Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Applied Mathematics and Control Sciences

A “BILLIARDS” SIMULATION OF AN UNIVERSAL LOGIC MODULES BASED ON THE FREDKIN GATES FOR THE QUANT-UTING

С Ф Тюрин

Published Jun 30, 2020• 1 citation
Publisher

Abstract

In the wave of the green computing trend, research has recently intensified on the so-called adiabatic logic, reversible computing, which is supposed to be the basis of quantum computers and bring to a new level of computing power, combined with low power consumption. The basis of this logic is special reversible gates, for example, Fredkin’s gates. Reversibility is a one-to-one correspondence (bijection) between the inputs and outputs of circuits, which means, on the one hand, the possibility of total control of the results of calculations, and on the other hand, the possibility of returning the obtained "energy" quanta for the perform calculations to their source. This approach can significantly reduce the power consumption of computers, as well as increase the reliability of calculations. There are a lot of publications on this topic, however, the development of universal logic modules on such a basis has not been fully considered. The aim of the study is the development and modeling of universal logic modules based on the Fredkin element. In this case, the methods of logical synthesis of a reversible scheme based on a binary Fredkin element, modeling and analysis of billiard calculations are used. The article presents the proposed schemes of the decoder and multiplexer based on the Fredkin element, the "billiard" simulation. The practical significance of the study lies in the fact that the obtained universal logic modules can be used in the synthesis of binary reversible circuits, for example, FPGAs. The performed simulation can be used as examples in practical exercises in the discrete mathematics, mathematical logic, mathematical modeling, and circuitry disciplines.

DOI
10.15593/2499-9873/2020.2.04

Related papers

Reversible Majority Voter Based on Fredkin Gates

Sergey Feofentovich Tyurin

As known Q-bits, Q-bytes, Quantum computing, Reversible calculations have recently become the perspective IT technologies. In such area, special elements are used, for example, Feynman gates, Toffoli gates, Fredkin gates etc. However, quantum calculations requires the solving a lot of problems of data representation. Nonetheless, reversible approach can be successfully used in binary case for the design of checkable and energy-efficient ("green") circuits. In such direction, so-called "adiabatic" and "billiard" logic is of most interest. However, binary reversible "billiard" gates have more inputs and outputs than usual gates, they have "trash" outputs. At the same time, the reliability problems of such circuits have not yet been fully resolved. The article discusses the question of tripling Fredkin’s circuits. The author develops and studies Reversible Majority Voter based on Fredkin’s gates. The analysis of three channels requires six additional bits, and the circuit has five Fredkin elements and five garbage outputs.

International Conference on Dependable Systems, Services and Technologies (DESSERT)•May 1, 2020•2 citations

Reversible 2:4 Decoder Using Universal Fredkin Gate

Gudipati Nikhil, Balkonda Sharanya, P. Bharath Reddy +1 more

The technologies like quantum computing, Nanotechnology is emerging due to the greater research in reversible logic. It has the power reduction capability the same mechanism is also having in the quantum computing. Designing a quantum circuit among various combinational circuits the decoder has capability to change binary information of input lines to distinct output lines and also there are many applications where decoder is the main basic component. In this paper a comprehensive introduction of basic gates used to design n to 2nUniversal Quantum decoder, here n represents the no of inputs are mentioned. The proposed 2:4 decoder circuit is designed using a universal reversible Fredkin gates and Feynman gate. The proposed work is simulated using IBM Quantum Composer. In comparison to existing quantum decoders the proposed decoder design has optimum values in all the parameters considered.

International Conference on Communication and Electronics Systems (ICCES)•Jul 8, 2021•6 citations

A Quick Guide to Implement Reversible Logic

Shaveta Thakral, Dipali Bansal

Increasing miniaturization and demand of low power electronics is highly motivating research on reversible logic. Reversible logic has attracted signification attention in fields of Low power VLSI design, computer graphics, quantum computing and communication. A lot of work has been done on synthesis and optimization of reversible circuits followed by quantitative analysis on various optimization metrics like ancillary inputs, garbage outputs and quantum cost. It is therefore obvious to present a quick guide on reversible logic implementation to bridge gap between theory and implementation. Taxonomy diagrams of work done in reversible logic domain are also presented to give a quick review of all about reversible logic. Quantum realization of popular reversible Fredkin gates using RCViewer tool is also presented which will be stepping stone for a new researcher to synthesize and optimize any complex reversible logic based circuit.

