We provide a non-unit disk framework to solve combinatorial optimization problems such as Maximum Cut (Max-Cut) and Maximum Independent Set (MIS) on a Rydberg quantum annealer. Our setup consists of a many-body interacting Rydberg system where locally controllable light shifts are applied to individual qubits in order to map the graph problem onto the Ising spin model. Exploiting the flexibility that optical tweezers offer in terms of spatial arrangement, our numerical simulations implement the local-detuning protocol while globally driving the Rydberg annealer to the desired many-body ground state, which is also the solution to the optimization problem. Using optimal control methods, these solutions are obtained for prototype graphs with varying sizes at time scales well within the system lifetime and with approximation ratios close to one. The non-blockade approach facilitates the encoding of graph problems with specific topologies that can be realized in two-dimensional Rydberg configurations and is applicable to both unweighted as well as weighted graphs. A comparative analysis with fast simulated annealing is provided which highlights the advantages of our scheme in terms of system size, hardness of the graph, and the number of iterations required to converge to the solution.

翻译：我们提出了一种非单位圆盘框架，用于在里德伯量子退火器上求解最大割（Max-Cut）和最大独立集（MIS）等组合优化问题。该装置由多体相互作用的里德伯系统构成，其中可对单个量子比特施加局部可控的光移，从而将图问题映射至伊辛自旋模型。利用光镊在空间排布上的灵活性，我们的数值模拟实现了局部失谐协议，同时对里德伯退火器进行全局驱动，使其收敛至目标多体基态——此状态即为优化问题的解。通过最优控制方法，我们在远小于系统寿命的时间尺度内，针对不同规模的典型图获得了近似比接近1的解。该非阻塞方法便于编码具有特定拓扑结构的图问题，可在二维里德伯构型中实现，且适用于无权图与加权图。与快速模拟退火算法的对比分析表明，本方案在系统规模、图复杂度及收敛所需迭代次数方面具有显著优势。