Unreasonable effectiveness of pairwise Markov random fields in finding ground states of stoquastic Hamiltonians

We introduce auto-regressive Markov random fields (MRF) as an ansatz for finding the ground states of stoquastic Hamiltonians. Using exact MRF learning methods, we find that an auto-regressive representation with only pairwise interactions can faithfully represent the ground states of many important classes of Hamiltonians, including frustrated and disordered models. For larger systems, we observe that this pairwise ansatz coupled with first-order optimization methods is capable of outperforming established methods in quantum-dominated regions of the phase space. Our work thus illustrates the computational benefits of the auto-regressive pairwise MRFs in capturing the ground-state properties of stoquastic quantum models.