: Synchronous finite state machines are very important for digital sequential designs. Among other important aspects, they represent a powerful way for synchronizing hardware components so that these components may cooperate adequately in the fulfillment of the main objective of the hardware design. In this paper, we propose an evolutionary methodology to solve one of the problems related to the design of finite state machines. We optimally solve the state assignment NP-complete problem using a quantum inspired evolutionary algorithm. This is motivated by the fact that with an optimal state assignment one can physically implement the state machine using a minimal hardware area and response time. Key Words: Quantum computation, finite state machine, state assignment problem.