Can neural quantum states learn volume-law ground states?

Abstract

We study whether neural quantum states based on multi-layer feed-forward networks can find ground states which exhibit volume-law entanglement entropy. As a testbed, we employ the paradigmatic Sachdev-Ye-Kitaev model. We find that both shallow and deep feed-forward networks require an exponential number of parameters in order to represent the ground state of this model. This demonstrates that sufficiently complicated quantum states, although being physical solutions to relevant models and not pathological cases, can still be difficult to learn to the point of intractability at larger system sizes. This highlights the importance of further investigations into the physical properties of quantum states amenable to an efficient neural representation.

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• Unifying view of fermionic neural network quantum states: From neural network backflow to hidden fermion determinant states
• Non-Stabilizerness of Sachdev-Ye-Kitaev Model
• Comment on "Can Neural Quantum States Learn Volume-Law Ground States?"
• Efficiency of the hidden fermion determinant states Ansatz in the light of different complexity measures
• Mott Transition and Volume Law Entanglement with Neural Quantum States
• Investigating Stark many-body localization with continuous unitary transformation flows
• Bound on entanglement in neural quantum states
• Seeding neural network quantum states with tensor network states
• Modal Backflow Neural Quantum States for Anharmonic Vibrational Calculations