Designing of Reversible Functions in Classical and Quantum Domains


  • Ryszard S. Romaniuk Warsaw University of Technology, Institute of Electronic Systems
  • Andrzej Skorupski Warsaw University of Technology, Institute of Computer Science


First sections of the paper contain some
considerations relevant to the reversibility of quantum gates. The
Solovay-Kitayev theorem shows that using proper set of
quantum gates one can build a quantum version of the nondeterministic
Turing machine. On the other hand the
Gottesmann-Knill theorem shows the possibility to simulate the
quantum machine consisting of only Clifford/Pauli group of
gates. This paper presents also an original method of designing
the reversible functions. This method is intended for the most
popular gate set with three types of gates CNT (Control, NOT
and Toffoli). The presented algorithm leads to cascade with
minimal number CNT gates. This solution is called optimal
reversible circuits. The paper is organized as follows. Section 5
recalls basic concepts of reversible logic. Section 6 contain short
description of CNT set of the reversible gates. In Section 7 is
presented form of result of designing as the cascade of gates.
Section 8 describes the algorithm and section 9 simple example.

Author Biography

Ryszard S. Romaniuk, Warsaw University of Technology, Institute of Electronic Systems

University Professor; Editor-in-Chief IJET; Chair Edit. Board Ph.Let.PL; Ed.Adv.Bd. Photonics Spectra; Director of ISE, FE&IT, WUT; Research Secretary, Committee of Electronics and Telecommunications, Polish Academy of Sciences; Eisenhower Fellow; SPIE Fellow; Member: IEEE, OSA, EOS, EPS, Jury - The Prism Awards for Photonics Innovation, Polish Physical Society, SEP - Assoc.Pol.El.Eng., Photonics Society of Poland.

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Quantum Information Technology