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This paper shows how the new field of quantum computing can be applied to the creation of neural network circuits. Quantum computing is capable of processing huge numbers of quantum states simultaneously, in parallel, ("quantum parallelism"). In theory, QC ought to be able to process all possible points in a 2N search space (of N bit bit-strings). If N is large, 2N is gigantic, making a systematic search with a classical computer impossible. This paper presents an extended example of a simple QC algorithm applied to the generation of neural network circuits.