One application of near-term quantum computing devices^1,2,3,4 is to solve combinatorial optimization problems such as non-deterministic polynomial-time hard problems^5,6,7,8. Here we present an experimental protocol with Rydberg atoms to determine the maximum independent set of graphs⁹, 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 subgraphs¹⁰ 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.

近期量子计算设备^1,2,3,4的一种应用是解决组合优化问题，例如非确定性多项式时间难题^5,6,7,8。在这里，我们提出了一个带有里德堡原子的实验协议，以确定最大独立图集⁹，定义为最大尺寸的独立顶点集。我们的提议基于里德堡量子线方案，该方案利用辅助原子来设计远程量子比特网络。我们在三维里德堡原子阵列上对该协议进行了实验测试，克服了二维阵列在解决组合问题和编码高度顶点方面的固有局限性。我们为 Kuratowski 子图^{10找到了最大的独立集合解决方案}和六度图，它们分别是非平面图和高度图的典型示例。我们的协议提供了一种通过多体纠缠来设计高度图的复杂连接的方法，朝着在组合优化中展示量子优势迈出了一步。