Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Science Advances

Improving potential energy surfaces using measured Feshbach resonance states

Karl P. Horn, Luis Itza Vazquez-Salazar, Christiane P. Koch, Markus Meuwly

Published Mar 1, 2024• 18 citations
Publisher

Abstract

The structure and dynamics of a molecular system is governed by its potential energy surface (PES), representing the total energy as a function of the nuclear coordinates. Obtaining accurate potential energy surfaces is limited by the exponential scaling of Hilbert space, restricting quantitative predictions of experimental observables from first principles to small molecules with just a few electrons. Here, we present an explicitly physics-informed approach for improving and assessing the quality of families of PESs by modifying them through linear coordinate transformations based on experimental data. We demonstrate this “morphing” of the PES for the He ‐ H 2 + complex using recent comprehensive Feshbach resonance (FR) measurements for reference PESs at three different levels of quantum chemistry. In all cases, the positions and intensities of peaks in the energy distributions are improved. We find these observables to be mainly sensitive to the long-range part of the PES.

DOI
10.1126/sciadv.adi6462

Related papers

Improving Potential Energy Surfaces Using Experimental Feshbach Resonance Tomography

Horn, Karl P., Vazquez-Salazar, Luis Itza, Christiane P. Koch +1 more

The structure and dynamics of a molecular system is governed by its potential energy surface (PES), representing the total energy as a function of the nuclear coordinates. Obtaining accurate potential energy surfaces is limited by the exponential scaling of Hilbert space, restricting quantitative predictions of experimental observables from first principles to small molecules with just a few electrons. Here, we present an explicitly physics-informed approach for improving and assessing the quality of families of PESs by modifying them through linear coordinate transformations based on experimental data. We demonstrate this "morphing" of the PES for the He-H$_{2}^{+}$ complex for reference surfaces at three different levels of quantum chemistry and using recent comprehensive Feshbach resonance(FR) measurements. In all cases, the positions and intensities of peaks in the collision cross-section are improved. We find these observables to be mainly sensitive to the long-range part of the PES.

arXiv:2309.16491•Sep 28, 2023•0 citations

Feshbach Resonances in Cold Collisions: Benchmarking State-of-the-Art Ab Initio Potential Energy Surfaces

Karl P. Horn, Meenu Upadhyay, Baruch Margulis +4 more

High Resolution Image Download MS PowerPoint Slide High-quality potential energy surfaces (PESs) are prerequisites for quantitative atomistic simulations with both quantum and classical dynamics approaches. The ultimate test for the validity of a PES entails comparisons with judiciously chosen experimental observables. Here we ask whether cold collision measurements are sufficiently informative to validate and distinguish between high-level, state-of-the art PESs for the strongly interacting Ne–H 2 + system. We show that measurement of the final state distributions for a process that involves several metastable intermediate states is sufficient to identify the PES that captures the long-range interactions properly. Furthermore, we show that a modest increase in the experimental energy resolution will allow for resolving individual Feshbach resonances and enable a quantitative probe of the interactions in the short and intermediate ranges.

arXiv:2408.13197•The Journal of Physical Chemistry Letters•Jul 28, 2025•5 citations

Exploring accurate potential energy surfaces via integrating variational quantum eigensovler with machine learning

Yanxian Tao, Xiongzhi Zeng, Fan Yi +3 more

The potential energy surface (PES) is crucial for interpreting a variety of chemical reaction processes. However, predicting accurate PESs with high-level electronic structure methods is a challenging task due to the high computational cost. As an appealing application of quantum computing, we show in this work that variational quantum algorithms can be integrated with machine learning (ML) techniques as a promising scheme for exploring accurate PESs. Different from using a ML model to represent the potential energy, we encode the molecular geometry information into a deep neural network (DNN) for representing parameters of the variational quantum eigensolver (VQE), leaving the PES to the wave function ansatz. Once the DNN model is trained, the variational optimization procedure that hinders the application of the VQE to complex systems is avoided and thus the evaluation of PESs is significantly accelerated. Numerical results demonstrate that a simple DNN model is able to reproduce accurate PESs for small molecules.

arXiv:2206.03637•Jun 8, 2022•0 citations

Exploring Accurate Potential Energy Surfaces via Integrating Variational Quantum Eigensolver with Machine Learning

Yanxian Tao, Xiongzhi Zeng, Yi Fan +3 more

The potential energy surface (PES) is crucial for interpreting a variety of chemical reaction processes. However, predicting accurate PESs with high-level electronic structure methods is a challenging task due to the high computational cost. As an appealing application of quantum computing, we show in this work that variational quantum algorithms can be integrated with machine learning (ML) techniques as a promising scheme for exploring accurate PESs. Different from using a ML model to represent the potential energy, we encode the molecular geometry information into a deep neural network (DNN) to represent parameters of the variational quantum eigensolver (VQE), leaving the PES to the wave function ansatz. Once the DNN model is trained, the variational optimization procedure that hinders the application of the VQE to complex systems is avoided, and thus the evaluation of PESs is significantly accelerated. Numerical results demonstrate that a simple DNN model is able to reproduce accurate PESs for small molecules.

