We suggest employing graph sparsification as a pre-processing step for maxcut programs using the QUBO solver. Quantum(-inspired) algorithms are recognized for their potential efficiency in handling quadratic unconstrained binary optimization (QUBO). Given that maxcut is an NP-hard problem and can be readily expressed using QUBO, it stands out as an exemplary case to demonstrate the effectiveness of quantum(-inspired) QUBO approaches. Here, the non-zero count in the QUBO matrix corresponds to the graph's edge count. Given that many quantum(-inspired) solvers operate through cloud services, transmitting data for dense graphs can be costly. By introducing the graph sparsification method, we aim to mitigate these communication costs. Experimental results on classical, quantum-inspired, and quantum solvers indicate that this approach substantially reduces communication overheads and yields an objective value close to the optimal solution.

翻译：我们建议将图稀疏化作为Maxcut问题的QUBO求解器中预处理步骤。量子（及量子启发式）算法在处理二次无约束二元优化（QUBO）问题方面展现出潜在的高效性。由于Maxcut是NP-hard问题且易于用QUBO形式表达，它成为展示量子（及量子启发式）QUBO方法有效性的典型案例。在此类问题中，QUBO矩阵的非零元素数量与图的边数直接对应。鉴于许多量子（及量子启发式）求解器通过云服务运行，传输稠密图数据的成本可能非常高昂。通过引入图稀疏化方法，我们旨在降低这些通信开销。在经典求解器、量子启发式求解器和量子求解器上的实验结果表明，该方法能够显著减少通信开销，同时获得接近最优解的客观值。