Exact quantum algorithm to distinguish Boolean functions of different weights

In this work, we exploit the Grover operator for the weight analysis of a Boolean function, specifically to solve the weight-decision problem. The weight w is the fraction of all possible inputs for which the output is 1. The goal of the weight-decision problem is to find the exact weight w from the given two weights w1 and w2 satisfying a general weight condition as w1 + w2 = 1 and 0 <w 1 <w 2 < 1. First, we propose a limited weightdecision algorithm where the function has another constraint: a weight is in � w1 = sin 2 � k

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