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This paper introduces a quantum computing algorithm called "QNN" (Quantum Neural Networks) which measures quantum mechanically and simultaneously the fitness values of all 2N possible chromosomes of N bits used to specify the structure of the networks. Previous attempts to apply quantum computing algorithms to evolutionary systems (e.g [1-4]) applied classical computing evolutionary algorithms to the choice and sequence of quantum operators, which is a hybrid approach (i.e. the EAs were classical, and the applications were quantum mechanical). Our QNN algorithm, on the other hand, is fully quantum mechanical, in the sense that the fitnesses are calculated quantum mechanically as well, thus allowing the fitness values of all possible 2N chromosomes to be measured simultaneously. Evolutionary algorithms (EAs) are a form of sampled search in a huge search space (of 2N points). If N is large, then 2N is astronomically large and computationally intractable. The QNN algorithm thus undermines the implicit basic assumption applicable to the field of evolutionary systems (ES), namely that one must employ a sampled search approach (i.e. an evolutionary algorithm (EA)) to explore the huge search space. The QNN algorithm is a form of what is called in this paper a "total search" algorithm. The whole space is searched and is done simultaneously, which makes the adjective "evolutionary" in the term "evolutionary systems" redundant. One can speculate that as the number of qubits implemented in real systems increases (currently the state of the art is 7 [5]), then it is likely that the current emphasis on evolutionary approaches to optimization problems and complex system building, will fade away and be replaced by the "total search" approach allowed by quantum computational methods.