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Journal of Circuits Systems and Computers

DESIGN AND OPTIMIZATION OF SINGLE AND MULTIPLE-LOOP REVERSIBLE AND QUANTUM FEEDBACK CIRCUITS

MAJID MOHAMMADI, Aliakbar Niknafs, Mohammad Eshghi, Gerhard W. Dueck

Published May 1, 2012• 8 citations
Publisher

Abstract

The majority of work in reversible logic circuits has been limited to combinational logic. Researchers are now beginning to suggest designs for sequential circuits. In this paper we propose a new method to design and optimize feedback reversible logic circuits and a specific group of quantum logic circuits based on the reversible state transition table and genetic algorithms (GA). To show the efficiency of the proposed method, some reversible sequential elements such as D and T flip-flops (FFs), with and without clock and reset, and edge triggered FFs are designed. We have also extended our method to multiple loop feedback circuits. The proposed circuits are highly optimized using a GA synthesis tool that allows don't care values. Some of the designs in this paper are presented in other papers; however, the comparisons show that the quantum cost and number of garbage inputs/outputs are reduced efficiently by our method.

DOI
10.1142/s0218126612500181

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The majority of work in reversible logic circuits has been limited to combinational logic. Researchers are now beginning to suggest designs for sequential circuits. In this paper we propose a new method to design and optimize feedback reversible logic circuits and a specific group of quantum logic circuits based on the reversible state transition table and genetic algorithms (GA). To show the efficiency of the proposed method, some reversible sequential elements such as D and T flip-flops (FFs), with and without clock and reset, and edge triggered FFs are designed. We have also extended our method to multiple loop feedback circuits. The proposed circuits are highly optimized using a GA synthesis tool that allows don't care values. Some of the designs in this paper are presented in other papers; however, the comparisons show that the quantum cost and number of garbage inputs/outputs are reduced efficiently by our method.
Various synthesis methods have been proposed in the literature for reversible and quantum logic circuits. However, there are few algorithms to optimize an existing circuit with multiple constraints simultaneously. In this paper, some heuristics in genetic algorithms (GA) to optimize a given circuit in terms of quantum cost, number of gates, location of garbage outputs, and delay, are proposed. The proposed methods can optimize an existing circuit with a given truth table, including don’t care values, for different aspects of optimality. The results show good enhancements in the optimization of benchmark circuits compared to the previously published methods.
Reversible logic gates are critical components in the field of quantum computing and low-power digital circuits, as they allow for the retrieval of input states from output states without any loss of information. This property ensures minimal energy dissipation, aligning with the principles of reversible computation. Their applications extend to quantum computing, cryptographic systems, and error detection and correction mechanisms. This paper presents a novel design for a Reversible D Flip-Flop (RDFF) and a 4-bit Linear Feedback Shift Register (LFSR). The Linear Feedback Shift Register (LFSR) is built utilizing four Register-Driven D Flip-Flops (RDFFs) and a feedback mechanism that incorporates a Feynman Gate. This configuration successfully showcases the capacity to generate pseudo-random sequences. The LFSR design demonstrates a 10% improvement in Total Reversible Logic Implementation Cost and 27% enhancement in quantum cost, making it a more resource-efficient option for reversible computing. This work makes a valuable contribution to the field of reversible computing by offering efficient designs for essential components.
Reversible quantum logic synthesis is to study given quantum gates and quantum circuits of the constraints and limitations and find the smallest or smaller quantum cost to achieve the desired quantum logic circuits.The quantum logic gate functions of the matrix is indicated by the mathematical model. The synthesis and optimization are achieved simultaneously by the genetic algorithm as global search tool. Genetic algorithm is applied to quantum reversible logic synthesis.The fourth-order quantum circuit experiment has achieved good results,and further analysis of this method in high-level synthesis of quantum circuits and its application is completed.
In the recent years reversible logic circuits have gained a remarkable interest in the light of advancements made in quantum computation. The promise of theoretically zero power consumption is a major driving force for researchers to develop circuits using this logic. Synthesis of reversible logic and generating reversible logic circuit automatically with lower cost always has been a challenging task as reducing the search space is one of the major issues in the synthesis process using permutation. In this work, we proposed an Adaptive Genetic Algorithm (AGA) for synthesizing reversible logic circuits. NCT (NOT, CNOT, Toffoli) gate based library has been considered for synthesis of reversible logic circuits (RLC). The proposed algorithm produces a cascade of Toffoli gates for a given reversible specification of a circuit. Comparison of experimental results for several benchmark circuits shows that proposed evolutionary algorithm enables optimal or near-optimal solutions with lesser Gate Counts.
Multiple-valued reversible logic is an emerging area in reversible and quantum logic circuit synthesis. Multiple-valued reversible logic circuits can potentially reduce the width of the reversible or quantum circuit which is a limitation in current quantum technology. In this paper we propose a method to synthesize the multiple-valued reversible sequential circuits. Implementations for ternary D and T flip flops and edge triggered D flip flop are proposed. Synthesis of generalized fanout circuit and generalized r-valued T flip flop are also presented.
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