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.Comment: 11 pages, 14 figures, Proceedings of the ULSI Workshop 2012 (@ISMVL
2012