SciPost Physics

SciPost Phys. 4, 013 (2018) · published 28 February 2018

• doi: 10.21468/SciPostPhys.4.2.013
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

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.

• Li et al., Extracting critical exponents by finite-size scaling with convolutional neural networks
  Phys. Rev. B 99, 075418 (2019) [Crossref]
• Matty et al., Entanglement clustering for ground-stateable quantum many-body states
  Phys. Rev. Research 3, 023212 (2021) [Crossref]
• Faridfar et al., Dynamical quantum phase transitions in Stark quantum spin chains
  Physica A: Statistical Mechanics and its Applications 619, 128732 128732 (2023) [Crossref]
• Kim et al., Real-time dynamics of one-dimensional and two-dimensional bosonic quantum matter deep in the many-body localized phase
  Phys. Rev. B 104, 144205 (2021) [Crossref]
• Vargas-Hernández et al.,
  968, 171 (2020) [Crossref]
• Czischek,
  , 111 (2020) [Crossref]
• Verdel et al., Variational classical networks for dynamics in interacting quantum matter
  Phys. Rev. B 103, 165103 (2021) [Crossref]
• van Nieuwenburg et al., Learning phase transitions from dynamics
  Phys. Rev. B 98, 060301 (2018) [Crossref]
• Xu 徐, Quantum-coherence-assisted dynamical phase transition in the one-dimensional transverse-field Ising model
  Commun. Theor. Phys. 76, 125104 (2024) [Crossref]
• De Nicola et al., Stochastic approach to non-equilibrium quantum spin systems
  J. Phys. A: Math. Theor. 52, 05LT02 (2019) [Crossref]
• Deng, Machine Learning Detection of Bell Nonlocality in Quantum Many-Body Systems
  Phys. Rev. Lett. 120, 240402 (2018) [Crossref]
• Czischek et al., Quenches near Ising quantum criticality as a challenge for artificial neural networks
  Phys. Rev. B 98, 024311 (2018) [Crossref]
• Carleo et al., Machine learning and the physical sciences
  Rev. Mod. Phys. 91, 045002 (2019) [Crossref]
• Trapin et al., Constructing effective free energies for dynamical quantum phase transitions in the transverse-field Ising chain
  Phys. Rev. B 97, 174303 (2018) [Crossref]
• Heyl, Dynamical quantum phase transitions: a review
  Rep. Prog. Phys. 81, 054001 (2018) [Crossref]
• Begg et al., Trajectory-resolved Weiss fields for quantum spin dynamics
  Phys. Rev. Research 5, 043288 (2023) [Crossref]
• Lange et al., From architectures to applications: a review of neural quantum states
  Quantum Sci. Technol. 9, 040501 (2024) [Crossref]
• Wong et al., Loschmidt amplitude spectrum in dynamical quantum phase transitions
  Phys. Rev. B 105, 174307 (2022) [Crossref]
• Mohseni et al., Deep learning of many-body observables and quantum information scrambling
  Quantum 8, 1417 1417 (2024) [Crossref]
• Klassert et al., Variational learning of quantum ground states on spiking neuromorphic hardware
  iScience 25, 104707 104707 (2022) [Crossref]
• Richter et al., Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters
  SciPost Phys. 9, 031 (2020) [Crossref]
• Schmitt et al., Quantum Many-Body Dynamics in Two Dimensions with Artificial Neural Networks
  Phys. Rev. Lett. 125, 100503 (2020) [Crossref]
• De Nicola et al., Entanglement View of Dynamical Quantum Phase Transitions
  Phys. Rev. Lett. 126, 040602 (2021) [Crossref]
• Bakthavatchalam et al., Bayesian Optimization of Bose-Einstein Condensates
  Sci Rep 11, 5054 (2021) [Crossref]
• Valenti et al., Correlation-enhanced neural networks as interpretable variational quantum states
  Phys. Rev. Research 4, L012010 (2022) [Crossref]
