Solving the quantum many-body problem with artificial neural networks

2017/02/10 by Giuseppe Carleo, Matthias Troyer · 6 citations
Physics and Astronomy · #Quantum many-body systems #Spectroscopy and Quantum Chemical Studies #Quantum, superfluid, helium dynamics

paper · doi:10.1126/science.aag2302

openalex publication_date 2017/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The challenge posed by the many-body problem in quantum physics originates from the difficulty of describing the nontrivial correlations encoded in the exponential complexity of the many-body wave function. Here we demonstrate that systematic machine learning of the wave function can reduce this complexity to a tractable computational form for some notable cases of physical interest. We introduce a variational representation of quantum states based on artificial neural networks with a variable number of hidden neurons. A reinforcement-learning scheme we demonstrate is capable of both finding the ground state and describing the unitary time evolution of complex interacting quantum systems. Our approach achieves high accuracy in describing prototypical interacting spins models in one and two dimensions.

Citations

• Efficient Simulation of One-Dimensional Quantum Many-Body Systems
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Localization and Glassy Dynamics Of Many-Body Quantum Systems
• Equation of State Calculations by Fast Computing Machines
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• The density-matrix renormalization group in the age of matrix product states
• Note on Exchange Phenomena in the Thomas Atom
• Learning Invariant Representations with Local Transformations
• Mastering the game of Go with deep neural networks and tree search

Cited by

• Quantum Many-Body Dynamics in Two Dimensions with Artificial Neural Networks
• Neural-network quantum state tomography
• Solving Classical and Quantum Spin Glasses with Deep Boltzmann Quantum States
• Learning Inhomogeneous Heisenberg Hamiltonians in Nanographene Spin Chains
• Unifying Variational and Dynamical Quantum Embedding: From Ghost Gutzwiller Approximation to Dynamical Mean-Field Theory
• Nuclear responses with neural-network quantum states
• Giuseppe Carleo [wikipedia]