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The construction of an all-optical frequency-encoded Toffoli gate employing a reflecting semiconductor optical amplifier (RSOA) is proposed in this article. By establishing fields such as quantum computing, optical quantum computing, quantum-dot cellular automata, and superconducting flux logic family, quantum gates have been proved to perform reliably in the present day. A nonzero-mass electron, on the other hand, moves far slower than a quantum particle with zero rest mass, such as a photon. Photons can also be utilized to store data while being sent. These photon qualities have motivated researchers to create quantum gates in the all-optical domain based on them. The RSOA-based implementation of the Toffoli gate gives a significant improvement in the case of high speed, low power, and fast switching time. MATLAB Simulink (R2018a) software is used to simulate the devised design. The theoretical prediction is satisfied by the simulation results. [ABSTRACT FROM AUTHOR]

All-optical quantum logic gates with qubit data are the essential components in optical signal processing and computing. Quantum optical Toffoli gate is one of the most useful logic gates in the logic family which is extensively used to perform ultrafast optical digital operations. Here, in this paper, an all-optical scheme for realization of frequency encoded tristate Toffoli gate is proposed. Semiconductor optical amplifier based optical switches like frequency converters and add/drop multiplexers are used to implement the system. Also, a proper truth table and gate matrix of tristate Toffoli gate is developed. Tristate based optical logic operations not only increase the data handling capacity, it also increases the speed of different optical logic operations because of inherent parallelism of light. As frequency encoding principle is used to encode the qubits, so bit error problem can be ignored by the proposed system. The system is entirely all-optical in nature, so the system exhibits very high speed of operation (above tera hertz) with improved signal to noise ratio. [ABSTRACT FROM AUTHOR]

In recent years, reversible logic gates have garnered significant interest because of their potential to decrease energy consumption and meet the growing need for low-power computing systems. Unlike conventional logic gates, reversible logic gates ensure that no information loss happens during computation, allowing for the reversal of the entire computation process. This unique characteristic opens up new avenues for developing energy-efficient digital circuits. This review paper serves as a vital contribution to the field by addressing a noticeable gap in the existing literature regarding reversible logic gates. The study not only comprehensively analyzes the array of reversible logic gates available but also underscores their practical applications and significance. It encompasses a wide variety of reversible logic gates, including Toffoli gates, Fredkin gates, and newer innovations. It is found that Toffoli gates outperformed in terms of gate count and quantum cost reduction, making them a preferred choice for quantum circuit optimization. Additionally, Fredkin gates showed exceptional performance in specific applications, like data swapping and quantum state control. The digital circuits like adders, multiplexers, ALU etc. are successfully designed using reversible gates like HNG, DKG etc. The significant gap this study fills lies in the need for a consolidated and in-depth analysis of the state-of-the-art reversible logic gates and their real-world utility. While prior research has discussed these gates individually, this paper takes a novel approach by offering a holistic assessment of their performance, quantum cost, gate count, and practical applications, thereby presenting a comprehensive resource for researchers, engineers, and designers in the field. This innovative contribution plays a pivotal role in shaping the progress of energy-efficient and quantum computing systems as well as in optimizing VLSI chip designs for various applications, with a particular emphasis on enhancing cryptographic and data processing capabilities. The findings of this review aim to stimulate further research and development in reversible computing, contributing to the advancement of energy-efficient and information-preserving computing systems. [ABSTRACT FROM AUTHOR]

Arithmetic primitives are necessary in order to conduct computations on large numbers in arithmetic circuit implementations including multiplications, additions, subtractions, and divisions. Because of the importance of computations in the central processing unit, effective design of arithmetic circuit has been part of the most important fields of research for design engineers. In order to create low-power and energy-efficient portable processors for image and digital signal processing, as well as cryptography applications, the switching activity factor and cell count must be reduced. This research focuses on the reversible digital full adder circuit, which is a key element in establishing the Energy Delay Product (EDP) for various computer applications. Here, a new reversible binary full adder is designed using the switching activity concept and the logic decomposition method. The internal blocks for reversible full adders such as Feynman Gate, Toffoli Gate, and New Gate are designed first, then a new reversible binary full adder is developed using the proposed method. In this paper, conventional and proposed reversible full adders are synthesized using the Xilinx Vivado design suite for the Zynq-7000 family of device configuration. According to the implementation results, the proposed reversible full adder circuit consumes less dynamic power dissipation than the existing method in comparison. Furthermore, a formulae-based evaluation is conducted on the implementation results to estimate the EDP of the design. The proposed reversible full adder design can achieve a 32.3% EDP improvement compared to the Proposed Full Adder. [ABSTRACT FROM AUTHOR]