International Conference on Computing, Communication and Automation•Dec 1, 2018•1 citation

Embedded tutorial: Applications of reversible logic in cryptography and coding theory

Kamalika Datta, Indranil Sengupta

Summary form only given, as follows. With the increasing emphasis on low-power design and quantum computation, research activities in the area of reversible logic synthesis and testing have gained momentum over the last couple of decades. It is expected that reversible logic will provide us with a viable alternative to building ultra-low power circuits and systems in not too distant future. In the classical works for synthesis of reversible circuits, gate libraries comprising of standard reversible gates like NOT, CNOT, TOFFOLI, FREDKIN, etc. are considered. To evaluate the goodness of a synthesized netlist, various metrics such as gate count, quantum cost, and equivalent transistor cost have been considered by various researchers. The synthesis approaches that have been reported can be broadly categorized into three groups: (a) exact synthesis approaches which try to obtain optimal reversible gate netlists, but can be used for small circuits only, (b) heuristic based approaches which try to utilize some domain knowledge intelligently to reduce the complexity of search, and can be used for somewhat larger circuits, and (c) synthesis approaches that rely on higher level functional representations like binary decision diagram (BDD) or exclusive sum-ofproducts (ESOP). The last approach is scalable to larger circuits (with 200 inputs or more), however, the synthesized netlist is not optimal and various rule-based heuristic approaches have been proposed to minimize the cost. There have been works also that report techniques for implementing sequential circuits with reversible properties, which will be useful for building complex systems containing finite-state machines. There are various transformations that are carried out as part of cryptographic algorithms that are inherently reversible in nature. For instance, any block cipher that uses a key K to transform a plaintext P into a ciphertext C during encryption must be reversible, because decryption will be doing just the reverse (C to P). Also, in standard symmetric block ciphers like DES or AES, there is a combinational block called substitution box or S-box which is also reversible in nature. In AES, the S-box has 8 inputs and 8 outputs, and implements a one-to-one onto mapping. The same reversibility requirements hold for stream ciphers and public-key ciphers like RSA. Although not much work has been carried out in the area of reversible implementations of cryptographic algorithms, this can be a very good area for future research. Similar considerations hold for various coding and decoding techniques used in communication, which are also inherently reversible in nature. Some examples of such coding/decoding are Manchester, Differential Manchester, Bipolar AMI, 4B/5B, 8B/10B, Hamming error correcting code, etc. All these techniques can potentially be implemented using reversible logic circuits. Specific case studies of some of the areas as mentioned will be reported, with synthesis results.

International Conference on VLSI Design•Jan 1, 2013•5 citations

Quantum Cost-Efficient Design of Synchronous Reversible Shift Registers using Reversible Logic

Shivangi Gupta, Rahul Kumar, Somesh Kumar

Reversible circuits are one of the most promising technologies for replicating inputs from recorded outputs, and it results in lower power dissipation. All gates such as NAND, AND, OR, NOR etc. are irreversible in nature and consume energy during calculations. Similar to quantum circuits, reversible logic circuitry does not consume energy throughout the calculation cycle. Due to this, reversible circuits can be used for quantum communication and other low-power applications. Registers are one of the most important storage components utilised in a wide range of real-time operations. Using expressions of exclusive-or sum of products (ESOP) and modified Fredkin gates, this work presents a novel way for creating a quantum cost-effective universal register circuit. The designed universal register circuitry for left and right shifts are tested in the Xilinx Vivado simulator to ensure that they are functional and logically correct. The proposed universal registers outperform the standard designs in terms of garbage outputs (GO), quantum cost (QC), gate count (GC), and Ancilla inputs (AI), according to the comparative analysis.

