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.

Keywords

• reversible logic
• reversible circuits
• reversible gate
• cnt set of the gates