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A Synthesis Method for Quaternary Quantum Logic Circuits

Sudhindu Bikash, Mandal Amlan, Chakrabarti Susmita Sur-kolay

Published Aug 17, 2016• 10 citations
OpenAlex

Abstract

Synthesis of quaternary quantum circuits involves basic quaternary gates and logic operations in the quaternary quantum domain. In this paper, we propose new projection operations and quaternary logic gates for synthesizing quaternary logic functions. We also demonstrate the realization of the proposed gates using basic quantum quaternary operations. We then employ our synthesis method to design of quaternary adder and some benchmark circuits. Our results in terms of circuit cost, are better than the existing works.

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Synthesis of quaternary quantum circuits involves basic quaternary gates and logic operations in the quaternary quantum domain. In this paper, we propose new projection operations and quaternary logic gates for synthesizing quaternary logic functions. We also demonstrate the realization of the proposed gates using basic quantum quaternary operations. We then employ our synthesis method to design of quaternary adder and some benchmark circuits. Our results in terms of circuit cost, are better than the existing works.
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Basic logic gates and their operations in ternary quantum domain are involved in the synthesis of ternary quantum circuits. Only a few works define ternary algebra for ternary quantum logic realization. In this paper, a ternary logic function is expressed in terms of projection operations including a new one. A method to realize new multi-qutrit ternary gates in terms of generalized ternary gates and projection operations is also presented. We also introduced ten simplification rules for reducing ancilla qutrits and gate levels. Our method yields lower gate cost and fewer gate levels and ancilla qutrits than that obtained by earlier methods for the ternary benchmark circuits. The nnn qutrit ternary sum function is synthesized without any ancilla qutrit by our proposed methodology.
In this paper, we propose a method to realize symmetric binary functions as quaternary quantum/reversible circuits. In contrast to the existing binary synthesis methods, our design in quaternary domain offers a simple and regular cascade structure composed of quaternary quantum modules which enables significant reductions with respect to number of lines, levels and quantum costs. Further, a method to obtain an optimal realization is presented, this uses a few special quaternary quantum modules of low quantum cost. Experimental results confirm that our new method leads to realizations in quaternary domain with a significant reduction in number of lines, levels and quantum cost compared to the existing approaches in binary domain. Hence, our design in quaternary logic offers a useful alternative to existing designs in binary logic for realizing symmetric functions.
While the role of ternary reversible and quantum computation has been growing, synthesis methodologies for such logic, have been addressed in only a few works. A reversible ternary logic function can be expressed as minterms by using projection operators. In this paper, a novel realization of the projection operators using a minimum number of permutative ternary Muthukrishnan-Stroud (M-S) gates is presented. Next, an efficient method for logic simplification for ternary reversible logic is proposed. This method along with the new construction of projection operators yields significantly lower gate cost of approximately 31% less than that obtained by earlier methodologies, for the synthesis of ternary benchmark circuits.
One of the major problems in designing highly compact digital systems is the rate of power consumption and internal heat generated by the loss of information during the computation. The tendency of current circuit design technologies is towards Nanoscale. Quaternary reversible logic is an emerging technology for the future designing of the quantum systems since quantum reversible circuits can be realized in Nanoscales. The adder building block is an essential part of any computer system. This block must be designed efficiently. We proposed a new quaternary quantum reversible half adder with the quantum cost of 17 and a quaternary quantum reversible full adder with a quantum cost of 23. For the first time in the literature, we report that we proposed quaternary quantum reversible half adder as well as full adder with an optimum number of constant inputs. As the circuit lines in the domain of quantum computation are considered to be a very limited resource, the achievements in this paper are promising. The proposed circuits are efficient in terms of all figures of merits in comparison to the existing counterparts. To design these adder circuits, we used 1-qudit and 2-qudit quaternary gates.
Multiple-valued quantum circuits are a promising choice for future quantum computing technology since they have several advantages over binary quantum circuits. In this paper, we propose quaternary multi-qudit controlled gate family and show their realization on the top of liquid ion-trap realizable 1-qudit gates and 2-qudit Muthukrishnan-Stroud gates. Then we show a method of synthesizing incompletely specified multi-output quaternary function using quaternary 1-qudit gates and multi-qudit controlled gates.