Real time evolution with neural-network quantum states

Abstract

A promising application of neural-network quantum states is to describe the time dynamics of many-body quantum systems. To realize this idea, we employ neural-network quantum states to approximate the implicit midpoint rule method, which preserves the symplectic form of Hamiltonian dynamics. We ensure that our complex-valued neural networks are holomorphic functions, and exploit this property to efficiently compute gradients. Application to the transverse-field Ising model on a one- and two-dimensional lattice exhibits an accuracy comparable to the stochastic configuration method proposed in [Carleo and Troyer, Science 355, 602-606 (2017)], but does not require computing the (pseudo-)inverse of a matrix.

11 pages, 8 figures

References in corpus (11)

• The density-matrix renormalization group in the age of matrix product states
• Real time evolution using the density matrix renormalization group
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space
• Quantum many-body dynamics in two dimensions with artificial neural networks
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Quantum Entanglement in Deep Learning Architectures
• Quenches near Ising quantum criticality as a challenge for artificial neural networks
• Unifying Neural-network Quantum States and Correlator Product States via Tensor Networks
• Generalized Transfer Matrix States from Artificial Neural Networks
• Approximating power of machine-learning ansatz for quantum many-body states

Cited by in corpus (8)

• Quantum many-body dynamics in two dimensions with artificial neural networks
• Autoregressive Transformer Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation
• Scalable Hamiltonian learning for large-scale out-of-equilibrium quantum dynamics
• Scaling of neural-network quantum states for time evolution
• Role of stochastic noise and generalization error in the time propagation of neural-network quantum states
• Variational classical networks for dynamics in interacting quantum matter
• Infinite Neural Network Quantum States: Entanglement and Training Dynamics
• Simulating quantum dynamics: Evolution of algorithms in the HPC context