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

arXiv:2607.09223

Medium-mass nuclei with neural quantum states

Bryce Fore, Jane Kim, Alessandro Lovato, Anthony J. Tropiano

Published Jul 10, 2026• 0 citations
arXivHTMLPDF

Abstract

We compute ground-state energies and charge radii of light- to medium-mass nuclei with up to $A=58$ nucleons, leveraging a variational Monte Carlo method based on Pfaffian-Jastrow neural quantum states. To further understand which elements of the nuclear Hamiltonian are "essential" to predict binding energies and charge radii across the nuclear chart with few-percent errors, we consider different interactions inspired by pionless effective field theory. Specifically, in addition to model "o" of [Phys. Rev. C 103, 054003 (2021)], we study the impact of charge-symmetry-breaking and charge-dependent terms in the nucleon-nucleon force, as well as $p$-wave contributions, which have been found to be critical for the stability of $p$-shell nuclei. In addition to its intrinsic interest, our work assesses the performance of neural quantum states in the medium-mass regime and examines the impact of these interaction modifications. Using the resulting ground-state simulations, we analyze the computational scaling of variational Monte Carlo with neural quantum states as a function of system size and computational resources, enabling projections for future large-scale calculations.

DOI
10.48550/arxiv.2607.09223

Related papers

Efficient emulation of nuclear ground states with neural-network variational Monte Carlo and eigenvector continuation

Mao Li, Yilong Yang, P. W. Zhao

An efficient emulator for \emph{ab initio} calculations of nuclear ground-state properties is developed by integrating the neural-network variational Monte Carlo framework, FeynmanNet, with the eigenvector continuation. It enables the calculation of observables for different Hamiltonians with minimal computational cost, while delivering ground-state energies with errors below $0.5\%$ compared to the full FeynmanNet results. With this emulator, the ground-state energies and charge radii of ${}^{16}\mathrm{O}$, ${}^{15}\mathrm{O}$, ${}^{14}\mathrm{O}$, ${}^{15}\mathrm{N}$, and ${}^{14}\mathrm{C}$ are computed using a nuclear Hamiltonian derived from the leading-order pionless effective field theory, with a large number of different values of low-energy constants (LECs). Then, we perform a global sensitivity analysis of the ground-state energies, charge radii, separation energies of selected nuclei for the three LECs in the Hamiltonian, to identify how each LEC contributes to the variances of these observables. It shows that the two-body LEC in the $^3S_1$ channel is the most influential LEC governing these nuclear bulk properties. Finally, the correlations among the ground-state energies of $^4$He, $^{12}$C, and $^{16}$O are investigated by varying the LECs in the Hamiltonian. The analysis reveals that the experimental ground-state energies of $^{12}$C and $^{16}$O cannot be reproduced simultaneously by varying the LECs in the leading-order pionless Hamiltonian. This suggests that additional ingredients in the leading-order Hamiltonian are required to improve its description of light nuclei. The present work establishes an efficient framework for global sensitivity analysis and uncertainty quantification in the quantum Monte Carlo calculations for light and medium-mass nuclei.

arXiv:2606.12998•Physical Review C•Jul 9, 2026•0 citations

Distilling the Essential Elements of Nuclear Binding via Neural-Network Quantum States

Alex Gnech, Bryce Fore, Anthony J. Tropiano +1 more

To distill the essential elements of nuclear binding, we seek the simplest Hamiltonian capable of modeling atomic nuclei with percent-level accuracy. A critical aspect of this endeavor consists of accurately solving the quantum many-body problem without incurring an exponential computing cost with the number of nucleons. We address this challenge by leveraging a variational Monte Carlo method based on a highly expressive neural-network quantum state ansatz. In addition to computing binding energies and charge radii of nuclei with up to A=20 nucleons, by evaluating their magnetic moments, we demonstrate that neural-network quantum states are able to correctly capture the self-emerging nuclear shell structure. To this end, we introduce a novel computational protocol based on adding an external magnetic field to the nuclear Hamiltonian, which allows the neural network to learn the preferred polarization of the nucleus within the given magnetic field.

