Resonating Kagome Dimer coverings in Rydberg atom arrays

Motivated by experiments on Rydberg atom arrays, we explore the properties of uniform quantum superpositions of kagome dimer configurations and construct an efficient algorithm for experimentally producing them. We begin by considering the thin cylinder limit, where these states have simple descriptions. We then develop a matrix product representation of the states on arbitrary cylinders, which leads to a natural protocol to efficiently grow them. We explain how our approach can be adapted to other quantum computing hardware.