An exact quantum algorithm for testing Boolean functions with one uncomplemented product of two variables

In this paper, we propose a novel quantum learning algorithm, based on Younes’ quantum circuit, to find dependent variables of the Boolean function f : 0 , 1 n → 0 , 1 with one uncomplemented product of two variables. Typically, in the worst-case scenario, two dependent variables are found by evaluating the function O n times. However, our proposed quantum algorithm only requires O log 2 n function operations in the worst-case. Additionally, we evaluate the average number to perform the function. In the average case, our algorithm requires O 1 function operations.