The Feistel-Toffoli construction of a bijective Boolean function out of an arbitrary one, a fundamental tool in reversible computing and in cryptography, has recently been analyzed (see [12]) to be a special instance of the construction of a monoid homomorphism from the X -fold cartesian power of a monoid M into the endomorphism monoid of the free M -set over the set X. It is the purpose of this note to show that this construction itself is in fact a genuine monoidal one. The generalization of the Feistel-Toffoli construction to internal categories in arbitrary finitely complete categories of [12] then becomes a special instance of this monoidal description. [ABSTRACT FROM AUTHOR]

We present an optical apparatus for polarization qubits based on quantum nondemolition measurement (QND) that has a probability of success of 0.95 considering real active devices. This apparatus can implement multiqubit Toffoli gates, reversible AND/NANDs, and Peres gates. [ABSTRACT FROM AUTHOR]

Set Intersection Cardinality (SI-CA) computes the intersection cardinality of two parties' sets, which has many important and practical applications such as data mining and data analysis. However, in the face of big data sets, it is difficult for two parties to execute the SI-CA protocol repeatedly. In order to reduce the execution pressure, a Private Set Intersection Cardinality (PSI-CA) protocol based on a quantum homomorphic encryption scheme for the Toffoli gate is proposed. Two parties encode their private sets into two quantum sequences and encrypt their sequences by way of a quantum homomorphic encryption scheme. After receiving the encrypted results, the semi-honest third party (TP) can determine the equality of two quantum sequences with the Toffoli gate and decrypted keys. The simulation of the quantum homomorphic encryption scheme for the Toffoli gate on two quantum bits is given by the IBM Quantum Experience platform. The simulation results show that the scheme can also realize the corresponding function on two quantum sequences. [ABSTRACT FROM AUTHOR]

Qubits, which are the quantum counterparts of classical bits, are used as basic information units for quantum information processing, whereas underlying physical information carriers, e.g., (artificial) atoms or ions, admit encoding of more complex multilevel states—qudits. Recently, significant attention has been paid to the idea of using qudit encoding as a way for further scaling quantum processors. In this work, we present an efficient decomposition of the generalized Toffoli gate on five-level quantum systems—so-called ququints—that use ququints' space as the space of two qubits with a joint ancillary state. The basic two-qubit operation we use is a version of the controlled-phase gate. The proposed N-qubit Toffoli gate decomposition has O (N) asymptotic depth and does not use ancillary qubits. We then apply our results for Grover's algorithm, where we indicate on the sizable advantage of using the qudit-based approach with the proposed decomposition in comparison to the standard qubit case. We expect that our results are applicable for quantum processors based on various physical platforms, such as trapped ions, neutral atoms, protonic systems, superconducting circuits, and others. [ABSTRACT FROM AUTHOR]

Energy consumption is one of the prime concerns in the computational process of large servers, which must be ultra-fast while minimizing heat generation. Beyond the Boltzmann limit, photons can play a vital role in reducing the heat energy and enabling the system to work swiftly. Also, logically reversible computation has the potential to save energy by avoiding bit erasures and associated heat, while dealing with static leakage and dynamic signal energy loss related to the switching mechanism. The optoelectronic approach for configuring a reversible logic has evolved as an emerging technology of computation, where an electro-optic Mach–Zehnder interferometer (EO-MZI)-based design is preferred due to its easy integrability with silicon chips. This paper explores a new approach for designing a reversible full adder (RFA) using EO-MZI carried out with the beam propagation method in the OptiBPM tool. Validation of the optical simulation of the RFA is done through mathematical power modelling performed in MATLAB. Furthermore, the performance is analysed in terms of insertion and excess loss, where titanium (Ti) thickness, electrode voltage and wavelength are varied from their optimal values at the system level. [ABSTRACT FROM AUTHOR]

Reversible logic enables ultra-low power circuit design and quantum computation. Quantum-dot Cellular Automata (QCA) is the most promising technology considered to implement reversible circuits, mainly due to the correspondence between features of reversible and QCA circuits. This work aims to push forward the state-of-the-art of the QCA-based reversible circuits implementation by proposing a novel QCA design of a reversible full adder\full subtractor (FA\FS). At first, we consider an efficient XOR-gate, and based on this, new QCA circuit layouts of Feynman, Toffoli, Peres, PQR, TR, RUG, URG, RQCA, and RQG are proposed. The efficient XOR gate significantly reduces the required clock phases and circuit area. As a result, all the proposed reversible circuits are efficient regarding cell count, delay, and circuit area. Finally, based on the presented reversible gates, a novel QCA design of a reversible full adder\full subtractor (FA\FS) is proposed. Compared to the state-of-the-art circuits, the proposed QCA design of FA\FS reversible circuit achieved up to 57% area savings, with 46% and 29% reduction in cell number and delay, respectively. [ABSTRACT FROM AUTHOR]

