Programmable quantum systems based on Rydberg atom arrays have recently been used for hardware-efficient tests of quantum optimization algorithms [Ebadi et al., Science, 376, 1209 (2022)] with hundreds of qubits. In particular, the maximum independent set problem on so-called unit-disk graphs, was shown to be efficiently encodable in such a quantum system. Here, we extend the classes of problems that can be efficiently encoded in Rydberg arrays by constructing explicit mappings from a wide class of problems to maximum weighted independent set problems on unit-disk graphs, with at most a quadratic overhead in the number of qubits. We analyze several examples, including: maximum weighted independent set on graphs with arbitrary connectivity, quadratic unconstrained binary optimization problems with arbitrary or restricted connectivity, and integer factorization. Numerical simulations on small system sizes indicate that the adiabatic time scale for solving the mapped problems is strongly correlated with that of the original problems. Our work provides a blueprint for using Rydberg atom arrays to solve a wide range of combinatorial optimization problems with arbitrary connectivity, beyond the restrictions imposed by the hardware geometry.

翻译：基于里德伯原子阵列的可编程量子系统近期已被用于实现硬件高效的量子优化算法测试[Ebadi等人，《科学》，376，1209（2022）]，该系统包含数百个量子比特。特别地，最大独立集问题在所谓单位圆盘图上已被证明能够高效编码于此类量子系统中。本文通过将广泛问题的显式映射构建为单位圆盘图上的最大加权独立集问题（量子比特数最多仅呈二次增长），拓展了可高效编码于里德伯阵列的问题类别。我们分析了多个示例，包括：任意连接图上的最大加权独立集、具有任意或受限连接性的二次无约束二元优化问题，以及整数分解。小规模系统的数值模拟表明，解决映射后问题的绝热时间尺度与原始问题高度相关。本研究为利用里德伯原子阵列解决具有任意连接性的广泛组合优化问题（突破硬件几何结构限制）提供了蓝图。