Solving the nuclear pairing model with neural network quantum states

Abstract

We present a variational Monte Carlo method that solves the nuclear many-body problem in the occupation number formalism exploiting an artificial neural network representation of the ground-state wave function. A memory-efficient version of the stochastic reconfiguration algorithm is developed to train the network by minimizing the expectation value of the Hamiltonian. We benchmark this approach against widely used nuclear many-body methods by solving a model used to describe pairing in nuclei for different types of interaction and different values of the interaction strength. Despite its polynomial computational cost, our method outperforms coupled-cluster and provides energies that are in excellent agreement with the numerically-exact full configuration interaction values.

9 pages, 3 figures

References in corpus (28)

• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Quantum Monte Carlo methods for nuclear physics
• Coupled-cluster computations of atomic nuclei
• Deep neural network solution of the electronic Schrödinger equation
• Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks
• Pairing in nuclear systems: from neutron stars to finite nuclei
• The In-Medium Similarity Renormalization Group: A Novel Ab Initio Method for Nuclei
• Quantum Natural Gradient
• Discrepancy between experimental and theoretical $\beta$-decay rates resolved from first principles
• Wave function optimization in the variational Monte Carlo method
• Ab initio predictions link the neutron skin of ${}^{208}$Pb to nuclear forces
• Fermionic neural-network states for ab-initio electronic structure
• Optimizing large parameter sets in variational quantum Monte Carlo
• Exact solution of the nuclear pairing problem
• Fermionic Wave Functions from Neural-Network Constrained Hidden States
• Variational Monte Carlo calculations of $\mathbf{A}\le 4$ nuclei with an artificial neural-network correlator ansatz
• Many-body characterization of topological superconductivity: The Richardson-Gaudin-Kitaev chain
• Localized Majorana-like modes in a number conserving setting: An exactly solvable model
• Self-consistent Green's function theory for atomic nuclei
• Nuclear Charge Radii of the Nickel Isotopes ${}^{58-68,70}$Ni
• Solving the Richardson equations for Fermions
• Machine learning the deuteron
• Phases of two-dimensional spinless lattice fermions with first-quantized deep neural-network quantum states
• Nuclear pairing: new perspectives
• Exactly solvable pairing Hamiltonian for heavy nuclei
• Nuclei with up to $\mathbf{A}=6$ nucleons with artificial neural network wave functions
• A Number-Conserving Theory for Nuclear Pairing
• Neural-Network Quantum States for Periodic Systems in Continuous Space

Cited by in corpus (8)

• Neural-network quantum states for many-body physics
• Quantum Magic and Multi-Partite Entanglement in the Structure of Nuclei
• Efficient Solutions of Fermionic Systems using Artificial Neural Networks
• Lee-Yang theory of quantum phase transitions with neural network quantum states
• Second-order optimisation strategies for neural network quantum states
• Machine learning one-dimensional spinless trapped fermionic systems with neural-network quantum states
• Exact nuclear pairing solution for large-scale configurations: I. The EP (v1.0) program at zero temperature
• Diagrammatic Monte Carlo for Finite Systems at Zero Temperature