Abstract: What bio-inspired algorithms mimic are natural mechanisms governing the macroscopic world for optimizing actual performances that are of vital importance. Neural and neurofuzzy networks, genetic, swarm-intelligence and other evolutionary algorithms are well-known results of this imitation. A completely different situation characterizes the microscopic world governed by quantum mechanics. All the possible solutions exist simultaneously in superposition and the problem is to extract the optimal one. In this case, basic mechanisms of quantum mechanics, i.e., superposition and entanglement, are necessary to mimic nature. Following the latter approach, in this paper a quantum architecture was proposed for determining the maximum/minimum in a set of positive integers which is a basic problem related to optimization. The proposed architecture is based on a suitable nonlinear quantum operator and it solves the said problem by an exhaustive search. This was illustrated in detail in the case of a typical NP-complete problem.