Quantum-Inspired Optimization of Graph Partitioning Algorithms

Abstract

Graph partitioning is a fundamental problem in various fields, including computer graphics, high-performance computing, and network design. Traditional graph partitioning algorithms often suffer from high computational complexity, particularly when dealing with large and complex graphs. This research investigates the potential of quantum-inspired optimization techniques, specifically leveraging concepts from quantum annealing, to accelerate the graph partitioning process. We formulate the graph partitioning problem as a Quadratic Unconstrained Binary Optimization (QUBO) problem, allowing us to simulate the behavior of a quantum annealer on classical hardware. The core of our approach involves mapping the graph's connectivity structure onto a QUBO, representing nodes as binary variables and edges as constraints. By exploiting the inherent parallelism of quantum annealing, we aim to find optimal or near-optimal partitions significantly faster than conventional methods. The results demonstrate the feasibility and potential advantages of this quantum-inspired strategy for graph partitioning, offering a promising direction for tackling computationally intensive graph problems.