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In this paper we present an evolutionary approach to the quantum symbolic logic synthesis. We use a genetic algorithm to synthesize quantum circuits from examples, allowing to synthesize functions that are both completely and incompletely specified. The symbolic synthesis is implemented in the GA so as to verify our approach. The Occam Razor principle, fundamental to inductive learning as well as to logic synthesis, is satisfied in this approach by seeking circuits of reduced complexity. The GA is tested on a set of benchmark functions representing single output quantum circuits as well as multiple entangled-qubit state generators.