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Saudi International Electronics, Communications and Photonics Conference

An introduction to reversible circuit design

Robert Wille

Published Apr 1, 2011• 10 citations
Publisher

Abstract

After decades of continuous improvements and shrinking feature sizes, the development of conventional computing technologies faces enormous challenges. In particular, power dissipation in today's computer chips becomes crucial. Reversible computation is a promising alternative to these technologies, where power dissipation can be reduced or even eliminated. Furthermore, reversible logic builds the basis for quantum computation - a completely new way of processing which enables to solve certain problems exponentially faster compared to conventional methods. However, the design of reversible and quantum circuits is significantly different. Thus, new methods e.g. for synthesis, optimization, or verification are needed. This paper provides a brief introduction into reversible circuits and their respective design methods that have been proposed within the last years.

DOI
10.1109/siecpc.2011.5876689

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After decades of continuous improvements and shrinking feature sizes, the development of conventional computing technologies faces enormous challenges. In particular, power dissipation in today's computer chips becomes crucial. Reversible computation is a promising alternative to these technologies, where power dissipation can be reduced or even eliminated. Furthermore, reversible logic builds the basis for quantum computation - a completely new way of processing which enables to solve certain problems exponentially faster compared to conventional methods. However, the design of reversible and quantum circuits is significantly different. Thus, new methods e.g. for synthesis, optimization, or verification are needed. This paper provides a brief introduction into reversible circuits and their respective design methods that have been proposed within the last years.
Reversible logic circuits are beneficial to both classical and quantum computer design. Present-day logic building-blocks (like OR gates and NAND gates) are logically irreversible and therefore cannot be used for designing reversible computers. Thus reversible computation needs an appropriate design methodology. In contrast to conventional digital logic circuits, reversible logic circuits (of a same logic width w) form a mathematical group. The reversible circuits of width w form a group isomorphic to the symmetric group S_{2^w}. Its Young subgroups allow systematic and efficient synthesis of an arbitrary reversible circuit. We can choose either a left coset, a right coset, or a double coset approach. The optimal design is reminiscent of the so-called banyan networks of telecommunication. As an illustration, three experimental prototypes (in c-MOS chip technology) of reversible computing devices are presented. Special care has been taken to avoid as much as possible the appearance of garbage bits. The examples illustrate how, in a near future, reversible computers will outperform conventional computers, in terms of power dissipation and heat generation.
Reversible circuits found great interest in the past as an alternative computation paradigm which can be beneficial e.g. for encoder circuits, low power design, adiabatic circuits, verification, and much more. Besides that, reversible circuits provide the basis for many components of quantum circuits, which by themselves emerged as a very promising computing technology that, particularly these days, gains more and more relevance. All that led to a steadily increasing demand for methods that efficiently and correctly design such circuits. Decision diagrams play an important role in the design of conventional circuitry. In the meantime, also their benefits for the design of the newly emerging reversible and quantum circuits become evident. In this overview paper, we review and illustrate past work on decision diagrams for such circuits and sketch corresponding design methods relying on them. By this, we demonstrate how broadly decision diagrams can be employed in this area and what benefits they yield for these emerging technologies.
Abstract Currently, there is an ongoing “race” to build the first practically useful quantum computer that provides substantial speed-ups for certain problems compared to conventional computers. In addition to the development of such devices, this also requires the development of automated tools and methods that provide assistance in the simulation and design of corresponding applications. Otherwise, a situation might be reached where we have powerful quantum computers but hardly any proper means to actually use them. This work provides an overview of corresponding solutions for the task of quantum circuit simulation, the task of quantum circuit design, as well as corresponding mapping tasks. The covered solutions utilise expertise on efficient data structures and algorithms gained in the design of conventional circuits and systems over the last decades. While the respective descriptions are kept brief and mainly convey the general ideas, references to further readings are provided for a more detailed treatment.
Reversible logic is introduced to overcome the problem of heat dissipation in conventional systems i.e using AND and OR gates.Quantum computing is one of the major and emerging applications of reversible logic.In conventional computers there are two states either ‘1’ or ‘0’ but quantum computing which is devolping based on the quantum theory where ‘0’ and ‘1’are used simultaneously . Reversible logic gates are designed using reversible logic.Reversible logic gates are the gates that have same number of inputs and outputs and have one-to-one mapping between input and output lines.Based on this reversible logic we have designed a reversible division circuit since division is one of the main building block in ALU and has crucial role in digital signal processing.The proposed design have reduced the hardware complexity of 24s+48δ when compared to the existing designs in reversible logic.
It has been realized that quantum computing is one of the latest technologies using reversible logic. It is observed that increasing growth of transistor density, power consumption will reach their limits in conventional technologies. In conventional Circuits during the logic operations bits of information is erased resulting dissipation of energy in significant amount. Thus, if Circuits are designed so that information bits can be preserved, the power use can be reduced. In case of reversible logic computation, the information bits are not lost. We can use reversible logic technology for minimizing the power consumption, heat dissipation, increasing speed etc. This paper describes various logic gates based on reversible logic like Toffoli, Peres, Fredkin, and Feynman etc. A comparative between classical and quantum logic gates is also given on various parameters along with limitations of conventional computing.
In recent years, reversible logic circuits have applications in the emerging field of digital signal processing, optical information processing, quantum computing and nano technology. Reversibility plays an important role when computations with minimal energy dissipation are considered. The main purpose of designing reversible logic is to decrease the number of reversible gates, garbage outputs, constant inputs, quantum cost, area, power, delay and hardware complexity of the reversible circuits. This paper reveals a comparative review on various reversible logic gates. This paper provides some reversible logic gates, which can be used in designing more complex systems having reversible circuits and can execute more complicated operations using quantum computers. Future digital technology will use reversible logic gates in order to reduce the power consumption and propagation delay as it effectively provides negligible loss of information in the circuit. Keywords: Garbage output, Power dissipation, quantum cost, Reversible Gate, Reversible logic,