Oczekiwany dalszy rozwój techniki cyfrowej związany jest dziś z technologią kwantową. Stwarza ona warunki do równoległego przetwarzania danych z nieosiągalną teraz szybkością. Badania w tej dziedzinie skupiają się wokół wielu zagadnień, z czego tu wymieniono trzy: architektura układów kwantowych, algorytmy i implementacja bramek. Oceniając stan badań można stwierdzić, że do wdrożenia ich wyników potrzeba jeszcze rozwiązania wielu problemów.
EN
The expected research and development of computer technology is now associated with quantum technology. It creates conditions for parallel data processing with high speed procedure. Research in this field focuses on many issues like for example: quantum system architecture, algorithms, and gate implementation. But actual results does not permit to applications in practice.
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 non-deterministic 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.
In this paper the new synthesis method for reversible networks is proposed. The method is suitable to generate optimal circuits. The examples will be shown for three variables reversible functions but the method is scalable to larger number of variables. The algorithm could be easily implemented with high speed execution and without big consuming storage software. Section 1 contains general concepts about the reversible functions. In Section 2 there are presented various descriptions of reversible functions. One of them is the description using partitions. In Section 3 there are introduced the cascade of the reversible gates as the target of the synthesis algorithm. In order to achieve this target the definitions of the rest and remain functions will be helpful. Section 4 contains the proposed algorithm. There is introduced a classification of minterms distribution for a given function. To select the successive gates in the cascade the condition of the improvement the minterms distribution must be fulfilled. Section 4 describes the algorithm how to improve the minterms distributions in order to find the optimal cascade. Section 5 shows the one example of this algorithm.
This paper presents an original method of designing some special reversible circuits. This method is intended for the most popular gate set with three types of gates CNT (Control, NOT and Toffoli). The presented algorithm is based on two types of cascades with these reversible gates. The problem of transformation between two reversible functions is solved. This method allows to find optimal reversible circuits. The paper is organized as follows. Section 1 and 2 recalls basic concepts of reversible logic. Especially the two types of cascades of reversible function are presented. In Section 3 there is introduced a problem of analysis of the cascades. Section 4 describes the method of synthesis of the optimal cascade for transformation of the given reversible function into another one.
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