Quantum state genetic algorithm was applied into the discrete design of broadband extreme-ultraviolet multilayer to solve the problem of solving accuracy in genetic algorithm. And the discrete design of layer thickness can be achieved in the process of quantum state genetic algorithm. It solves the problem that the layer can be accurately fabricated when the magnetron sputtering system is controlled by the deposition time. According to the results designed by quantum state genetic algorithm, broadband extreme-ultraviolet multilayers have been fabricated by magnetron sputtering system. The measured results show two kinds of multilayers designed by quantum state genetic algorithm were fabricated, one has a reflectivity of more than 45% in the 0°~15° range of incidence angle, and the other reaches the reflectivity of more than 20% for the wavelength range from 13 nm to 15 nm. The relative work shows the potential value of quantum state genetic algorithm and offers another alternative optimizing algorithm in the field of broadband extreme-ultraviolet multilayer design. And then the algorithm can achieve the discrete design of multilayer, which makes fabricated multilayer have better spectral properties.