arXiv:2308.16266•Physical Review Letters•Oct 4, 2024•23 citations

Variational Monte Carlo Calculations of A≤4 Nuclei with an Artificial Neural-Network Correlator Ansatz

C. Adams, Giuseppe Carleo, Alessandro Lovato +1 more

The complexity of many-body quantum wave functions is a central aspect of several fields of physics and chemistry where nonperturbative interactions are prominent. Artificial neural networks (ANNs) have proven to be a flexible tool to approximate quantum many-body states in condensed matter and chemistry problems. In this work we introduce a neural-network quantum state ansatz to model the ground-state wave function of light nuclei, and approximately solve the nuclear many-body Schrödinger equation. Using efficient stochastic sampling and optimization schemes, our approach extends pioneering applications of ANNs in the field, which present exponentially scaling algorithmic complexity. We compute the binding energies and point-nucleon densities of A≤4 nuclei as emerging from a leading-order pionless effective field theory Hamiltonian. We successfully benchmark the ANN wave function against more conventional parametrizations based on two- and three-body Jastrow functions, and virtually exact Green's function Monte Carlo results.

arXiv:2007.14282•Physical Review Letters•Jul 7, 2021•92 citations

Deep-neural-network approach to solving the ab initio nuclear structure problem

Yilong Yang, P. W. Zhao

Predicting the structure of quantum many-body systems from the first principles of quantum mechanics is a common challenge in physics, chemistry, and material science. Deep machine learning has proven to be a powerful tool for solving condensed matter and chemistry problems, while for atomic nuclei it is still quite challenging because of the complicated nucleon-nucleon interactions, which strongly couple the spatial, spin, and isospin degrees of freedom. By combining essential physics of the nuclear wave functions and the strong expressive power of artificial neural networks, we develop FeynmanNet, a deep-learning variational quantum Monte Carlo approach for ab initio nuclear structure. We show that FeynmanNet can provide very accurate solutions of ground-state energies and wave functions for $^{4}\mathrm{He}, ^{6}\mathrm{Li}$, and even up to $^{16}\mathrm{O}$ as emerging from the leading-order and next-to-leading-order Hamiltonians of pionless effective field theory. Compared to the conventional diffusion Monte Carlo approaches, which suffer from the severe inherent fermion-sign problem, FeynmanNet reaches such a high accuracy in a variational way and scales polynomially with the number of nucleons. Therefore, it paves the way to a highly accurate and efficient ab initio method for predicting nuclear properties based on the realistic interactions between nucleons.

arXiv:2211.13998•Physical Review C•Mar 31, 2023•32 citations

Neural Quantum States for Light Nuclei with Chiral Two- and Three-Body Interactions

Pengsheng Wen, Alexandros Gezerlis, Jeremy W. Holt

Finding high-quality trial wave functions for quantum Monte Carlo calculations of light nuclei requires a strong intuition for modeling the interparticle correlations as well as large computational resources for exploring the space of variational parameters. Moreover, for systems with three-body interactions, the wave function should account for many-body effects beyond simple pairwise correlations. In this Letter, we design neural networks that efficiently incorporate these factors to generate expressive wave function Ansätze for light nuclei using variational Monte Carlo. Our neural-network approach for A=3 nuclei can capture, already at the level of variational Monte Carlo, the overwhelming majority of the ground-state energy estimated by Green's function Monte Carlo (GFMC). It achieves a ground-state energy within 0.45% of the GFMC result for ^{3}H using the softest chiral interaction, representing a substantial improvement over standard variational Monte Carlo, which exhibits a 3.7% deviation. The result indicates the potential of neural networks to construct effective trial wave functions for quantum Monte Carlo calculations.

