Rydberg quantum wires for maximum independent set problems

One application of near-term quantum computing devices(1-4) is to solve combinatorial optimization problems such as non-deterministic polynomial-time hard problems(5-8). Here we present an experimental protocol with Rydberg atoms to determine the maximum independent set of graphs(9), defined as an independent set of vertices of maximal size. Our proposal is based on a Rydberg quantum wire scheme, which exploits auxiliary atoms to engineer long-ranged networks of qubits. We experimentally test the protocol on three-dimensional Rydberg atom arrays, overcoming the intrinsic limitations of two-dimensional arrays for tackling combinatorial problems and encode high-degree vertices. We find the maximum independent set solutions with our programmable quantum-wired Rydberg simulator for Kuratowski subgraphs(10) and a six-degree graph, which are paradigmatic examples of non-planar and high-degree graphs, respectively. Our protocol provides a way to engineer the complex connections of high-degree graphs through many-body entanglement, taking a step towards the demonstration of quantum advantage in combinatorial optimization.