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The paper discusses theevolutionary computation approach to theproblem of optimal synthesis of Quantum andReversible Logic circuits. Our approach usesstandard Genetic Algorithm (GA) and itsrelative power as compared to previousapproaches comes from the encoding and theformulation of the cost and fitness functionsfor quantum circuits synthesis. We analyze newoperators and their role in synthesis andoptimization processes. Cost and fitnessfunctions for Reversible Circuit synthesis areintroduced as well as local optimizingtransformations. It is also shown that ourapproach can be used alternatively forsynthesis of either reversible or quantumcircuits without a major change in thealgorithm. Results are illustrated onsynthesized Margolus, Toffoli, Fredkin andother gates and Entanglement Circuits. This isfor the first time that several variants ofthese gates have been automatically synthesizedfrom quantum primitives.