This paper proposes a novel quantum learning algorithm based on Bernstein and Vazirani’s quantum circuit to find the dependent variables of the 2-junta problem. Typically, for a given Boolean function f : {0, 1} n → {0, 1} that depends on only 2 out of n variables, the dependent variables are obtained by evaluating the function 4 n times in the worst-case. However, the proposed quantum algorithm only requires O ( log 2 n ) function operations in the worst-case. Moreover, the algorithm requires an average of 5.3 function operations at the most when n ≥ 8.

中文翻译：

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2-Junta 问题的精确量子算法

本文提出了一种基于 Bernstein 和 Vazirani 的量子电路的新型量子学习算法来寻找 2-junta 问题的因变量。通常，对于给定的布尔函数 f : {0, 1} n → {0, 1} 仅依赖于 n 个变量中的 2 个，在最坏情况下通过对函数求值 4 n 次来获得因变量。然而，所提出的量子算法在最坏的情况下只需要 O (log 2 n ) 个函数操作。而且，当n≥8时，该算法平均最多需要5.3次函数操作。