The Journal of Physical Chemistry Letters•Jul 11, 2022•17 citations

Quantum eigenvector continuation for chemistry applications

Carlos Mejuto-Zaera, Alexander F. Kemper

Abstract A typical task for classical and quantum computing in chemistry is finding a potential energy surface (PES) along a reaction coordinate, which involves solving the quantum chemistry problem for many points along the reaction path. Developing algorithms to accomplish this task on quantum computers has been an active area of development, yet finding all the relevant eigenstates along the reaction coordinate remains a difficult problem, and determining PESs is thus a costly proposal. In this paper, we demonstrate the use of a eigenvector continuation—a subspace expansion that uses a few eigenstates as a basis—as a tool for rapidly exploring PESs. We apply this to determining the binding PES or torsion PES for several molecules of varying complexity. In all cases, we show that the PES can be captured using relatively few basis states; suggesting that a significant amount of (quantum) computational effort can be saved by making use of already calculated ground states in this manner.

arXiv:2305.00060•Electronic Structure•Oct 9, 2023•11 citations

Generating Approximate Ground States of Molecules Using Quantum Machine Learning

Jack Ceroni, Torin F. Stetina, Mária Kieferová +3 more

The potential energy surface (PES) of molecules with respect to their nuclear positions is a primary tool in understanding chemical reactions from first principles. However, obtaining this information is complicated by the fact that sampling a large number of ground states over a high-dimensional PES can require a vast number of state preparations. In this work, we propose using a generative quantum machine learning model to prepare quantum states at arbitrary points on the PES. The model is trained using quantum data consisting of ground-state wavefunctions associated with different classical nuclear coordinates. Our approach uses a classical neural network to convert the nuclear coordinates of a molecule into quantum parameters of a variational quantum circuit. The model is trained using a fidelity loss function to optimize the neural network parameters. We show that gradient evaluation is efficient and numerically demonstrate our method's ability to prepare wavefunctions on the PES of hydrogen chains, water, and beryllium hydride. In all cases, we find that a small number of training points are needed to achieve very high overlap with the groundstates in practice. From a theoretical perspective, we further prove limitations on these protocols by showing that if we were able to learn across an avoided crossing using a small number of samples, then we would be able to violate Grover's lower bound. Additionally, we prove lower bounds on the amount of quantum data needed to learn a locally optimal neural network function using arguments from quantum Fisher information. This work further identifies that quantum chemistry can be an important use case for quantum machine learning.

