Efficient classical simulation of two-dimensional long-range systems: Rydberg arrays and beyond

In variational Monte Carlo (VMC) calculations of N-site quantum systems with arbitrary all-to-all two-body interactions, evaluating the local energy generally costs O\(N³\). We introduce a new framework that reduces this cost to O(N) for tensor network states, capable of scalable and accurate computation of real-time dynamics and ground states. As a result, we obtain accurate simulations of the adiabatic real-time protocol of a 10times10 dipolar XY model realized in a Rydberg simulator [C. Chen et al., Nature 616, 691 (2023)], which was previously beyond the reach of classical simulation. Going beyond quantum experiments, we also directly perform ground state VMC to compare with the adiabatic state preparation. Our work demonstrates tensor network VMC as a powerful classical simulator for long-range quantum platforms such as Rydberg and ion-trap simulators, which are currently in urgent need of scalable classical benchmarking tools. As a separate technical contribution, we resolve the pathology of evolving from product states within of tensor network VMC.