Recently, a parallel computation for all of the combinations of values in variables of a logical function is proposed (Nagata and Nakamura, Int. J. Theor. Phys. 59, 611 2020). Here, we propose a quantum algorithm for evaluating simultaneously two of logical functions which are constructed based on a boolean algebra stemmed from atoms in it. Finally, we discuss that all of the logical functions are evaluated simultaneously by using parallel computing based on many quantum systems.