Rydberg-atom graphs for quadratic unconstrained binary optimization problems

There is a growing interest in harnessing the potential of the Rydberg-atom system to address complex combinatorial optimization challenges. Here we present an experimental demonstration of how the quadratic unconstrained binary optimization (QUBO) problem can be effectively addressed using Rydberg-atom graphs. The Rydberg-atom graphs are configurations of neutral atoms organized into mathematical graphs, facilitated by programmable optical tweezers, and designed to exhibit many-body ground states that correspond to the maximum independent set (MIS) of their respective graphs. We have developed four elementary Rydberg-atom subgraph components, not only to eliminate the need of local control but also to be robust against interatomic distance errors, while serving as the building blocks sufficient for formulating generic QUBO graphs. To validate the feasibility of our approach, we have conducted a series of Rydberg-atom experiments selected to demonstrate proof-of-concept operations of these building blocks. These experiments illustrate how these components can be used to programmatically encode the QUBO problems to Rydberg-atom graphs and, by measuring their many-body ground states, how their QUBO solutions are determined subsequently.