Can Neural Quantum States Learn Volume-Law Ground States?

Area of Science:

• Quantum Information Science
• Machine Learning in Physics
• Condensed Matter Theory

Background:

• Neural quantum states offer a novel approach to studying complex quantum systems.
• Volume-law entanglement entropy is a characteristic of highly entangled quantum states.
• The Sachdev-Ye-Kitaev (SYK) model is a key theoretical framework for studying quantum chaos and entanglement.

Purpose of the Study:

• To investigate the capability of multilayer feed-forward neural networks in representing quantum ground states with volume-law entanglement entropy.
• To assess the scalability and efficiency of neural quantum states for complex models like the SYK model.

Main Methods:

• Utilized multilayer feed-forward neural networks to parameterize quantum states.
• Employed the Sachdev-Ye-Kitaev model as a testbed for evaluating network performance.
• Analyzed the number of parameters required by the networks to represent the ground state.

Main Results:

• Both shallow and deep feed-forward networks necessitated an exponential number of parameters to capture the SYK model's ground state.
• The representational complexity of the ground state proved intractable for neural networks at larger system sizes.
• The variational neural network approach showed no advantage over exact diagonalization for this specific problem.

Conclusions:

• Neural quantum states, while promising, face significant challenges in efficiently representing highly entangled quantum states.
• The tractability of learning quantum states depends heavily on their physical properties, not just their validity.
• Further research is crucial to identify quantum states amenable to efficient neural representation and to develop improved neural network architectures.