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Facta universitatis - series Electronics and Energetics

Representations, operations, and applications of switching circuits in the reversible and quantum spaces

Anas N. Al‐Rabadi

Published Jan 1, 2007• 6 citations
Publisher

Abstract

This paper reviews recent developments in the use of reversible synthesis techniques in the reversible and quantum logic circuit design of binary and multiple valued switching functions. In particular, this paper reviews the specific developments and various uses of spectral transforms and functional expansions, group theory, and cellular automata in the reversible logic synthesis of digital functions.

DOI
10.2298/fuee0703507a

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This paper reviews recent developments in the use of reversible synthesis techniques in the reversible and quantum logic circuit design of binary and multiple valued switching functions. In particular, this paper reviews the specific developments and various uses of spectral transforms and functional expansions, group theory, and cellular automata in the reversible logic synthesis of digital functions.
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, postsynthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms—search based, cycle based, transformation based, 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.
Research on reversible circuits has gained significance due to its application in quantum computations and many further areas such as the design of encoders. At the same time, the use of multiple-valued logic gained importance since this reduces the number of required entities in physical systems (e.g. in a future quantum computer). While most research is still conducted in the Boolean domain, there exist only few approaches which realize reversible circuits for multiple-valued logic. Moreover, most of the previously proposed solutions for synthesis of multiple-valued reversible circuits are not scalable and consider ternary (i.e. 3-valued circuits) only. Instead of overcoming these issues by developing new synthesis approaches for multiple-valued reversible circuits from scratch, we propose to utilize the recent accomplishments in the design of Boolean reversible circuits and to generalize them for multiple-valued logic. To this end, we discuss how to generalize Quantum Multiple-valued Decision Diagram based (QMDD-based) synthesis - a synthesis approach for Boolean reversible circuits which has been proven to be scalable and which has been used in several recently developed design flows. The discussions eventually show how to bridge the development gap between Boolean and multiple-valued logic for reversible circuits.
With increase in emphasis on low-power design and quantum computation, research in reversible logic synthesis has gained great attention. Various methods of synthesis exist in the literature, like exact synthesis, heuristic approaches, methods based on group theory, and those based on higher level representation of functions like Binary Decision Diagram (BDD). In this paper a group theory based synthesis approach for reversible circuits is presented, using both positive-control and negative-control Toffoli gates. The method uses group theoretic rules for factoring permutation cycles for synthesis. The use of both positive and negative control Toffoli gates results in reduction of total number of gates required as compared to previous methods based on group theory. Several worked out examples illustrate the advantage of the proposed approach.
Reversible quantum circuits are a necessary subclass of quantum computation and its realization is required for any quantum computer to be universal. This paper investigates how to synthesis of arbitrary ternary non-reversible logic circuits by adding inputs with constant value and garbage outputs. Group theory has been also used to solve the synthesis of reversible logic circuits. Our algorithm uses the SNT (ternary Swap gate, ternary NOT gate, ternary Toffoli gate) library, by reducing the ternary non-reversible logic circuit synthesis problem to group theory representation. The main result shows the relationship of ternary non-reversible logic circuits and the reversible circuits. The realization approach is constructive and can be further used to develop software for synthesis of arbitrary d-level circuits. This result is significantly different from the binary non-reversible logic circuits.
Many-valued quantum circuit synthesis of many-valued reversible expansions and fast transforms is introduced in this paper. Since the reduction of power consumption is a major requirement for the circuit design in future technologies, such as in quantum computing, the main features of several future technologies will include reversibility. Consequently, the new quantum circuits can play an important task in the design of future circuits that consume minimal power. In addition, the new quantum circuit methodology is general and can be used to realize any multiple-valued function in the quantum space. It is also shown that the structural generality advantage that results from the new design methodology is opposed with the increased quantum structural complexity disadvantage which may be considered in any further cost-benefit design analysis.