Infinite neural network quantum states: entanglement and training dynamics

Journal Article · Sat Jun 03 00:00:00 EDT 2023 · Machine Learning: Science and Technology

DOI:https://doi.org/10.1088/2632-2153/ace02f· OSTI ID:2425540

Luo, Di ^[1]; Halverson, James ^[2]

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1. University of Illinois at Urbana-Champaign, IL (United States); Massachusetts Institute of Technology, Cambridge, MA (United States); Harvard, Cambridge, MA (United States)
2. Northeastern University, Boston, MA (United States)

We study infinite limits of neural network quantum states (∞-NNQS), which exhibit representation power through ensemble statistics, and also tractable gradient descent dynamics. Ensemble averages of entanglement entropies are expressed in terms of neural network correlators, and architectures that exhibit volume-law entanglement are presented. The analytic calculations of entanglement entropy bound are tractable because the ensemble statistics are simplified in the Gaussian process limit. A general framework is developed for studying the gradient descent dynamics of neural network quantum states (NNQS), using a quantum state neural tangent kernel (QS-NTK). For ∞-NNQS the training dynamics is simplified, since the QS-NTK becomes deterministic and constant. An analytic solution is derived for quantum state supervised learning, which allows an ∞-NNQS to recover any target wavefunction. Numerical experiments on finite and infinite NNQS in the transverse field Ising model and Fermi Hubbard model demonstrate excellent agreement with theory. ∞-NNQS opens up new opportunities for studying entanglement and training dynamics in other physics applications, such as in finding ground states.

• Research Organization: Brookhaven National Laboratory (BNL), Upton, NY (United States); National Quantum Information Science (QIS) Research Centers (United States). Co-design Center for Quantum Advantage (C2QA)
• Sponsoring Organization: NSF CAREER; USDOE Office of Science (SC)
• Grant/Contract Number: SC0012704
• OSTI ID: 2425540
• Journal Information: Machine Learning: Science and Technology, Journal Name: Machine Learning: Science and Technology Journal Issue: 2 Vol. 4; ISSN 2632-2153
• Publisher: IOP Publishing
• Country of Publication: United States
• Language: English

Related Subjects

quantum state supervised learning
97 MATHEMATICS AND COMPUTING
Computer Science
Fermi Hubbard model
Science & Technology - Other Topics
entanglement entropy
neural network Gaussian process
neural network quantum state
neural tangent kernel
transverse field Ising model