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arXiv:2503.08149 · The Journal of Physical Chemistry A

Construction of Chemistry-Inspired Dynamic Ansatz Utilizing Generative Machine Learning

Sonaldeep Halder, Kartikey Anand, Rahul Maitra

Published Jun 17, 2025• 6 citations
arXivHTMLPDF

Abstract

Generative machine learning models like the Restricted Boltzmann Machine (RBM) provide a practical approach for ansatz construction within the quantum computing framework. This work introduces a method that efficiently leverages RBM and many-body perturbative measures to build a compact chemistry-inspired ansatz for determining accurate molecular energetics. By training on low-rank determinants derived from an approximate wave function, RBM predicts the key high-rank determinants that dominate the ground-state wave function. A shallow depth ansatz is constructed to explicitly incorporate these dominant determinants after dynamically decomposing them into low-rank components and applying many-body perturbative measures for further screening. The method requires no additional measurements beyond the initial training phase. Moreover, it incorporates Bayesian hyperparameter optimization for the RBM, ensuring efficient performance with minimal training data during its limited usage. This approach facilitates the efficient computation of molecular properties, paving the way for exploring new chemical phenomena with near-term quantum computers.

DOI
10.1021/acs.jpca.5c02346

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Generative machine learning models like the Restricted Boltzmann Machine (RBM) provide a practical approach for ansatz construction within the quantum computing framework. This work introduces a method that efficiently leverages RBM and many-body perturbative measures to build a compact chemistry-inspired ansatz for determining accurate molecular energetics. By training on low-rank determinants derived from an approximate wave function, RBM predicts the key high-rank determinants that dominate the ground-state wave function. A shallow depth ansatz is constructed to explicitly incorporate these dominant determinants after dynamically decomposing them into low-rank components and applying many-body perturbative measures for further screening. The method requires no additional measurements beyond the initial training phase. Moreover, it incorporates Bayesian hyperparameter optimization for the RBM, ensuring efficient performance with minimal training data during its limited usage. This approach facilitates the efficient computation of molecular properties, paving the way for exploring new chemical phenomena with near-term quantum computers.
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-electron Hilbert space to identify the dominant high-rank excited determinants without requiring a large number of quantum measurements. These selected excited determinants are iteratively incorporated within the ansatz through their low-rank decomposition. The reduction in the number of quantum measurements and ansatz depth manifests in the robustness of our method towards hardware noise, as demonstrated through numerical applications. Furthermore, the proposed method is highly compatible with state-of-the-art neural error mitigation techniques. This resource-efficient approach is quintessential for determining spectroscopic and other molecular properties, thereby facilitating the study of emerging chemical phenomena in the near-term quantum computing framework.
Abstract We propose a data-driven approach using a restricted Boltzmann machine (RBM) to solve the Schrödinger equation in configuration space. Traditional configuration interaction (CI) methods construct the wavefunction as a linear combination of Slater determinants, but this becomes computationally expensive due to the factorial growth in the number of configurations. Our approach extends the use of a generative model such as the RBM by incorporating a taboo list strategy to enhance efficiency and convergence. The RBM is used to efficiently identify and sample the most significant determinants, thus accelerating convergence and substantially reducing computational cost. This method achieves up to 99.99% of the correlation energy while using up to four orders of magnitude fewer determinants compared to full CI calculations and up to two orders of magnitude fewer than previous state of the art methods. Beyond efficiency, our analysis reveals that the RBM learns electron distributions over molecular orbitals by capturing quantum patterns that resemble radial distribution functions linked to molecular bonding. This suggests that the learned pattern is interpretable, highlighting the potential of machine learning for explainable quantum chemistry
An artificial neural network (ANN) with the restricted Boltzmann machine (RBM) architecture was recently proposed as a versatile variational quantum many-body wave function. In this work we provide physical insights into the performance of this ansatz. We uncover the connection between the structure of the RBM and perturbation series, which explains the excellent precision achieved by the RBM ansatz in certain simple models, demonstrated in G. Carleo and M. Troyer [Science 355, 602 (2017)]. Based on this relation, we improve the numerical algorithm to achieve a better performance of the RBM in cases where local minima complicate the convergence to the global one. Furthermore, we study the performance of a sparse RBM for approximating ground states of random, translationally invariant models in one dimension, as well as random matrix-product states. We find that the error in approximating such states exhibits a broad distribution and shows a positive correlation with the entanglement properties of the targeted state.
Machine learning has made significant contributions to the fields of chemistry and materials science, enabling the exploration of vast chemical space through large-scale quantum chemical calculations. These models provide fast and accurate predictions of atomistic chemical properties, but they have limitations when it comes to capturing the electronic degrees of freedom of a molecule. This restricts their application in reactive chemistry and chemical analysis. To address this limitation, we introduce a deep learning framework that predicts the quantum mechanical wavefunction of a molecule in a local basis of atomic orbitals. The wavefunction serves as a foundational representation from which all other ground-state properties can be derived. Our approach maintains complete access to the electronic structure through the wavefunction, while achieving computational efficiency comparable to force-field methods. Moreover, the framework captures quantum mechanics in a form that can be analytically differentiated, allowing for efficient optimization and exploration of chemical systems. We demonstrate the potential of our approach through several examples. By leveraging the predicted wavefunction, we showcase the ability to perform inverse design of molecular structures to target specific electronic property optimizations. This opens exciting avenues for tailoring molecular structures to achieve desired electronic characteristics. Additionally, our framework paves the way for enhanced synergy between machine learning and quantum chemistry, enabling more comprehensive investigations into complex chemical systems.
Sample-based Quantum Diagonalization (SQD), an extension of Quantum Selected Configuration Interaction (QSCI), has emerged as a promising hybrid quantum-classical paradigm for computing molecular ground state energies. By leveraging quantum sampling instead of variational optimization, QSCI avoids barren plateaus and enables direct reconstruction of correlated electronic wavefunctions. However, existing configuration recovery techniques primarily enforce symmetry constraints without guaranteeing optimal selection of the most physically relevant configurations, often leading to unnecessarily large subspaces and increased classical diagonalization costs. In this work, we introduce a machine-learned compact subspace generation protocol based on Restricted Boltzmann Machines (RBMs), termed QSCI-RBM, and integrate it within the Density Matrix Embedding Theory (DMET) framework. The RBM is trained on quantum-sampled configurations to learn the underlying probability distribution of dominant determinants, enabling the targeted generation of high-probability configurations. We apply this framework to the simulation of a protein-ligand complex involving the inhibitor Carmofur bound to the SARS-CoV-2 main protease (MproM^{\text{pro}}Mpro). Our results demonstrate that DMET-QSCI-RBM achieves energies within the chemical accuracy threshold by accessing only approximately 4% of the configuration subspace. In contrast, standard DMET-SQD simulations failed to reach chemical accuracy while accessing up to 20% of the subspace, even as the chemical potential itself nearly converged. These findings highlight that RBM-assisted configuration generation produces significantly more compact subspaces while preserving physical accuracy, thereby reducing classical computational overhead and enabling the scalable quantum embedding simulation of complex biological systems.