The goal of this research is to create a QCA-based reversible priority encoder. It is one of the most crucial parts of the encoding and decoding process. This novel nanotechnology, known as quantum-dot cellular automata (QCA), shows promise as a foundation for the development of reversible circuits. This paper proposes a simple, reversible, 4-2 line priority encoder design for the QCA platform. Using the simple and cheap Toffoli gate architecture, a reversible encoder circuit may be built. To analyze the proposed designs’ structural soundness, the simulation program QCA Designer is used.

Multiqubit quantum logic gates play a critical role in quantum information processing and serve as a stepping stone to implementing a scalable quantum computation. In this paper, based on the photon-scattering property of a four-level emitter coupled to one-dimensional waveguide, we propose two heralded schemes for implementing Toffoli and Fredkin gates simultaneously on polarization and spatial degrees of freedom (DoFs) of two-photon systems. The undesired scattering processes between two photons and waveguide-emitter system can be detected by the single-photon detectors. That is, two multiqubit quantum gates are implemented in a heralded way, and the fidelity of each gate is near to unit in principle under current technical conditions, which ensures the feasibility of the experiment. Moreover, the quantum circuits for the two gates are robust against the decoherence, and require less quantum resource compared with the ones in one DoF only. [ABSTRACT FROM AUTHOR]

Reversible logic has found itself to a new height ever since the semiconductor industry has observed the saturation in Moore's law along with sizable power/heat dissipation. Many overhead factors in lower nodes of conventional CMOS result in heat dissipation and it seems like an uphill task in near future to at least getting near to Landauer's limit. Though the research is just beginning to roll out, one of the potential solutions is to use optical switches, which can function at a much faster speed since photons are ultra-fast. These switches are easy to understand as the presence/absence of light defines logic '1/0' and can configure reversible gates. This paper explores a design of optimal count electro-optic Mach–Zehnder interferometer based reversible Toffoli Gate (TG) under beam propagation method. The material composition used in designing the optical switch is Titanium in diffused in Lithium Niobate. We have also studied various logic operations derived from TG. The validation of its truth table is done by simulating the mathematical power model on MATLAB. Furthermore, arithmetical application as TG gate based 1-bit full adder is also proposed along with analysis of performance metrics for single unit MZI whereas at system level by varying some of the parameters such has wavelength, diffusion constant, Ti-thickness against coupling, extinction ratio, insertion and excess loss. [ABSTRACT FROM AUTHOR]

Power dissipation is one of the on-demand problems of low power Very large-scale integration (VLSI) circuit design and it is related with threshold voltage. Generally, the subthreshold leakage current and the leakage power dissipation are increased while reducing the threshold voltage. The overall performance of the total power dissipation is completely depending on this leakage power dissipation. This leakage power causes the components that are functioned by battery for a long period washed-out rapidly. In this paper, a new read decoupled and write enhanced macro memory design is proposed using transistor stacking and reversible logic to reduce the leakage power. For the reduction of power consumption of Static Random Access Memory (SRAM) that are placed in System on Chips (SoCs), the proposed model includes three features: a reversible cross coupled stacked inverter with Transmission gate is adopted in SRAM cell to reduce the leakage power, a reversible differential power generator is adopted to improve the write ability of the design with less power and a read burst mode is used to reduce the read energy while reading consecutive addresses. Furthermore, a reversible logic is applied in all the peripheral circuits, which gives additional level of confidence in terms of leakage power. The simulation results show that the leakage power of the proposed macro memory design is reduced to 2.22nW at 0.6V supply, which is 4.32nW less than that of the conventional macro design. Furthermore, the write and read power consumption of the proposed macro design is reduced by 57% and 66% as compared to conventional one at a supply voltage of 0.6 V. [ABSTRACT FROM AUTHOR]

