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.
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.
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.
Quantum phase slip junction (QPSJ) can offer very low power switching operation and represent near adiabatic switching operation for using in designing of the reversible logic gates. The reversible gates have logical reversibility, where the inputs can be logically reconstructed from the outputs and no data is lost, and physical (adiabatic) reversibility, where the energy dissipation can be decreased even below the Landauer limit. In this manuscript, for the first time, designing of the QPSJ-based basic reversible gates, namely Feynman, Toffoli, Peres and Fredkin, from the logical reversibility point of view is represented. The main logic function in these gates is the XOR function. First, a new two-input QPSJ-based XOR gate with simple circuit is designed in which the outputs of the previous gate can be connected directly to its inputs without the need for splitter lines. Second, the proposed XOR gate is used to design the Feynman and Toffoli gates. Further, the Peres and Fredkin gates are designed by using the proposed Feynman and Toffoli gates. Proper operation of the proposed gates are verified by simulation results. Logical reversibility of the Feynman and Toffoli gates is verified by cascading them and operating their logical function two times, i.e.f(f(x))=x.
Reversible logic is expanding grounds with its applicability to various upcoming technologies and quantum computation. Numerous reversible gates has also been proposed for designing logic circuits apart of basic quantum controlled Toffoli and Fredkin gates. A comparative study and analysis of a range of reversible gates from the literature is presented in this paper to obtain an optimal solution for designing these circuits. The gates are synthesized and implemented to obtain equivalent quantum circuits and operating cost in terms of number of inputs, gate cost, quantum cost, garbage output and ancilla input. The comparison is done at two subsequent levels i.e. gates structural level and circuit design level, providing a better solution for designing logic circuits. It is calculated that, basic gates are 50% efficient at gate level and 33% at design level analysis in terms of gate cost, as compared to the most efficient gates proposed in the literature.
Reversible logic has applications in quantum computing, low power CMOS, nanotechnology, optical computing, and DNA computing. The most common reversible gates are the Toffoli gate and the Fredkin gate. Our synthesis algorithm first finds a cascade of Toffoli and Fredkin gates with no backtracking and minimal look-ahead. Next we apply transformations that reduce the size of the circuit. Transformations are accomplished via template matching. The basis for a template is a network with m gates that realizes the identity function. If a sequence in the network to be synthesized matches more than half of a template, then a transformation that reduces the gate count can be applied. In this paper we show that Toffoli and Fredkin gates behave in a similar manner. Therefore, some gates in the templates may not need to be specified-they can match a Toffoli or a Fredkin gate. We formalize this by introducing the box gate. All templates with less than six gates are enumerated and classified. We synthesize all three input, three output reversible functions and compare our results to those obtained previously.
Reversible logic, also known as information lossless logic, is a promising technology that allows embedded data within circuits to be retrieved in case of failure.This study explores the use of reversible gates, such as Feynman gates, Toffoli gates, Fredkin gates, Peres gates, Double Feynman gates, NFT gates, DKG gates, and DFT gates, to construct logic circuits.These reversible logic gates can be effectively used for the implementation of any higher logic circuits-based applications.In the proposed paper the Arithmetic logic unit based on reversible logic hates is implemented in Verilog as well as IBM quantum software.The major applications of reversible logic gates include quantum computing, low power circuits, nano and CMOS technologies, photonics.In the last part of the paper the circuits implemented using Verilog and IBM quantum a chip level design using Cadance layout is implemented.
Reversible logic has promising applications in the field of quantum computing, optical computing, low power computing, and other emerging computing technologies. A barrel shifter that can shift and rotate multiple bits in a single cycle is an important component of many computing units. This paper presents the reversible design of bidirectional arithmetic and logical barrel shifter. The proposed design consists of the reversible Fredkin and Feynman gates. The Fredkin gate used in the design of reversible bidirectional arithmetic and logical barrel shifter can implement the 2:1 MUX with minimum quantum cost, minimum number of ancilla bits and minimum number of garbage outputs while the Feynman gate is used to avoid the fanout as fanout is not allowed in the reversible logic. The design is evaluated in terms of number of garbage outputs, quantum cost and number of ancilla bits.