Quantum computing provides powerful algorithmic tools that have been shown to outperform established classical solvers in specific optimization tasks. A core step in solving optimization problems with known quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) is the problem formulation. While quantum optimization has historically centered around Quadratic Unconstrained Optimization (QUBO) problems, recent studies show, that many combinatorial problems such as the TSP can be solved more efficiently in their native Polynomial Unconstrained Optimization (PUBO) forms. As many optimization problems in practice also contain continuous variables, our contribution investigates the performance of the QAOA in solving continuous optimization problems when using PUBO and QUBO formulations. Our extensive evaluation on suitable benchmark functions, shows that PUBO formulations generally yield better results, while requiring less qubits. As the multi-qubit interactions needed for the PUBO variant have to be decomposed using the hardware gates available, i.e., currently single- and two-qubit gates, the circuit depth of the PUBO approach outscales its QUBO alternative roughly linearly in the order of the objective function. However, incorporating the planned addition of native multi-qubit gates such as the global Molmer-Sorenson gate, our experiments indicate that PUBO outperforms QUBO for higher order continuous optimization problems in general.
Evaluating the Quantum Approximate Optimization Algorithms for QUBO problems Across Quantum Hardware Platforms: Performance Analysis, Challenges, and Strategies
University of Oulu（奥卢大学）；Indian Institute of Science（印度科学学院）；OP Financial Group（OP金融集团）
Reducing QUBO Complexity in Drone Delivery Through Classical Feasibility Preprocessing
Gran Sasso Science Institute（格兰萨索科学研究所）；VSB – Technical University of Ostrava（俄斯特拉发科技大学）；IT4Innovations National Supercomputing Center（IT4创新国家超级计算中心）；Klaipeda University（克莱佩达大学）；Università dell’Aquila（阿奎拉大学）
Hybrid Quantum-Classical Optimization for Emergency-Priority Traffic Signal Control
Gran Sasso Science Institute（格兰萨索科学研究所）；VSB – Technical University of Ostrava（俄斯特拉发理工大学）；IT4Innovations National Supercomputing Center, VSB – Technical University of Ostrava（俄斯特拉发理工大学IT4创新国家超级计算中心）；Klaipeda University（克莱佩达大学）
Disentangling QAOA: From Weakly Entangled Circuits to a Classical QUBO Solver
International Center for Quantum Optics and Quantum Technologies（国际量子光学与量子技术研究中心）；National University of Science and Technology “MISIS”（莫斯科国立科技大学（MISIS））；Steklov Mathematical Institute of Russian Academy of Sciences（俄罗斯科学院斯捷克洛夫数学研究所）
Scaling QAOA: transferring optimal adiabatic schedules from small-scale to large-scale variational circuits
Aix-Marseille Université, Université de Toulon（艾克斯-马赛大学、土伦大学）；ENSTA, Institut Polytechnique de Paris（巴黎理工学院）；Conservatoire National des Arts et Métiers（国立工艺博物馆）；Université Paris Cité（巴黎西岱大学）
Quantum Approaches to Urban Logistics: From Core QAOA to Clustered Scalability
Politecnico di Milano（米兰理工大学）；International Foundation Big Data And Artificial Intelligence For Human Development Via Galliera n. 32 – Bologna（大数据与人工智能促进人类发展的国际基金会，via Galliera n. 32 – 玻利维亚）
Coordinated optimization of departure sequencing and section-track allocation in railway short-term concentrated departure scenarios based on qubo and hybrid quantum algorithms
Hardware-Aware QAOA for Honeypot Traffic Partitioning on 100+ Qubit IBM Quantum Processors
Future of Computing Institute, Rensselaer Polytechnic Institute（未来计算研究所，伦斯勒理工学院）；School of Computer Science and Mathematics, Marist University（计算机科学与数学学院，玛里斯特大学）
