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This paper presents a review of quantum-inspired population-based metaheuristics. Quantum-inspired algorithms were born when there were no quantum computers; they demonstrated to have interesting characteristics providing good results in classical computers. At present, when the first quantum computers are available, scientists are working to confirm the quantum supremacy in different fields. After almost 20 years that the first metaheuristic inspired in quantum phenomena was published, a large number of works have been proposed. This paper aims to look back to see which quantum-inspired metaheuristics could be translated to be used in the existing quantum computers based on the circuit model programming paradigm. Reviewed metaheuristics were classified according to their main source of inspiration; just some representative works of each classification were selected because of the vast number of existing works on each one. The analysis was done for the circuit model and metrics as width, size, and length were used to determine their viability of being implemented in a real quantum computer. Moreover, comparative results using metrics such as performance and running time for quantum-inspired metaheuristic were included.

A Review of Quantum-Inspired Metaheuristics: Going From Classical Computers to Real Quantum Computers