arXiv:2210.05489•Oct 11, 2022•6 citations
The structure and dynamics of a molecular system is governed by its potential energy surface (PES), representing the total energy as a function of the nuclear coordinates. Obtaining accurate potential energy surfaces is limited by the exponential scaling of Hilbert space, restricting quantitative predictions of experimental observables from first principles to small molecules with just a few electrons. Here, we present an explicitly physics-informed approach for improving and assessing the quality of families of PESs by modifying them through linear coordinate transformations based on experimental data. We demonstrate this “morphing” of the PES for the He ‐ H 2 + complex using recent comprehensive Feshbach resonance (FR) measurements for reference PESs at three different levels of quantum chemistry. In all cases, the positions and intensities of peaks in the energy distributions are improved. We find these observables to be mainly sensitive to the long-range part of the PES.
The structure and dynamics of a molecular system is governed by its potential energy surface (PES), representing the total energy as a function of the nuclear coordinates. Obtaining accurate potential energy surfaces is limited by the exponential scaling of Hilbert space, restricting quantitative predictions of experimental observables from first principles to small molecules with just a few electrons. Here, we present an explicitly physics-informed approach for improving and assessing the quality of families of PESs by modifying them through linear coordinate transformations based on experimental data. We demonstrate this "morphing" of the PES for the He-H2+_{2}^{+}2+​ complex for reference surfaces at three different levels of quantum chemistry and using recent comprehensive Feshbach resonance(FR) measurements. In all cases, the positions and intensities of peaks in the collision cross-section are improved. We find these observables to be mainly sensitive to the long-range part of the PES.
High Resolution Image Download MS PowerPoint Slide High-quality potential energy surfaces (PESs) are prerequisites for quantitative atomistic simulations with both quantum and classical dynamics approaches. The ultimate test for the validity of a PES entails comparisons with judiciously chosen experimental observables. Here we ask whether cold collision measurements are sufficiently informative to validate and distinguish between high-level, state-of-the art PESs for the strongly interacting Ne–H 2 + system. We show that measurement of the final state distributions for a process that involves several metastable intermediate states is sufficient to identify the PES that captures the long-range interactions properly. Furthermore, we show that a modest increase in the experimental energy resolution will allow for resolving individual Feshbach resonances and enable a quantitative probe of the interactions in the short and intermediate ranges.
The potential energy surface (PES) is crucial for interpreting a variety of chemical reaction processes. However, predicting accurate PESs with high-level electronic structure methods is a challenging task due to the high computational cost. As an appealing application of quantum computing, we show in this work that variational quantum algorithms can be integrated with machine learning (ML) techniques as a promising scheme for exploring accurate PESs. Different from using a ML model to represent the potential energy, we encode the molecular geometry information into a deep neural network (DNN) for representing parameters of the variational quantum eigensolver (VQE), leaving the PES to the wave function ansatz. Once the DNN model is trained, the variational optimization procedure that hinders the application of the VQE to complex systems is avoided and thus the evaluation of PESs is significantly accelerated. Numerical results demonstrate that a simple DNN model is able to reproduce accurate PESs for small molecules.
The potential energy surface (PES) is crucial for interpreting a variety of chemical reaction processes. However, predicting accurate PESs with high-level electronic structure methods is a challenging task due to the high computational cost. As an appealing application of quantum computing, we show in this work that variational quantum algorithms can be integrated with machine learning (ML) techniques as a promising scheme for exploring accurate PESs. Different from using a ML model to represent the potential energy, we encode the molecular geometry information into a deep neural network (DNN) to represent parameters of the variational quantum eigensolver (VQE), leaving the PES to the wave function ansatz. Once the DNN model is trained, the variational optimization procedure that hinders the application of the VQE to complex systems is avoided, and thus the evaluation of PESs is significantly accelerated. Numerical results demonstrate that a simple DNN model is able to reproduce accurate PESs for small molecules.
Abstract A typical task for classical and quantum computing in chemistry is finding a potential energy surface (PES) along a reaction coordinate, which involves solving the quantum chemistry problem for many points along the reaction path. Developing algorithms to accomplish this task on quantum computers has been an active area of development, yet finding all the relevant eigenstates along the reaction coordinate remains a difficult problem, and determining PESs is thus a costly proposal. In this paper, we demonstrate the use of a eigenvector continuation—a subspace expansion that uses a few eigenstates as a basis—as a tool for rapidly exploring PESs. We apply this to determining the binding PES or torsion PES for several molecules of varying complexity. In all cases, we show that the PES can be captured using relatively few basis states; suggesting that a significant amount of (quantum) computational effort can be saved by making use of already calculated ground states in this manner.
The potential energy surface (PES) of molecules with respect to their nuclear positions is a primary tool in understanding chemical reactions from first principles. However, obtaining this information is complicated by the fact that sampling a large number of ground states over a high-dimensional PES can require a vast number of state preparations. In this work, we propose using a generative quantum machine learning model to prepare quantum states at arbitrary points on the PES. The model is trained using quantum data consisting of ground-state wavefunctions associated with different classical nuclear coordinates. Our approach uses a classical neural network to convert the nuclear coordinates of a molecule into quantum parameters of a variational quantum circuit. The model is trained using a fidelity loss function to optimize the neural network parameters. We show that gradient evaluation is efficient and numerically demonstrate our method's ability to prepare wavefunctions on the PES of hydrogen chains, water, and beryllium hydride. In all cases, we find that a small number of training points are needed to achieve very high overlap with the groundstates in practice. From a theoretical perspective, we further prove limitations on these protocols by showing that if we were able to learn across an avoided crossing using a small number of samples, then we would be able to violate Grover's lower bound. Additionally, we prove lower bounds on the amount of quantum data needed to learn a locally optimal neural network function using arguments from quantum Fisher information. This work further identifies that quantum chemistry can be an important use case for quantum machine learning.