Utilizing Graph Sparsification for Pre-processing in Max Cut QUBO Solver

We suggest employing graph sparsification as a pre-processing step for max cut programs using the QUBO solver. Quantum(-inspired) algorithms are recognized for their potential efficiency in handling quadratic unconstrained binary optimization (QUBO). Various meta-heuristic approaches, including those based on the Quantum Approximate Optimization Algorithm, have been suggested for addressing QUBO challenges in this context. Given that max cut 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 and quantum-inspired solvers indicate that this approach substantially reduces communication overheads and yields an objective value close to the optimal solution.