VeloxQ: A Fast and Efficient QUBO Solver (2501.19221v1)

Abstract: We introduce VeloxQ, a fast and efficient solver for Quadratic Unconstrained Binary Optimization (QUBO) problems, which are central to numerous real-world optimization tasks. Unlike other physics-inspired approaches to optimization problems, such as quantum annealing and quantum computing, VeloxQ does not require substantial progress of technology to unlock its full potential. We benchmark VeloxQ against the state-of-the-art QUBO solvers based on emerging technologies. Our comparison includes quantum annealers, specifically D-Wave's Advantage, and Advantage2 prototype platforms, the digital-quantum algorithm designed to solve Higher-Order Unconstrained Binary Optimization (HUBO) developed by Kipu Quantum, physics-inspired algorithms: Simulated Bifurcation and Parallel Annealing and an algorithm based on tropical tensor networks. We also take into account modern developments of conventional algorithms: Branch and Bound algorithm, an optimal implementation of the brute-force algorithm and BEIT QUBO solver. Our results show that VeloxQ not only matches but often surpasses the mentioned solvers in solution quality and runtime. Additionally, VeloxQ demonstrates excellent scalability being the only solver capable of solving large-scale optimization problems, including up to $2\times 10^{8}$ sparsely connected variables, that are currently intractable for its competitors. These findings position VeloxQ as a powerful and practical tool for tackling large-scale QUBO and HUBO problems, offering a compelling alternative to existing quantum and classical optimization methods.