Can neural quantum states learn volume-law ground states?

TL;DR

This paper investigates whether neural quantum states can efficiently learn volume-law entangled ground states, finding that they require exponential resources for complex states like those in the Sachdev-Ye-Kitaev model.

Contribution

It demonstrates the limitations of neural quantum states in representing highly entangled ground states, highlighting the need for further research into physically tractable quantum states.

Findings

Neural quantum states require exponential parameters for volume-law states.

Both shallow and deep networks face intractability at larger system sizes.

Highlights the challenge of representing complex quantum states with neural networks.

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.