Quantum dynamics in transverse-field Ising models from classical networks

TL;DR

This paper introduces a classical network approach to efficiently simulate quantum dynamics in transverse-field Ising models, enabling accurate computation of local observables, entanglement, and Loschmidt amplitudes across multiple dimensions.

Contribution

The authors develop an analytical, perturbative classical network construction for quantum dynamics in Ising models, generalizable to other spin systems, and demonstrate its accuracy with Monte Carlo simulations.

Findings

Accurately reproduces quantum dynamics in 1D, 2D, and 3D Ising models.

Enables efficient Monte Carlo computation of local observables and entanglement.

Provides a mapping to artificial neural networks for classical wave function representation.

Abstract

The efficient representation of quantum many-body states with classical resources is a key challenge in quantum many-body theory. In this work we analytically construct classical networks for the description of the quantum dynamics in transverse-field Ising models that can be solved efficiently using Monte Carlo techniques. Our perturbative construction encodes time-evolved quantum states of spin-1/2 systems in a network of classical spins with local couplings and can be directly generalized to other spin systems and higher spins. Using this construction we compute the transient dynamics in one, two, and three dimensions including local observables, entanglement production, and Loschmidt amplitudes using Monte Carlo algorithms and demonstrate the accuracy of this approach by comparisons to exact results. We include a mapping to equivalent artificial neural networks, which were recently introduced to provide a universal structure for classical network wave functions.