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We present a method to split quantum circuits of variational quantum algorithms (VQAs) to allow for parallel training and execution, that maximally exploits the limited number of qubits in hardware to solve large problem instances. We apply this specifically to combinatorial optimization problems, where inherent structures from the problem can be identified, thus directly informing how to create these parallelized quantum circuits, which we call slices. We test our method by creating a parallelized version of the Quantum Approximate Optimization Algorithm, which we call pQAOA, and explain how our methods apply to other quantum algorithms like the Variational Quantum Eigensolver and quantum annealing. We show that not only can our method address larger problems, but that it is also possible to run full VQA models while training parameters using only one slice. These results show that the loss of information induced by splitting does not necessarily affect the training of parameters in quantum circuits for optimization. This implies that combinatorial optimization problems are encoded with redundant information in quantum circuits of current VQAs. Therefore, to attain quantum advantage for combinatorial optimization, future quantum algorithms should be designed to incorporate information that is free of such redundancies.

Optimization problems are ubiquitous in various industrial settings, and multi-knapsack optimization is one recurrent task faced daily by several industries. The advent of quantum computing has opened a new paradigm for computationally intensive tasks, with promises of delivering better and faster solutions for specific classes of problems. This work presents a comprehensive study of quantum computing approaches for multi-knapsack problems, by investigating some of the most prominent and state-of-the-art quantum algorithms using different quantum software and hardware tools. The performance of the quantum approaches is compared for varying hyperparameters. We consider several gate-based quantum algorithms, such as QAOA and VQE, as well as quantum annealing, and present an exhaustive study of the solutions and the estimation of runtimes. Additionally, we analyze the impact of warm-starting QAOA to understand the reasons for the better performance of this approach. We discuss the implications of our results in view of utilizing quantum optimization for industrial applications in the future. In addition to the high demand for better quantum hardware, our results also emphasize the necessity of more and better quantum optimization algorithms, especially for multi-knapsack problems., 20 pages

Many emerging commercial services are based on the sharing or pooling of resources for common use with the aim of reducing costs. Businesses such as delivery-, mobility-, or transport-as-a-service have become standard in many parts of the world, fulfilling on-demand requests for customers in live settings. However, it is known that many of these problems are NP-hard, and therefore both modeling and solving them accurately is a challenge. Here we focus on one such routing problem, the Ride Pooling Problem (RPP), where multiple customers can request on-demand pickups and drop-offs from shared vehicles within a fleet. The combinatorial optimization task is to optimally pool customer requests using the limited set of vehicles, akin to a small-scale flexible bus route. In this work, we propose a quadratic unconstrained binary optimization (QUBO) program and introduce efficient formulation methods for the RPP to be solved using metaheuristics, and specifically emerging quantum optimization algorithms.