arXiv:2505.11442•Physical Review Letters•Apr 14, 2026•2 citations

Machine learning the single-Λ hypernuclei with neural-network quantum states

Zixiao Zhang, Yilong Yang, W. He +3 more

A thorough description of baryonic system beyond first-generation quark sector is indispensable for the maturation of nuclear ab initio methods. This study pioneers the application of neural-network quantum states to hypernuclei, with trainable parameters determined by variational Monte Carlo approach (VMC-NQS). In order to reduce the numerical uncertainty and treat the nucleons and hyperons in a unified manner, spinor grouping (SG) method is proposed to analytically integrate out isospin degrees of freedom. With SG method and spin symmetry enforcement, the Λ separation energies of s -shell hypernuclei are computed with one-thousandth level accuracy and benchmarked against existing results from stochastic variational method, showing superior performance. By comparing two different sets of Hamiltonian based on pionless effective field theory ( π ̸ EFT), we choose an optimal model and further carry out calculations of selected p -shell charge-symmetric hypernuclei with mass number up to 13, exhibiting satisfactory consistency with experimental results. Our work underscores the potential of the VMC-NQS family for the in-depth probing of hypernuclear systems.

arXiv:2508.03575•Physics Letters B•Feb 22, 2026•2 citations
We compute ground-state energies and charge radii of light- to medium-mass nuclei with up to A=58A=58A=58 nucleons, leveraging a variational Monte Carlo method based on Pfaffian-Jastrow neural quantum states. To further understand which elements of the nuclear Hamiltonian are "essential" to predict binding energies and charge radii across the nuclear chart with few-percent errors, we consider different interactions inspired by pionless effective field theory. Specifically, in addition to model "o" of [Phys. Rev. C 103, 054003 (2021)], we study the impact of charge-symmetry-breaking and charge-dependent terms in the nucleon-nucleon force, as well as ppp-wave contributions, which have been found to be critical for the stability of ppp-shell nuclei. In addition to its intrinsic interest, our work assesses the performance of neural quantum states in the medium-mass regime and examines the impact of these interaction modifications. Using the resulting ground-state simulations, we analyze the computational scaling of variational Monte Carlo with neural quantum states as a function of system size and computational resources, enabling projections for future large-scale calculations.
An efficient emulator for \emph{ab initio} calculations of nuclear ground-state properties is developed by integrating the neural-network variational Monte Carlo framework, FeynmanNet, with the eigenvector continuation. It enables the calculation of observables for different Hamiltonians with minimal computational cost, while delivering ground-state energies with errors below 0.5%0.5\%0.5% compared to the full FeynmanNet results. With this emulator, the ground-state energies and charge radii of 16O{}^{16}\mathrm{O}16O, 15O{}^{15}\mathrm{O}15O, 14O{}^{14}\mathrm{O}14O, 15N{}^{15}\mathrm{N}15N, and 14C{}^{14}\mathrm{C}14C are computed using a nuclear Hamiltonian derived from the leading-order pionless effective field theory, with a large number of different values of low-energy constants (LECs). Then, we perform a global sensitivity analysis of the ground-state energies, charge radii, separation energies of selected nuclei for the three LECs in the Hamiltonian, to identify how each LEC contributes to the variances of these observables. It shows that the two-body LEC in the 3S1^3S_13S1​ channel is the most influential LEC governing these nuclear bulk properties. Finally, the correlations among the ground-state energies of 4^44He, 12^{12}12C, and 16^{16}16O are investigated by varying the LECs in the Hamiltonian. The analysis reveals that the experimental ground-state energies of 12^{12}12C and 16^{16}16O cannot be reproduced simultaneously by varying the LECs in the leading-order pionless Hamiltonian. This suggests that additional ingredients in the leading-order Hamiltonian are required to improve its description of light nuclei. The present work establishes an efficient framework for global sensitivity analysis and uncertainty quantification in the quantum Monte Carlo calculations for light and medium-mass nuclei.
To distill the essential elements of nuclear binding, we seek the simplest Hamiltonian capable of modeling atomic nuclei with percent-level accuracy. A critical aspect of this endeavor consists of accurately solving the quantum many-body problem without incurring an exponential computing cost with the number of nucleons. We address this challenge by leveraging a variational Monte Carlo method based on a highly expressive neural-network quantum state ansatz. In addition to computing binding energies and charge radii of nuclei with up to A=20 nucleons, by evaluating their magnetic moments, we demonstrate that neural-network quantum states are able to correctly capture the self-emerging nuclear shell structure. To this end, we introduce a novel computational protocol based on adding an external magnetic field to the nuclear Hamiltonian, which allows the neural network to learn the preferred polarization of the nucleus within the given magnetic field.
