Advanced QUBO Formulation Techniques for Improved Quantum Annealing Efficiency
José Gabriel Carrasco Ramirez
Abstract
This paper addresses the challenges inherent in optimizing Quadratic Unconstrained Binary Optimization (QUBO) formulations for quantum annealing, particularly focusing on the trade-off between solution quality and qubit usage. As quantum annealers such as those developed by D-Wave and Qilimanjaro offer a promising approach to solving NP-complete problems, effective QUBO formulations are critical for leveraging their computational power. We propose two novel methods—the Adaptive Pruning Technique and the Hybrid Heuristic-QA Approach—that aim to reduce the number of qubits required while maintaining high solution quality. Through rigorous theoretical analysis and extensive experimentation using both quantum hardware and classical simulators, we demonstrate that these methods can significantly enhance qubit efficiency without compromising the accuracy of solutions. Our findings indicate that the Adaptive Pruning Technique can achieve up to a 25% reduction in qubit usage, while the Hybrid Heuristic-QA Approach offers reductions of up to 50%, particularly for larger problem instances. These advancements not only contribute to the theoretical understanding of QUBO optimization but also provide practical strategies for enhancing the performance of quantum annealers in real-world applications.
