Gaussian Boson Sampling (GBS) is a quantum computational model that leverages linear optics to solve sampling problems believed to be classically intractable. Recent experimental breakthroughs have demonstrated quantum advantage using GBS, motivating its application to real-world combinatorial optimization problems. In this work, we reformulate the graph coloring problem as an integer programming problem using the independent set formulation. This enables the use of GBS to identify cliques in the complement graph, which correspond to independent sets in the original graph. Our method is benchmarked against classical heuristics and exact algorithms on two sets of instances: Erdős-Rényi random graphs and graphs derived from a smart-charging use case. The results demonstrate that GBS can provide competitive solutions, highlighting its potential as a quantum-enhanced heuristic for graph-based optimization.

翻译：高斯玻色子采样（GBS）是一种量子计算模型，它利用线性光学来解决被认为在经典计算上难以处理的采样问题。最近的实验突破已展示了使用GBS实现的量子优势，这推动了其在实际组合优化问题中的应用。在本工作中，我们利用独立集表述将图着色问题重新表述为一个整数规划问题。这使得能够使用GBS来识别补图中的团，这些团对应于原图中的独立集。我们的方法在两组实例上进行了基准测试：Erdős-Rényi随机图以及源自智能充电应用场景的图。测试结果证明，GBS能够提供具有竞争力的解决方案，凸显了其作为基于图的优化的量子增强启发式方法的潜力。