The generative quantum eigensolver (GQE) and its application for ground state search

• URL: http://arxiv.org/abs/2401.09253v2
• Date: Tue, 30 Sep 2025 16:22:46 GMT
• Title: The generative quantum eigensolver (GQE) and its application for ground state search
• Authors: Kouhei Nakaji, Lasse Bjørn Kristensen, Ryota Kemmoku, Jorge A. Campos-Gonzalez-Angulo, Mohammad Ghazi Vakili, Haozhe Huang, Mohsen Bagherimehrab, Christoph Gorgulla, FuTe Wong, Alex McCaskey, Jin-Sung Kim, Thien Nguyen, Pooja Rao, Qi Gao, Michihiko Sugawara, Naoki Yamamoto, Alán Aspuru-Guzik,
• Abstract summary: We introduce the generative quantum eigensolver (GQE), a new quantum computational framework that operates outside the variational quantum algorithm paradigm.<n>The GQE algorithm optimize a classical generative model to produce quantum circuits with desired properties.<n>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.
• Score: 7.450827979218242
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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