Unconventional computing devices leverage the intrinsic dynamics of a physical substrate to perform fast, energy-efficient, and special-purpose computations. Granular metamaterials have great potential for creating such computing devices. However, there is no general framework for the inverse design of large-scale granular materials. Here, we develop a gradient-based optimization framework for harmonically driven granular materials to obtain a target wave response. Using this framework, we design basic logic gates in which mechanical vibrations carry the information at predetermined frequencies. Our findings show that a gradient-based optimization method can greatly expand the design space of computational metamaterials and provide the opportunity to systematically traverse their parameter space to find materials with the desired functionalities.