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