Neural networks have recently emerged as a powerful tool in quantum chemistry, particularly for computing the ground state energy of large molecules. This approach, known as neural quantum states, represents the wave function of a molecular Hamiltonian using modern machine learning architectures. Optimized for GPU hardware, these methods aim to compete with and surpass traditional techniques. In this talk, I will introduce the mathematical foundations of neural quantum states and discuss our work in scaling these algorithms to thousands of GPU nodes on high-performance computing (HPC) systems, enabling simulations of unprecedented size and complexity.