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Since the dawn of Quantum Computing (QC), theoretical developments like Shor’s algorithm proved the conceptual superiority of QC over traditional computing. However, such quantum supremacy claims are difficult to achieve in practice because of the techni-cal challenges of realizing noiseless qubits. In the near future, QC applications will need to rely on noisy quantum devices that offload part of their work to classical devices. One way to achieve this is by using Parameterized Quantum Circuits (PQCs) in optimization or even in machine learning tasks. The energy requirements of quantum algorithms have not yet been studied extensively. In this article we explore several optimization algorithms using both theoretical insights and numerical experiments to understand their impact on energy consumption. Specifically, we highlight why and how algorithms like Quantum Natural Gradient Descent, Simultaneous Perturbation Stochastic Approximations or Circuit Learning methods, are at least 2× to 4× more energy efficient than their classical counterparts; why Feedback-Based Quantum Optimization is energy-inefficient; and how techniques like Rosalin can improve the energy efficiency of other algorithms by a factor of ≥ 20×. Finally, we use the NchooseK high-level programming model to run optimization problems on both gate-based quantum computers and quantum annealers. Empirical data indicate that these optimization problems run faster, have better success rates, and consume less energy on quantum annealers than on their gate-based counterparts., Los Alamos National Laboratory, Grant/Award Number: 20210397ER; Laboratory Directed Research and Development; National Nuclear Security Administration of U.S. Department of Energy, Grant/Award Number: 89233218CNA000001, Peer Reviewed, Postprint (author's final draft)