Samuel L Braunstein et al 2007 J. Phys. A: Math. Theor. 40 8441 doi:10.1088/1751-8113/40/29/017
Exact quantum algorithm to distinguish Boolean functions of different weights
Samuel L Braunstein1, Byung-Soo Choi1,2, Subhroshekhar Ghosh3 and Subhamoy Maitra4
Show affiliationsIn 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 < w1 < w2 < 1. First, we propose a limited weight-decision algorithm where the function has another constraint: a weight is in 
for integer k. Second, by changing the phases in the last two Grover iterations, we propose a general weight-decision algorithm which is free from the above constraint. Finally, we show that when our algorithm requires O(k) queries to find w with a unit success probability, any classical algorithm requires at least Ω(k2) queries for a unit success probability. In addition, we show that our algorithm requires fewer queries to solve this problem compared with the quantum counting algorithm.
- PACS
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03.67.Lx Quantum computation architectures and implementations
- MSC
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81P68 Quantum computation and quantum cryptography (See also 68Q05, 94A60)
- Subjects
- Dates
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Issue 29 (20 July 2007)
Received 24 November 2006, in final form 26 May 2007
Published 3 July 2007
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Exact quantum algorithm to distinguish Boolean functions of different weights
Samuel L Braunstein et al 2007 J. Phys. A: Math. Theor. 40 8441
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