We design an experimental feasible Toffoli gate, comprising nonlinear optical gates via cross-Kerr nonlinearities (XKNLs) and linear optical devices, on three photonic qubits (photons). The Toffoli gate is a three-qubit universal quantum controlled gate for various quantum information processing schemes. Thus, we propose an efficient method to construct a Toffoli gate using nonlinear optical gates that employ weak XKNLs, quantum bus beams, and photon-number-resolving measurements. Furthermore, to ensure the reliable performance of the Toffoli gate (via XKNLs), we describe an experimental condition to reduce the influence (photon loss and dephasing) of the decoherence effect induced in nonlinear optical gates. [ABSTRACT FROM AUTHOR]

In distributed quantum computation, quantum remote-controlled gates are used frequently and applied on separate nodes or subsystems of a network. One of the universal and well-known controlled gates is the n-qubit controlled-NOT gate, especially Toffoli gate for the case of three qubits, which are frequently used to synthesize quantum circuits. In this paper, we considered a more general case, an n-qubit controlled-U gate, and present a general protocol for implementing these gates remotely with minimum required resources. Then, the proposed method is applied to implement a Toffoli gate in bipartite and tripartite systems. In this method, we considered cases in which a group of qubits belongs to one subsystem of the network. Then, we improved its consumption resources. [ABSTRACT FROM AUTHOR]

Investigations in reversible computation have been one of the notable dimensions among the emerging research domains. Reversible circuits promise near-zero heat dissipation resulting in a considerable amount of literary proposals. This article proposes a reversible synchronous decimal counter using Toffoli and Fredkin gates. Decimal counter forms an important Boolean specification as they are used for clock generators, frequency dividers, clock division, integrated oscillation, etc. Although literature witnesses exhaustive research in reversible mod-2/4/8/16 counters, there is a void in the domain of reversible decimal counters. We propose three designs D1, D2, and D3. Design D1 and D2 are synchronous decimal up and down counters, respectively, using Toffoli Netlist. Design D3 is the integration of designs D1 and D2 using the Fredkin Gate array. The proposed designs have been checked using a state-of-the-art optimization algorithm in literature and the results reflect our design to be best optimized. Peer analysis reflects a summary of existing literary proposals exhibiting the uniqueness of the proposed designs. [ABSTRACT FROM AUTHOR]

As a basic operation in quantum computers, quantum logic gates and particularly controlled NOT (CNOT) gates are important in quantum information processing. In this paper, we propose a one-step scheme to generate a CNOT gate via transitionless quantum driving. In this scheme, an effective Hamiltonian is obtained based on quantum Zeno dynamics to drive the system to evolve into the target state when the parameters are reasonably set. The results of explicit numerical simulations indicate that the proposed scheme is robust against instability related to variation in experimental parameters and decoherence. The scheme can also be extended to generate a Toffoli gate, which is useful for large-scale quantum computers. Moreover, the generation process involves only a single step, greatly simplifying its implementation. [ABSTRACT FROM AUTHOR]

The effect of frequency noise on correct operation of the multiple-control Toffoli, Fredkin, and Peres gates has been discussed. In the framework of the Ising model, the energy spectrum of a chain of atoms with nuclear spins one-half in a spinless semiconductor matrix has been obtained, and allowed transitions corresponding to the operation algorithm of these gates have been determined. The fidelities of the obtained transitions were studied depending on the number of control qubits and parameters of the radio-frequency control pulses. It has been shown that correct operation of the Toffoli and Fredkin gates does not depend on the number of control qubits, while the Peres gate fidelity decreases significantly with the increasing number of control signals. The calculated ratios of the Larmor frequency to the exchange interaction constant correspond with the results of other studies. [ABSTRACT FROM AUTHOR]

All-optical reversible logic gates can play crucial roles in the next generation of all-optical computing systems. In this paper, we will propose and design an all-optical Toffoli gate using photonic crystal-based nonlinear ring resonators. The proposed structure has three input and three output ports. There is a one-by-one mapping between the input and output ports; therefore, the proposed structure is a reversible gate with the maximum time delay about 2 ps and suitable for optical communication applications. [ABSTRACT FROM AUTHOR]

In this paper, firstly we propose a new protocol for quantum bidirectional teleportation of two particles in a six-qubit entangled channel, which is based on GHZ measurement and unitary operation. Then, also based on the six-qubit entangled state channel, a protocol for quantum bidirectional teleportation of two-three particles is proposed. The protocol utilizes Toffoli gate to convert three-qubit states into two-qubit states and a single qubit, and the rest of the teleportation is the same as the first protocol. Finally, we introduce an auxiliary bit to restore the state of the sender. Both these proposed protocols are more efficient than others in the same situation, which will be compared at the end of the paper. [ABSTRACT FROM AUTHOR]