QE). We show a proof-of-concept of training and pretraining of GPT-QE applied to electronic structure Hamiltonians, and demonstrate its ability illustrated by surpassing coupled cluster singles and doubles (CCSD) for the strong bond dissociation of the nitrogen molecule and approaching chemical accuracy. We also demonstrate the method on real quantum hardware.
@article{arxiv.2401.09253,
title = {The generative quantum eigensolver (GQE) and its application for ground state search},
author = {Kouhei Nakaji and Lasse Bjørn Kristensen and Ryota Kemmoku and Jorge A. Campos-Gonzalez-Angulo and Mohammad Ghazi Vakili and Haozhe Huang and Mohsen Bagherimehrab and Christoph Gorgulla and FuTe Wong and Alex McCaskey and Jin-Sung Kim and Thien Nguyen and Pooja Rao and Qi Gao and Michihiko Sugawara and Naoki Yamamoto and Alán Aspuru-Guzik},
journal= {arXiv preprint arXiv:2401.09253},
year = {2025}
}