This paper modifies Chen’s algorithm, which is the first exact quantum algorithm for testing 2-junta, and proposes an exact quantum learning algorithm for finding dependent variables of the Boolean function \( f: \left\{ {0, 1} \right\}^{n} \to \left\{ {0, 1} \right\} \) with one uncomplemented product of three variables. Typically, the dependent variables are obtained by evaluating the function \( 2n \) times in the worst case. However, our proposed quantum algorithm only requires \( O\left( {\log_{2} n} \right) \) function operations in the worst case. In addition, the average number to perform the function is evaluated. Our algorithm requires an average of \( 7.23 \) function operations at the most when \( n \ge 16 \). We also show that our algorithm cannot solve \( k \)-junta problem with one uncomplemented product if \( 4 \le k < n/2 \).

本文修改了Chen算法，它是第一个测试2军政府的精确量子算法，并提出了一种精确的量子学习算法，用于查找布尔函数\（f：\ left \ {{0，1} \ right \ } ^ {n} \ to \ left \ {{0，1} \ right \} \），其中三个变量是一个不互补的乘积。通常，在最坏的情况下，通过评估函数\（2n \）来获得因变量。但是，在最坏的情况下，我们提出的量子算法只需要\（O \ left（{\ log_ {2} n} \ right）\）函数操作。另外，评估执行该功能的平均数。当\（n \ ge 16 \）时，我们的算法最多需要平均\（7.23 \）个函数操作。我们还表明，如果\（4 \ le k <n / 2 \），则我们的算法无法用一个不互补积来解决\（k \）- junta问题。