An Empirical Study of Quantum Dynamics as a Ground State Problem with Neural Quantum States

Abstract

We consider the Feynman-Kitaev formalism applied to a spin chain described by the transverse field Ising model. This formalism consists of building a Hamiltonian whose ground state encodes the time evolution of the spin chain at discrete time steps. To find this ground state, variational wave functions parameterised by artificial neural networks -- also known as neural quantum states (NQSs) -- are used. Our work focuses on assessing, in the context of the Feynman-Kitaev formalism, two properties of NQSs: expressivity (the possibility that variational parameters can be set to values such that the NQS is faithful to the true ground state of the system) and trainability (the process of reaching said values). We find that the considered NQSs are capable of accurately approximating the true ground state of the system, i.e., they are expressive enough ansätze. However, extensive hyperparameter tuning experiments show that, empirically, reaching the set of values for the variational parameters that correctly describe the ground state becomes ever more difficult as the number of time steps increase because the true ground state becomes more entangled, and the probability distribution starts to spread across the Hilbert space canonical basis.

arXiv comment20 pages, 4 figures

References in corpus (27)

• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Area laws for the entanglement entropy - a review
• Barren plateaus in quantum neural network training landscapes
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• The power of quantum neural networks
• Many-body quantum state tomography with neural networks
• The effect of data encoding on the expressive power of variational quantum machine learning models
• Quantum Entanglement in Neural Network States
• Recurrent Neural Network Wave Functions
• Weak binding between two aromatic rings: feeling the van der Waals attraction by quantum Monte Carlo methods
• Quantum many-body dynamics in two dimensions with artificial neural networks
• Beyond Barren Plateaus: Quantum Variational Algorithms Are Swamped With Traps
• Solving Statistical Mechanics Using Variational Autoregressive Networks
• NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems
• Violation of area-law scaling for the entanglement entropy in spin 1/2 chains
• Neural tensor contractions and the expressive power of deep neural quantum states
• Unbiased Monte Carlo Cluster Updates with Autoregressive Neural Networks
• Quantum many-body systems in thermal equilibrium
• 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
• Dynamics with autoregressive neural quantum states: application to critical quench dynamics
• The Feynman-Kitaev computer's clock: bias, gaps, idling and pulse tuning
• Feynman's clock, a new variational principle, and parallel-in-time quantum dynamics
• Entanglement Features of Random Neural Network Quantum States
• Variational dynamics as a ground-state problem on a quantum computer
• Neural Network Operations and Susuki-Trotter evolution of Neural Network States
• Phase diagram reconstruction of the Bose-Hubbard model with a Restricted Boltzmann Machine wavefunction