Quantum optimization has emerged as a promising frontier of quantum computing, providing novel numerical approaches to mathematical optimization problems. The main goal of this paper is to facilitate interdisciplinary research between the Operations Research (OR) and quantum computing communities by helping OR scientists to build initial intuition for-, and offering them a hands-on gateway to quantum-powered methods in the context of discrete optimization. To this end, we consider three quantum-powered optimization approaches that make use of different types of quantum hardware available on the market. To illustrate these approaches, we solve three classical optimization problems: the Traveling Salesperson Problem, Weighted Maximum Cut, and Maximum Independent Set. With a general OR audience in mind, we attempt to provide an intuition behind each approach along with key references, describe the corresponding high-level workflow, and highlight crucial practical considerations. In particular, we emphasize the importance of problem formulations and device-specific configurations, and their impact on the amount of resources required for computation (where we focus on the number of qubits). These points are illustrated with a series of experiments on three types of quantum computers: a neutral atom machine from QuEra, a quantum annealer from D-Wave, and gate-based devices from IBM.
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