The complexity of many-body quantum wave functions is a central aspect of several fields of physics and chemistry where nonperturbative interactions are prominent. Artificial neural networks (ANNs) have proven to be a flexible tool to approximate quantum many-body states in condensed matter and chemistry problems. In this work we introduce a neural-network quantum state ansatz to model the ground-state wave function of light nuclei, and approximately solve the nuclear many-body Schrödinger equation. Using efficient stochastic sampling and optimization schemes, our approach extends pioneering applications of ANNs in the field, which present exponentially scaling algorithmic complexity. We compute the binding energies and point-nucleon densities of A≤4 nuclei as emerging from a leading-order pionless effective field theory Hamiltonian. We successfully benchmark the ANN wave function against more conventional parametrizations based on two- and three-body Jastrow functions, and virtually exact Green's function Monte Carlo results.
Predicting the structure of quantum many-body systems from the first principles of quantum mechanics is a common challenge in physics, chemistry, and material science. Deep machine learning has proven to be a powerful tool for solving condensed matter and chemistry problems, while for atomic nuclei it is still quite challenging because of the complicated nucleon-nucleon interactions, which strongly couple the spatial, spin, and isospin degrees of freedom. By combining essential physics of the nuclear wave functions and the strong expressive power of artificial neural networks, we develop FeynmanNet, a deep-learning variational quantum Monte Carlo approach for ab initio nuclear structure. We show that FeynmanNet can provide very accurate solutions of ground-state energies and wave functions for 4He,6Li^{4}\mathrm{He}, ^{6}\mathrm{Li}4He,6Li, and even up to 16O^{16}\mathrm{O}16O as emerging from the leading-order and next-to-leading-order Hamiltonians of pionless effective field theory. Compared to the conventional diffusion Monte Carlo approaches, which suffer from the severe inherent fermion-sign problem, FeynmanNet reaches such a high accuracy in a variational way and scales polynomially with the number of nucleons. Therefore, it paves the way to a highly accurate and efficient ab initio method for predicting nuclear properties based on the realistic interactions between nucleons.
Finding high-quality trial wave functions for quantum Monte Carlo calculations of light nuclei requires a strong intuition for modeling the interparticle correlations as well as large computational resources for exploring the space of variational parameters. Moreover, for systems with three-body interactions, the wave function should account for many-body effects beyond simple pairwise correlations. In this Letter, we design neural networks that efficiently incorporate these factors to generate expressive wave function Ansätze for light nuclei using variational Monte Carlo. Our neural-network approach for A=3 nuclei can capture, already at the level of variational Monte Carlo, the overwhelming majority of the ground-state energy estimated by Green's function Monte Carlo (GFMC). It achieves a ground-state energy within 0.45% of the GFMC result for ^{3}H using the softest chiral interaction, representing a substantial improvement over standard variational Monte Carlo, which exhibits a 3.7% deviation. The result indicates the potential of neural networks to construct effective trial wave functions for quantum Monte Carlo calculations.
A thorough description of baryonic system beyond first-generation quark sector is indispensable for the maturation of nuclear ab initio methods. This study pioneers the application of neural-network quantum states to hypernuclei, with trainable parameters determined by variational Monte Carlo approach (VMC-NQS). In order to reduce the numerical uncertainty and treat the nucleons and hyperons in a unified manner, spinor grouping (SG) method is proposed to analytically integrate out isospin degrees of freedom. With SG method and spin symmetry enforcement, the Λ separation energies of s -shell hypernuclei are computed with one-thousandth level accuracy and benchmarked against existing results from stochastic variational method, showing superior performance. By comparing two different sets of Hamiltonian based on pionless effective field theory ( π ̸ EFT), we choose an optimal model and further carry out calculations of selected p -shell charge-symmetric hypernuclei with mass number up to 13, exhibiting satisfactory consistency with experimental results. Our work underscores the potential of the VMC-NQS family for the in-depth probing of hypernuclear systems.