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An exact quantum algorithm for testing Boolean functions with one uncomplemented product of two variables

  • 01-07-2020
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Abstract

In this paper, we propose a novel quantum learning algorithm, based on Younes’ quantum circuit, to find dependent variables of the Boolean function \( f: \left\{ {0, 1} \right\}^{n} \to \left\{ {0, 1} \right\} \) with one uncomplemented product of two variables. Typically, in the worst-case scenario, two dependent variables are found by evaluating the function \( O\left( n \right) \) times. However, our proposed quantum algorithm only requires \( O\left( {\log_{2} n} \right) \) function operations in the worst-case. Additionally, we evaluate the average number to perform the function. In the average case, our algorithm requires \( O\left( 1 \right) \) function operations.

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Title
An exact quantum algorithm for testing Boolean functions with one uncomplemented product of two variables
Author
Chien-Yuan Chen
Publication date
01-07-2020
Publisher
Springer US
Published in
Quantum Information Processing / Issue 7/2020
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-020-02711-8
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