Quantum Monte Carlo Simulations of Rydberg Atom Arrays

Arrays of Rydberg atoms are a powerful platform to realize strongly-interacting quantum many-body systems. Through the use of optical tweezers ⁸⁷Rb atoms are arranged into a programmable 2D lattice and excited into a high principal quantum number state (called a "Rydberg" state) by lasers. It is then possible to encode a physical qubit into the Hilbert space spanned by an atom’s groundstate and excited state. The atoms interact with each other through a distance dependent potential which penalizes simultaneous excitation. A common Hamiltonian implemented on such arrays takes a form similar to a Transverse-Field Ising Model and is free of the sign problem, meaning its equilibrium properties are amenable to efficient simulation via quantum Monte Carlo (QMC).

Classically simulating such systems is useful both for verifying experimental results, and for probing the physics of larger systems which may not yet be available experimentally. While the stoquasticity of the Hamiltonian does in principle allow exact QMC simulations, devising an efficient simulation scheme is not always trivial. We discuss our recent QMC algorithm for exact simulations of Rydberg arrays in which we devise updates that allow for the efficient estimation of physical observables for typical experimental parameters, and show that the algorithm can reproduce experimental results of groundstates of large Rydberg arrays in two dimensions.