Merali, Ejaaz2025-07-072025-07-072025-07-072025-06-06https://hdl.handle.net/10012/21974Rydberg atom arrays form a promising platform for quantum computation. Through their strong, long-range interaction, they are able to encode various difficult combinatorial problems, as well as hosting a plethora of intriguing physical phenomena. In this thesis, we develop and apply a Stochastic Series Expansion Quantum Monte Carlo method to simulate Rydberg systems at zero-temperature and above. We then apply this simulation method alongside variational models to verify correctness of both methods. The data produced from the simulations is also used to train Neural Network wavefunctions, which we find are effectively able to grasp some of the physics of the Rydberg atom array on a square lattice.enquantum monte carlorydberg atom arraysgenerative modellingstochastic series expansionmarkov chain monte carloDoctoral Thesis