VeloxQ: A Fast and Efficient QUBO Solver

TL;DR

VeloxQ is a new classical solver for QUBO problems that offers competitive performance and scalability, rivaling quantum and traditional methods on large-scale instances.

Contribution

VeloxQ provides a fast, scalable, and practical classical solution for large QUBO/HUBO problems, outperforming several state-of-the-art solvers in various regimes.

Findings

VeloxQ achieves competitive solution quality and runtime.

It can handle problems with up to 10^8 variables.

VeloxQ outperforms some quantum and classical solvers on large instances.

Abstract

We introduce VeloxQ, a fast solver for Quadratic Unconstrained Binary Optimization (QUBO) problems, which are central to many real-world optimization tasks. Unlike approaches that depend on emerging quantum hardware, VeloxQ can be deployed on conventional computing infrastructure. We benchmark VeloxQ against state-of-the-art QUBO solvers from several families. These include quantum annealers, specifically D-Wave's Advantage and Advantage2 platforms; the digital-quantum BF-DCQO algorithm for Higher-Order Unconstrained Binary Optimization (HUBO) developed by Kipu Quantum; physics-inspired algorithms including Simulated Bifurcation, Parallel Annealing, and tropical tensor networks; and conventional methods including CPLEX, brute force, BEIT's Chimera solver, and Branch-and-Bound variants. The benchmark suite covers native quantum-annealer topologies, embedded all-to-all instances, HUBO-derived instances, planted-solution instances, certified-solver regimes, and dense Branch-and-Bound test cases. Across the benchmark suite, VeloxQ delivers competitive solution quality and runtime, and in several regimes outperforms the compared solvers. VeloxQ also demonstrates strong scalability. Among the solvers considered in this study, it was the only method we could run on the largest sparse instances within our computational budget, including problems with up to $10^{8}$ sparsely connected variables. These findings position VeloxQ as a competitive and practical tool for tackling large-scale QUBO/HUBO problems, offering a practical alternative to existing quantum and classical optimization methods.