A Quantum Evolutionary Computational Technique (QECT) is proposed in this paper. The approach is based on the integration of quantum computing concepts such as superposition of states, application of quantum gate with the concept of genetic algorithm and simulated annealing. To demonstrate effectiveness and applicability of QECT, simulations are carried out on five Benchmark Test functions, which are well-known combinatorial optimization problems. These exemplify that the proposed algorithm has a capability to obtain near global optimum, without premature convergence unlike other variants. QECT has the strong capability to explore the nonlinear search regions and it is a step forward in the area of hybrid stochastic search. It is applied on a problem of mechanical engineering design of a pressure vessel. The application of proposed heuristic technique in mechanical engineering design is a step towards agility in design and manufacturing.