  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.