• Vargas-Hernández et al., Extrapolating Quantum Observables with Machine Learning: Inferring Multiple Phase Transitions from Properties of a Single Phase
  Phys. Rev. Lett. 121, 255702 (2018) [Crossref]
• Czischek,
  , 53 (2020) [Crossref]
• Melko et al., Restricted Boltzmann machines in quantum physics
  Nat. Phys. 15, 887 (2019) [Crossref]
• Saito, Method to Solve Quantum Few-Body Problems with Artificial Neural Networks
  J. Phys. Soc. Jpn. 87, 074002 (2018) [Crossref]
• De Tomasi et al., Efficiently solving the dynamics of many-body localized systems at strong disorder
  Phys. Rev. B 99, 241114 (2019) [Crossref]
• Karpov et al., Disorder-Free Localization in an Interacting 2D Lattice Gauge Theory
  Phys. Rev. Lett. 126, 130401 (2021) [Crossref]
• Burau et al., Unitary Long-Time Evolution with Quantum Renormalization Groups and Artificial Neural Networks
  Phys. Rev. Lett. 127, 050601 (2021) [Crossref]
• Shi et al., Learning topological defects formation with neural networks in a quantum phase transition
  Commun. Theor. Phys. 76, 055101 (2024) [Crossref]
• Gutiérrez et al., Real time evolution with neural-network quantum states
  Quantum 6, 627 627 (2022) [Crossref]
• Czischek et al., Quenches near criticality of the quantum Ising chain—power and limitations of the discrete truncated Wigner approximation
  Quantum Sci. Technol. 4, 014006 (2018) [Crossref]
• Tepaske et al., Three-dimensional isometric tensor networks
  Phys. Rev. Research 3, 023236 (2021) [Crossref]
• Hartmann et al., Neural-Network Approach to Dissipative Quantum Many-Body Dynamics
  Phys. Rev. Lett. 122, 250502 (2019) [Crossref]
• Matty et al., Multifaceted machine learning of competing orders in disordered interacting systems
  Phys. Rev. B 100, 155141 (2019) [Crossref]
• Iten et al., Discovering Physical Concepts with Neural Networks
  Phys. Rev. Lett. 124, 010508 (2020) [Crossref]
• Wu et al., Artificial neural network based computation for out-of-time-ordered correlators
  Phys. Rev. B 101, 214308 (2020) [Crossref]
• Heyl, Dynamical quantum phase transitions: A brief survey
  EPL 125, 26001 (2019) [Crossref]
• Medvidović et al., Neural-network quantum states for many-body physics
  Eur. Phys. J. Plus 139, 631 (2024) [Crossref]
• Kosut et al., Quantum system compression: A Hamiltonian guided walk through Hilbert space
  Phys. Rev. A 103, 012406 (2021) [Crossref]
• Wong et al., Entanglement in quenched extended Su-Schrieffer-Heeger model with anomalous dynamical quantum phase transitions
  Phys. Rev. B 110, 054312 (2024) [Crossref]
• Kaneko et al., Dynamics of correlation spreading in low-dimensional transverse-field Ising models
  Phys. Rev. A 108, 023301 (2023) [Crossref]
• Wong et al., Quantum spin fluctuations in dynamical quantum phase transitions
  Phys. Rev. B 108, 064305 (2023) [Crossref]
• De Nicola et al., Entanglement and precession in two-dimensional dynamical quantum phase transitions
  Phys. Rev. B 105, 165149 (2022) [Crossref]
• Zhou et al., Dynamical quantum phase transitions in non-Hermitian lattices
  Phys. Rev. A 98, 022129 (2018) [Crossref]
• Yu, Dynamical phase transition and scaling in the chiral clock Potts chain
  Phys. Rev. A 108, 062215 (2023) [Crossref]
• Richter et al., Combining dynamical quantum typicality and numerical linked cluster expansions
  Phys. Rev. B 99, 094419 (2019) [Crossref]
• Bukov et al., Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape
  SciPost Phys. 10, 147 (2021) [Crossref]