IEEE Bombay Section Signature Conference (IBSSC)•Nov 18, 2021•2 citations

Implementation of frequency encoded all optical reversible logic

Nikhlesh Kumar Mishra, Upendra Chaurasiya, Saumya Srivastava +2 more

Abstract Reversible gate has been one of the emerging research areas that ensure continual process of innovation trends that explore and utilizes the resources. Due to the increasing power consumption of electronic circuits, it has been observed that quantum computing is one of its latest applications. This technology can be utilized by reducing the energy consumption by preserving the bits of information that are still useful. A photon has zero rest mass, while an electron has a nonzero rest mass. These characteristics inspired the researchers to develop an all-optical Fredkin gate. The proposed gate design overcomes the shortcomings of conventional Fredkin gates and provides better performance.

Journal of Optical Communications•Nov 8, 2021•3 citations
In the wave of the green computing trend, research has recently intensified on the so-called adiabatic logic, reversible computing, which is supposed to be the basis of quantum computers and bring to a new level of computing power, combined with low power consumption. The basis of this logic is special reversible gates, for example, Fredkin’s gates. Reversibility is a one-to-one correspondence (bijection) between the inputs and outputs of circuits, which means, on the one hand, the possibility of total control of the results of calculations, and on the other hand, the possibility of returning the obtained "energy" quanta for the perform calculations to their source. This approach can significantly reduce the power consumption of computers, as well as increase the reliability of calculations. There are a lot of publications on this topic, however, the development of universal logic modules on such a basis has not been fully considered. The aim of the study is the development and modeling of universal logic modules based on the Fredkin element. In this case, the methods of logical synthesis of a reversible scheme based on a binary Fredkin element, modeling and analysis of billiard calculations are used. The article presents the proposed schemes of the decoder and multiplexer based on the Fredkin element, the "billiard" simulation. The practical significance of the study lies in the fact that the obtained universal logic modules can be used in the synthesis of binary reversible circuits, for example, FPGAs. The performed simulation can be used as examples in practical exercises in the discrete mathematics, mathematical logic, mathematical modeling, and circuitry disciplines.
As known Q-bits, Q-bytes, Quantum computing, Reversible calculations have recently become the perspective IT technologies. In such area, special elements are used, for example, Feynman gates, Toffoli gates, Fredkin gates etc. However, quantum calculations requires the solving a lot of problems of data representation. Nonetheless, reversible approach can be successfully used in binary case for the design of checkable and energy-efficient ("green") circuits. In such direction, so-called "adiabatic" and "billiard" logic is of most interest. However, binary reversible "billiard" gates have more inputs and outputs than usual gates, they have "trash" outputs. At the same time, the reliability problems of such circuits have not yet been fully resolved. The article discusses the question of tripling Fredkin’s circuits. The author develops and studies Reversible Majority Voter based on Fredkin’s gates. The analysis of three channels requires six additional bits, and the circuit has five Fredkin elements and five garbage outputs.
The technologies like quantum computing, Nanotechnology is emerging due to the greater research in reversible logic. It has the power reduction capability the same mechanism is also having in the quantum computing. Designing a quantum circuit among various combinational circuits the decoder has capability to change binary information of input lines to distinct output lines and also there are many applications where decoder is the main basic component. In this paper a comprehensive introduction of basic gates used to design n to 2nUniversal Quantum decoder, here n represents the no of inputs are mentioned. The proposed 2:4 decoder circuit is designed using a universal reversible Fredkin gates and Feynman gate. The proposed work is simulated using IBM Quantum Composer. In comparison to existing quantum decoders the proposed decoder design has optimum values in all the parameters considered.
Increasing miniaturization and demand of low power electronics is highly motivating research on reversible logic. Reversible logic has attracted signification attention in fields of Low power VLSI design, computer graphics, quantum computing and communication. A lot of work has been done on synthesis and optimization of reversible circuits followed by quantitative analysis on various optimization metrics like ancillary inputs, garbage outputs and quantum cost. It is therefore obvious to present a quick guide on reversible logic implementation to bridge gap between theory and implementation. Taxonomy diagrams of work done in reversible logic domain are also presented to give a quick review of all about reversible logic. Quantum realization of popular reversible Fredkin gates using RCViewer tool is also presented which will be stepping stone for a new researcher to synthesize and optimize any complex reversible logic based circuit.
