26 January 2023 Thu 5 pm

The exponential complexity of representing general quantum many-body states is a key challenge in computational quantum physics. Well established numerical methods, such as tensor network approaches, are limited by the entanglement entropy scaling of the problem at hand, thus their application is limited to particular classes of systems. In recent years, neural quantum states have been shown to be capable to represent volume law quantum states, potentially allowing the study of physical systems beyond the reach for tensor networks. As this technique have been developed only recently, its limitations and ideal usecases are not yet clear.

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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