Nuclear quantum many-body methods rely on integral transform techniques to infer properties of electroweak response functions from ground-state expectation values. Retrieving the energy dependence of these responses is highly non-trivial, especially for quantum Monte Carlo methods, as it requires inverting the Laplace transform -- a notoriously ill-posed problem. In this work, we propose an artificial neural network architecture suitable for accurate response function reconstruction with precise estimation of the uncertainty of the inversion. We demonstrate the capabilities of this new architecture benchmarking it against Maximum Entropy and previously developed neural network methods designed for a similar task, paying particular attention to its robustness against increasing noise in the input Euclidean responses.
Nuclear quantum many-body methods rely on integral transform techniques to infer properties of electroweak response functions from ground-state expectation values. Retrieving the energy dependence of these responses is highly non-trivial, especially for quantum Monte Carlo methods, as it requires inverting the Laplace transform -- a notoriously ill-posed problem. In this work, we propose an artificial neural network architecture suitable for accurate response function reconstruction with precise estimation of the uncertainty of the inversion. We demonstrate the capabilities of this new architecture benchmarking it against Maximum Entropy and previously developed neural network methods designed for a similar task, paying particular attention to its robustness against increasing noise in the input Euclidean responses.
We introduce a variational Monte Carlo framework that combines neural-network quantum states with the Lorentz integral transform technique to compute the dynamical properties of self-bound quantum many-body systems in continuous Hilbert spaces. While broadly applicable to various quantum systems, including atoms and molecules, in this initial application we focus on the photoabsorption cross section of light nuclei, where benchmarks against numerically exact techniques are available. Our accurate theoretical predictions are complemented by robust uncertainty quantification, enabling meaningful comparisons with experiments. We demonstrate that a relatively simple nuclear Hamiltonian-based on a leading-order pionless EFT expansion and known to accurately reproduce ground-state energies of nuclei with A≤40-also provides a reliable description of the photoabsorption cross section.
A long-standing goal of nuclear theory is to explain how the structure and dynamics of atomic nuclei and neutron-star matter emerge from the underlying interactions among protons and neutrons. Achieving this goal requires solving the nuclear quantum many-body problem with high accuracy across a wide range of length scales and density regimes. In this review, we discuss how artificial neural network representations of the nuclear many-body wave function have significantly extended the capabilities of continuum quantum Monte Carlo methods. In particular, neural network quantum states enable calculations of larger systems than were previously accessible and provide a flexible framework for capturing phenomena that challenge conventional approaches, including the emergence of nuclear clusters and superfluid phases in dense matter. We highlight recent applications to finite nuclei, infinite nuclear and neutron matter, and dynamical processes relevant to lepton-nucleus and nucleus-nucleus scattering. We also discuss conceptual and methodological connections with condensed matter physics, emphasizing developments in neural network quantum states that bridge strongly correlated systems across disciplines. Together, these developments demonstrate how neural-network methods open new avenues toward unified and accurate descriptions of nuclear structure, matter, and reactions.
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, and even up to 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.
Recent advances in machine learning have facilitated numerically accurate solution of the electronic Schrödinger equation (SE) by integrating various neural network (NN)-based wave function ansatzes with variational Monte Carlo methods. Nevertheless, such NN-based methods are all based on the Born-Oppenheimer approximation (BOA) and require computationally expensive training for each nuclear configuration. In this work, we propose a novel NN architecture, SchrödingerNet, to solve the full electronic-nuclear SE by defining a loss function designed to equalize local energies across the system. This approach is based on a translationally, rotationally and permutationally symmetry-adapted total wave function ansatz that includes both nuclear and electronic coordinates. This strategy not only allows for an efficient and accurate generation of a continuous potential energy surface at any geometry within the well-sampled nuclear configuration space, but also incorporates non-BOA corrections, through a single training process. Comparison with benchmarks of atomic and small molecular systems demonstrates its accuracy and efficiency.
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 16O, 15O, 14O, 15N, and 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 channel is the most influential LEC governing these nuclear bulk properties. Finally, the correlations among the ground-state energies of 4He, 12C, and 16O are investigated by varying the LECs in the Hamiltonian. The analysis reveals that the experimental ground-state energies of 12C and 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.
Quantum many-body computation is a central challenge across multiple domains of scientific research, and Monte Carlo method has emerged as one of the most effective numerical techniques for investigating large-scale many-body systems. In recent years, the integration of Monte Carlo methods with machine learning has led to the development of neural quantum state approach. Quantum neural networks (QNNs) offer superior expressiveness compared to classical neural networks. In this paper, we propose a novel Quantum Neural Network Quantum State (QNNQS) method, based on the variational Monte Carlo framework. This approach leverages a quantum neural network to represent the many-body quantum state, and optimizes it iteratively through gradient descent to determine the ground-state energy. To assess the performance of this method, we conduct simulations of the one-dimensional transverse-field Ising model, investigating the influence of quantum circuit architecture on circuit expressibility, entangling capability, and computational accuracy. The results demonstrate that the QNNQS method achieves comparable simulation accuracy while utilizing significantly fewer parameters and requiring less training resources than classical network quantum state methods.