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IEEE Ukraine Conference on Electrical and Computer Engineering (UKRCON)

Ternary reversible/quantum latches

Zhengbing Hu, Ivan Yuriychuk, V. G. Deı̆buk

Published May 1, 2017• 0 citations
Publisher

Abstract

Ternary reversible latches on the basis of one- and two-qutrit permutative Muthukrishnan-Stroud (MS) gates were synthesized for the first time. Such gates can be physically implemented on the basis of liquid ion-trap quantum technology. The use of adaptive genetic algorithm allowed designing the circuits of latches that are optimal with respect to quantum cost, number of gates, and delay time. Comparisons of synthesized circuits with known results of other authors were carried out.

DOI
10.1109/ukrcon.2017.8100380

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Ternary reversible latches on the basis of one- and two-qutrit permutative Muthukrishnan-Stroud (MS) gates were synthesized for the first time. Such gates can be physically implemented on the basis of liquid ion-trap quantum technology. The use of adaptive genetic algorithm allowed designing the circuits of latches that are optimal with respect to quantum cost, number of gates, and delay time. Comparisons of synthesized circuits with known results of other authors were carried out.
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Multiple-valued logic is a promising choice for future computer technologies, which provides a set of advantages comparing to binary circuits. We have developed an adaptive genetic algorithm for ternary reversible circuits using Muthukrishnan-Stroud gates. The method for chromosomes coding, as well as a reasonable choice of algorithm parameters, allowed obtaining circuits for ternary arithmetic devices, which are better than other known methods in terms of quantum cost, delay time and amount of input ancillary and output garbage qutrits. Based on our realization of ternary parallel full-adder we synthesized reversible ternary parallel adder/subtractor, which has better parameters over the previously reported devices.
Multiple-valued logic is a promising choice for future computer technologies, which provides a set of advantages comparing to binary circuits. In this paper, we have developed a genetic algorithm-based synthesis of ternary reversible circuits using Muthukrishnan-Stroud gates. The method for chromosomes coding, as well as a reasonable choice of algorithm parameters, allowed obtaining circuits for ternary Toffoli and modified Fredkin gates, which are better than other published methods in terms of quantum cost, delay times and amount of input ancillary and output garbage qutrits.
Typical methods of quantum/reversible synthesis are based on using the binary character of quantum computing.However, multi-valued logic is a promising choice for future computer technologies, given a set of advantages when comparing to binary circuits.In this work, we have developed a genetic algorithm-based synthesis of ternary reversible circuits using Muthukrishnan-Stroud gates.The method for chromosomes coding that we present, as well as a judicious choice of algorithm parameters, allowed obtaining circuits for half-adder and full adder which are better than other published methods in terms of cost, delay times and amount of input ancillary bits.A structure of the circuits is analyzed in details, based on their decomposition.
We present a new type of quantum realizable reversible cascade. Next we present a new algorithm to synthesize arbitrary single-output ternary functions using these reversible cascades. The cascades use “Generalized Multi-Valued Gates” introduced here, which extend the concept of Generalized Ternary Gates introduced previously. While there were 216 GTGs, a total of 12 ternary gates of the new type are sufficient to realize arbitrary ternary functions. (The count can be further reduced to 5 gates, three 2-qubit and two 1-qubit). Such gates are realizable in quantum ion trap devices. For some functions, the algorithm requires fewer gates than results previously published [1, 5, 8, 14]. In addition, the algorithm also does conversion from arbitrary ternary logic to reversible logic at the cost of relatively small garbage. The algorithm is implemented here in ternary logic, but generalization to arbitrary radix is both straightforward and sees a reduction in growth of cost as the radix is increased.