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Ibn AL- Haitham Journal For Pure and Applied Science

Quantum Gates to Implement the Reversible Logic Circuits

Ali Hassan Khidhir

Published Apr 27, 2017• 0 citations
OpenAlex

Abstract

Quantum gates which are represented by unitary matrices have potentials to implement the reversible logic circuits. M and M+ gates are two well-known quantum gates which are used to synthesize the reversible logic circuits. In this work, we have used behavioral description of these gates, instead of unitary matrix description, to synthesize reversible logic circuits. By this method, M and M+ gates are shown in the truth table form.

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Quantum gates which are represented by unitary matrices have potentials to implement the reversible logic circuits. M and M+ gates are two well-known quantum gates which are used to synthesize the reversible logic circuits. In this work, we have used behavioral description of these gates, instead of unitary matrix description, to synthesize reversible logic circuits. By this method, M and M+ gates are shown in the truth table form.
Quantum gates which are represented by unitary matrices have potentials to implement reversible logic circuits. V and V+gates are two well known quantum gates which are used to synthesize the reversible logic circuits. In this paper we have used behavioral description of these gates, instead of unitary matrix description, to synthesize reversible logic circuits. By this method, V and V+gates are shown in the truth table form. Results show that bigger circuits with more number of gates can be synthesized using proposed method. Some benchmarks of reversible logic circuits are also optimized and compared to other works.
This paper addresses using quantum gates to implement binary reversible logic circuits. We propose behavioral models for well known V and V+quantum gates. Our proposed representation is used to synthesize reversible logic circuits instead of using the known unitary matrix form of quantum gates. This technique allows V and V+gates to be represented in truth table forms. Results show that our technique can be used to synthesize circuits with bigger sizes and gate counts in compare with unitary matrix form of these gates. Several reversible circuit benchmarks are optimized and compared to related works.
Reversible logic is expanding grounds with its applicability to various upcoming technologies and quantum computation. Numerous reversible gates has also been proposed for designing logic circuits apart of basic quantum controlled Toffoli and Fredkin gates. A comparative study and analysis of a range of reversible gates from the literature is presented in this paper to obtain an optimal solution for designing these circuits. The gates are synthesized and implemented to obtain equivalent quantum circuits and operating cost in terms of number of inputs, gate cost, quantum cost, garbage output and ancilla input. The comparison is done at two subsequent levels i.e. gates structural level and circuit design level, providing a better solution for designing logic circuits. It is calculated that, basic gates are 50% efficient at gate level and 33% at design level analysis in terms of gate cost, as compared to the most efficient gates proposed in the literature.
This paper provides the initial threshold to building of more complex system having reversible sequential circuits as a primitive component and which can execute more complicated operations using quantum computers. The reversible circuits form the basic building block of quantum computers as all quantum operations are reversible. The important reversible gates used for reversible logic synthesis are Feynman Gate, New Gate and Fredkin gate. The novelty of the paper is the reversible designs of Flip Flops. The Flip Flops that are synthesized using reversible logic are RS Flip Flop, JK Flip Flop, D Flip Flop, T Flip Flop and Master Slave Flip Flop
Algorithms specifically designed for quantum computers have been developed. In quantum circuits, the Feynman, Toffoli, and Fredkin gates are employed instead of traditional inputs such as AND, OR, NAND, NOR, XOR, and XNOR in combinational logic gates. The ability to convert quantum circuits into combinational logic circuits, or vice versa, is of utmost importance. This essay study (or paper) aims to demonstrates the process of deriving combinational logic circuits from reversible quantum circuits. To achieve this, the Quine-McCluskey technique was utilized along with state tables generated from the quantum circuits to obtain an optimal logic expression that serves as the basis for constructing the combinational logic circuit. The resultant obtained combinational logic circuit was implemented within the MATLAB Simulink environment, and state tables were obtained. A comparison was made between the state tables derived from the quantum circuit and the combinational circuit, yielding successful results.
In order to efficiently automatically construct quantum reversible logic circuits with low cost,a novel method for quantum circuit's synthesis is proposed.Through the line topology transformation and truth table permutation,it converts an n-qubit circuit synthesis problem into single quantum circuit synthesis using traditional recursive thought.Then directly generate relevant circuit.After optimization,the quantum reversible logic circuit is synthesized finally.All 3-qubit reversible logic circuits have been synthesized by this method.The average number of EGT gates is only 6.41,and the number is down to 5.22 after optimization.Experimental results show that the number of gates to construct reversible logic circuits is less than other methods.For any n-qubit binary logic function,the number of EGT gates is less than n2n-1.Meanwhile,it voids the exponential nature of the memory or run-time complexity,and is very simple to implement in classical computer.