Designing of Reversible Functions in Classical and Quantum Domains
Abstract
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.
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