Eur. Phys. J. Plus (2015) 130: 34
https://doi.org/10.1140/epjp/i2015-15034-4

Regular Article

A fast quantum algorithm for the affine Boolean function identification

¹ Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt
² School of Computer Science, University of Birmingham, B15 2TT, Birmingham, UK

^* e-mail: ayounes@alexu.edu.eg

Received: 25 October 2014
Revised: 25 January 2015
Accepted: 29 January 2015
Published online: 25 February 2015

Abstract

Bernstein-Vazirani algorithm (the one-query algorithm) can identify a completely specified linear Boolean function using a single query to the oracle with certainty. The first aim of the paper is to show that if the provided Boolean function is affine, then one more query to the oracle (the two-query algorithm) is required to identify the affinity of the function with certainty. The second aim of the paper is to show that if the provided Boolean function is incompletely defined, then the one-query and the two-query algorithms can be used as bounded-error quantum polynomial algorithms to identify certain classes of incompletely defined linear and affine Boolean functions respectively with probability of success at least 2/3.