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We exploit Grover operator of database search algorithm for weight decisionalgorithm. In this research, weight decision problem is to find an exact weightw from given two weights as w1 and w2 where w1+w2=1 and 0<w1<w2<1. Firstly, ifa Boolean function is given and when weights are {1/4,3/4}, we can find w withonly one application of Grover operator. Secondly, if we apply k many times ofGrover operator, we can decide w from the set of weights{sin^2(\frac{k}{2k+1}\frac{\pi}{2}) cos^2(\frac{k}{2k+1}\frac{\pi}{2})}.Finally, by changing the last two Grover operators with two phase conditions,we can decide w from given any set of two weights. To decide w with a suresuccess, if the quantum algorithm requires O(k) Grover steps, then the bestknown classical algorithm requires \Omega(k^s) steps where s>2. Hence thequantum algorithm achieves at least quadratic speedup.Comment: Extended to the case w1+w2=1. Accepted to EQIS200

Exact quantum algorithm to distinguish Boolean functions of different weights