Save Big on Coursera Plus. 7,000+ courses at $160 off. Limited Time Only! Grab it Explore the challenges and potential of Neural Quantum States in representing complex quantum many-body systems through this comprehensive lecture. Delve into the exponential complexity of quantum state representation and the limitations of traditional tensor network approaches. Examine the emerging field of neural quantum states and their ability to represent volume law quantum states. Investigate the application of multi-layer feed-forward networks to find ground states with volume-law entanglement entropy, using the Sachdev-Ye-Kitaev model as a testbed. Discover the limitations of both shallow and deep feed-forward networks in representing complex quantum states, highlighting the need for further research into efficient neural representations of physical quantum states. Gain insights into various topics including entanglement entropy, matrix product states, single neural layers, neural networks, tensor networks, and modified Allen Chester models.