Summary form only given, as follows. With the increasing emphasis on low-power design and quantum computation, research activities in the area of reversible logic synthesis and testing have gained momentum over the last couple of decades. It is expected that reversible logic will provide us with a viable alternative to building ultra-low power circuits and systems in not too distant future. In the classical works for synthesis of reversible circuits, gate libraries comprising of standard reversible gates like NOT, CNOT, TOFFOLI, FREDKIN, etc. are considered. To evaluate the goodness of a synthesized netlist, various metrics such as gate count, quantum cost, and equivalent transistor cost have been considered by various researchers. The synthesis approaches that have been reported can be broadly categorized into three groups: (a) exact synthesis approaches which try to obtain optimal reversible gate netlists, but can be used for small circuits only, (b) heuristic based approaches which try to utilize some domain knowledge intelligently to reduce the complexity of search, and can be used for somewhat larger circuits, and (c) synthesis approaches that rely on higher level functional representations like binary decision diagram (BDD) or exclusive sum-ofproducts (ESOP). The last approach is scalable to larger circuits (with 200 inputs or more), however, the synthesized netlist is not optimal and various rule-based heuristic approaches have been proposed to minimize the cost. There have been works also that report techniques for implementing sequential circuits with reversible properties, which will be useful for building complex systems containing finite-state machines. There are various transformations that are carried out as part of cryptographic algorithms that are inherently reversible in nature. For instance, any block cipher that uses a key K to transform a plaintext P into a ciphertext C during encryption must be reversible, because decryption will be doing just the reverse (C to P). Also, in standard symmetric block ciphers like DES or AES, there is a combinational block called substitution box or S-box which is also reversible in nature. In AES, the S-box has 8 inputs and 8 outputs, and implements a one-to-one onto mapping. The same reversibility requirements hold for stream ciphers and public-key ciphers like RSA. Although not much work has been carried out in the area of reversible implementations of cryptographic algorithms, this can be a very good area for future research. Similar considerations hold for various coding and decoding techniques used in communication, which are also inherently reversible in nature. Some examples of such coding/decoding are Manchester, Differential Manchester, Bipolar AMI, 4B/5B, 8B/10B, Hamming error correcting code, etc. All these techniques can potentially be implemented using reversible logic circuits. Specific case studies of some of the areas as mentioned will be reported, with synthesis results.
Reversible circuits are one of the most promising technologies for replicating inputs from recorded outputs, and it results in lower power dissipation. All gates such as NAND, AND, OR, NOR etc. are irreversible in nature and consume energy during calculations. Similar to quantum circuits, reversible logic circuitry does not consume energy throughout the calculation cycle. Due to this, reversible circuits can be used for quantum communication and other low-power applications. Registers are one of the most important storage components utilised in a wide range of real-time operations. Using expressions of exclusive-or sum of products (ESOP) and modified Fredkin gates, this work presents a novel way for creating a quantum cost-effective universal register circuit. The designed universal register circuitry for left and right shifts are tested in the Xilinx Vivado simulator to ensure that they are functional and logically correct. The proposed universal registers outperform the standard designs in terms of garbage outputs (GO), quantum cost (QC), gate count (GC), and Ancilla inputs (AI), according to the comparative analysis.
Abstract Reversible gate has been one of the emerging research areas that ensure continual process of innovation trends that explore and utilizes the resources. Due to the increasing power consumption of electronic circuits, it has been observed that quantum computing is one of its latest applications. This technology can be utilized by reducing the energy consumption by preserving the bits of information that are still useful. A photon has zero rest mass, while an electron has a nonzero rest mass. These characteristics inspired the researchers to develop an all-optical Fredkin gate. The proposed gate design overcomes the shortcomings of conventional Fredkin gates and provides better performance.