Minimization of Quantum Circuits using Quantum Operator Forms

Authors

Martin Lukac, Tohoku UniversityFollow
Michitaka Kameyama, Tohoku University
Marek Perkowski, Portland State UniversityFollow
Pawel Kerntopf, Warsaw University of TechnologyFollow

Published In

eprint arXiv:1701.01999

Document Type

Pre-Print

Publication Date

1-2017

Subjects

Quantum computers -- Circuits, Reversible computing, Quantum theory

Abstract

In this paper we present a method for minimizing reversible quantum circuits using the Quantum Operator Form (QOF); a new representation of quantum circuit and of quantum-realized reversible circuits based on the CNOT, CV and CV† quantum gates. The proposed form is a quantum extension to the well known Reed-Muller but unlike the Reed-Muller form, the QOF allows the usage of different quantum gates. Therefore QOF permits minimization of quantum circuits by using properties of different gates than only the multi-control Toffoli gates. We introduce a set of minimization rules and a pseudo-algorithm that can be used to design circuits with the CNOT, CV and CV† quantum gates. We show how the QOF can be used to minimize reversible quantum circuits and how the rules allow to obtain exact realizations using the above mentioned quantum gates.

Description

This paper was subsequently published in the Proceedings of the ULSI Workshop 2012 (@ISMVL 2012).

Persistent Identifier

http://archives.pdx.edu/ds/psu/19906

Citation Details

Lukac, M., Kameyama, M., Perkowski, M., & Kerntopf, P. (2017). Minimization of quantum circuits using quantum operator forms. arXiv preprint arXiv:1701.01999.