Quantum Inf Process (2018) 17:104 https://doi.org/10.1007/s11128-018-1874-1 Improving the quantum cost of reversible Boolean functions using reorder algorithm Taghreed Ahmed 1 · Ahmed Younes 1,2 · Ashraf Elsayed 1 Received: 4 November 2017 / Accepted: 9 March 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract This paper introduces a novel algorithm to synthesize a low-cost reversible circuits for any Boolean function with n inputs represented as a Positive Polarity Reed–Muller expansion. The proposed algorithm applies a predefined rules to reorder the terms in the function to minimize the multi-calculation of common parts of the Boolean function to decrease the quantum cost of the reversible circuit. The paper achieves a decrease in the quantum cost and/or the circuit length, on average, when compared with relevant work in the literature. Keywords Boolean function · Reversible Boolean circuits · Quantum cost · Factorization algorithm · Reorder algorithm 1 Introduction The study of Boolean functions is important in science and engineering because they have many applications such as cryptography [4]. Synthesis of reversible circuits for Boolean function is one of the areas of interest in research [3, 6] because there is no lose of information during the reversible computation [17]. The reversible circuits have B Taghreed Ahmed taghreed_ebed@yahoo.com Ahmed Younes ayounes@alexu.edu.eg Ashraf Elsayed ashraf.elsayed@alexu.edu.eg 1 Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt 2 School of Computer Science, University of Birmingham, Birmingham B15 2TT, UK 123