Synthesis and optimization of reversible circuits—a survey (original) (raw)
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A Synthesis and Optimization of Reversible Circuits -A Survey
Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit-manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, post-synthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms -search-based, cycle-based, transformationbased, and BDD-based -as well as specific algorithms for reversible synthesis, both exact and heuristic. We conclude the survey by outlining key open challenges in synthesis of reversible and quantum logic, as well as most common misconceptions.
An extension of transformation-based reversible and quantum circuit synthesis
2016 IEEE International Symposium on Circuits and Systems (ISCAS), 2016
Transformation-based synthesis is a well established systematic approach to determine a circuit implementation from a reversible function specification. Due to the inherent bidirectionality of reversible circuits the basic method can be applied in a bidirectional manner. In the approaches to date, gates are added either to the input side or the output side of the circuit on each iteration. In this paper, we introduce a new variation where gates may be added at both ends during a single iteration when this is advantageous to reducing the cost of the circuit. Experimental results show the advantage of the new approach over previous transformation-based synthesis methods and that the additional computation is justified by the possibility of improved circuit costs.
Design, Automation, and Test in Europe, 2004
A function is reversible if each input vector produces a unique output vector. Reversible functions find applications in low power design, quantum computing, and nanotechnology. Logic synthesis for reversible circuits differs substantially from traditional logic synthesis. In this paper, we present the .rst practical synthesis algorithm and tool for reversible functions with a large number of inputs. It uses positive-polarity
Synthesis of reversible circuits by different methods and their optimization
In the recent years, reversible logic has emerged as a promising technology having its applications in low power CMOS, quantum computing, nanotechnology, and optical computing. A reversible circuit maps each output vector into a unique input vector, and vice versa. There always has been a hurdle in realization and optimization of reversible circuit. One way of realizing reversible logic is quantum computers. Quantum computing has been a field of growing interest in the last decade because of its promises to reduce power consumption. This paper presents realization of reversible circuits such as adder and multiplier using three different methods which are as follows CMOS logic, Quantum cellular automata (QCA), and jQuantum. Although CMOS don’t take full benefit of reversibility criteria but it is used for functional verification of reversible circuit design. In this paper we have implemented few reversible circuits in CMOS and their layout is presented. QCA is a new technology for realization of quantum circuits. Minimum area full adder has been implemented in QCAD and presented in this paper. This paper also proposes a design of a reversible multiplier with minimum complexity in terms of gates. This multiplier design has been verified using jQuantum which is a JAVA simulator which designs reversible circuits based on quantum wires. A novel design of a 4x4 multiplier has also been proposed. Thus, this paper proposes different methods for realising reversible logic and their optimization techniques.
Bi-Direction Synthesis for Reversible Circuits
IEEE Computer Society Annual Symposium on VLSI: New Frontiers in VLSI Design (ISVLSI'05), 2005
Quantum computing is one of the most promising emerging technologies of the future. Reversible circuits are an important class of Quantum circuits. In this paper, we investigate the problem of optimally synthesizing fourqubit reversible circuits. We present an enhanced bidirectional synthesis approach. Due to the superexponential increase on the memory requirement, all the existing methods can only perform four steps for the CNP (Control-Not gate, NOT gate, and Peres gate) library. Our novel method can achieve 12 steps. As a result, we augment the number of circuits that can be optimally synthesized by over 5*10 6 times. Moreover, our approach is faster than the existing approaches by orders of magnitude. The promising experimental results demonstrate the effectiveness of our approach.
Reversible circuit synthesis using a cycle-based approach
ACM Journal on Emerging Technologies in Computing Systems, 2010
Reversible logic has applications in various research areas including signal processing, cryptography and quantum computation. In this paper, direct NCT-based synthesis of a given k-cycle in a cycle-based synthesis scenario is examined. To this end, a set of seven building blocks is proposed that reveals the potential of direct synthesis of a given permutation to reduce both quantum cost and average runtime. To synthesize a given large cycle, we propose a decomposition algorithm to extract the suggested building blocks from the input specification. Then, a synthesis method is introduced which uses the building blocks and the decomposition algorithm. Finally, a hybrid synthesis framework is suggested which uses the proposed cycle-based synthesis method in conjunction with one of the recent NCT-based synthesis approaches which is based on Reed-Muller (RM) spectra. The time complexity and the effectiveness of the proposed synthesis approach are analyzed in detail. Our analyses show that the proposed hybrid framework leads to a better quantum cost in the worst-case scenario compared to the previously presented methods. The proposed framework always converges and typically synthesizes a given specification very fast compared to the available synthesis algorithms. Besides, the quantum costs of benchmark functions are improved about 20% on average (55% in the best case).
Synthesis of reversible circuits for large reversible functions
Facta universitatis - series: Electronics and Energetics, 2010
This paper presents a new algorithm MP (multiple pass) to synthesize large reversible binary circuits without ancilla bits. The well-known MMD algorithm for synthesis of reversible circuits requires to store a truth table (or a Reed-Muller-RM transform) as a 2n vector to represent a reversible function of n variables. This representation prohibits synthesis of large functions. However, in MP we do not store such an exponentially growing data structure. The values of minterms are calculated in MP dynamically, one-by-one, from a set of logic equations that specify the reversible circuit to be designed. This allows for synthesis of large scale reversible circuits (30-bits), which is not possible with any existing algorithm. In addition, our unique multi-pass approach where the circuit is synthesized with various, yet specific, minterm orders yields quasi-optimal solution. The algorithm returns a description of the quasi-optimal circuit with respect to gate count or to its "quantum cost". Although the synthesis process in MP is relatively slower, the solution is found in real-time for smaller circuits of 8 bits or less.
Bi-Directional Synthesis of 4-Bit Reversible Circuits
The Computer Journal, 2007
Reversible circuits play an important role in quantum computing, which is one of the most promising emerging technologies. In this paper, we investigate the problem of optimally synthesizing 4-bit reversible circuits. We present an enhanced bi-directional synthesis approach. Owing to the exponential nature of the memory and run-time complexity, all existing methods can only perform four steps for the Controlled-Not gate NOT gate, and Peres gate library. Our novel method can achieve 12 steps. As a result, we augment the number of circuits that can optimally be synthesized by over 5 3 10 6 times. We synthesized 1000 random 4-bit reversible circuits. The statistical analysis result supports our estimation. The quantum cost of our result is also better than the quantum cost of other approaches. The promising experimental results demonstrate the effectiveness of our approach.