Reversible Logic Research Articles

Управление реверсивной логистикой на рынке электронной торговли Китая

A study of the features of reverse logistics management has been conducted. The Chinese electronic commerce market for 2019-2023 is analyzed. The dynamics of the main indicators of electronic commerce at the national level, as well as the volume of courier business in China over five years, are illustrated. In order to fully and comprehensively assess the development potential of reverse logistics in the e-commerce market, a PEST analysis of reverse flows was conducted in order to identify the strengths and weaknesses of reverse commodity movement. A balanced assessment of the influence of the following factors is given: political, economic, social, technical and technological, as well as environmental. As a result of the PEST analysis of reverse flows, it was determined that there are both obstacles and drivers for the development of reverse logistics in the Chinese e-commerce market. It is revealed that the most significant growth points are technological and political factors contributing to the development of reverse logic in the e-commerce market, effectively organized and managed through the formation of a digital logistics infrastructure. It is concluded that, in general, these factors have a positive impact on the organization and management of both direct and reverse flows. It is recommended to carry out educational work among the population and form a model of responsible consumer behavior in order to reduce the volume of returned products, as well as improve the quality of life without overconsumption.

Entanglement Trajectory and its Boundary

In this article, we present a novel approach to investigating entanglement in the context of quantum computing. Our methodology involves analyzing reduced density matrices at different stages of a quantum algorithm's execution and representing the dominant eigenvalue and von Neumann entropy on a graph, creating an "entanglement trajectory." To establish the trajectory's boundaries, we employ random matrix theory. Through the examination of examples such as quantum adiabatic computation, the Grover algorithm, and the Shor algorithm, we demonstrate that the entanglement trajectory remains within the established boundaries, exhibiting unique characteristics for each example. Moreover, we show that these boundaries and features can be extended to trajectories defined by alternative entropy measures. The entanglement trajectory serves as an invariant property of a quantum system, maintaining consistency across varying situations and definitions of entanglement. Numerical simulations accompanying this research are available via open access.

Advancing nanoscale computing: Efficient reversible ALU in quantum-dot cellular automata

This paper presents a significant contribution to the field of nanoscale computing by proposing an innovative reversible Arithmetic and Logic Unit (ALU) implemented in Quantum-Dot Cellular Automata (QCA). Reversible logic and QCA technology offer promising alternatives to conventional CMOS technology, addressing the challenges of operating at nanoscale dimensions. The primary objective is to develop a highly efficient ALU capable of performing 26 distinct arithmetic and logical operations. The ALU design is based on a novel reversible full adder-subtractor optimized for minimal quantum cost, which is crucial for energy-efficient quantum computation. The evaluation encompasses various criteria related to reversibility, such as gate count, number of constant inputs, number of garbage outputs, and quantum cost. QCA-specific criteria, including cell count, occupied area, and clock cycles, are also considered. The outcomes of this research contribute to the advancement of cell-efficient nanoscale computing, with implications for quantum computation, emerging technologies, and future integrated circuit design.

Design of optically controlled read and write memory unit with reversible logic gates using GaAs–AlGaAs-based micro-ring resonators

Design of optically controlled read and write memory unit with reversible logic gates using GaAs–AlGaAs-based micro-ring resonators

Design and Analysis of a New Fault-Tolerant QCA-based Nano-Scale Circuit for Morphological Operations in Image Processing

Quantum-dot cellular automata (QCA) is based on traditional cellular automata models in which each cell has one of the finite distinct states at any given time. Cellular automata refer to the use of Coulombic contact rather than wires to connect cells. The discrete character of cellular automata and quantum mechanics have been exploited to develop nano-scale devices that can conduct computations with high switching frequency and low power dissipation. QCA has been utilized in many categories for fault-tolerant and reversible logic computing. On the other hand, the morphology algorithm is an area of image processing that provides a unified methodology and strong tools for image/video processing applications. This work proposes a unique fault-tolerant approach based on QCA to execute the morphological operations in image processing. Two fault-tolerant 5-input majority gates are employed in the implemented QCA architecture, and a control line is used to accomplish dilation and erosion. To assess the capabilities of the proposed fault-tolerant circuit for morphological procedures, its performance is analyzed and confirmed. The proposed design is compared to earlier results, which significantly improve fault-tolerant ability.

Design of Reversible Quantum Vigenere Cryptographic Cipher in QCA and IBMQ Platforms for Secure Nanocommunication

Using cryptography correctly is crucial in the current situation to safeguard data and ensure data security during data transfer. In this digital era, messages must be appropriately encrypted and decoded to prevent data misuse and ensure its accessibility to the intended recipient. Conventional cryptography techniques mostly depend on the mathematical intricacy of the encoding functions and the shared key. One such encoding approach that we may take into consideration is the Vigenere cipher algorithm. In this study, we want to apply this strategy utilizing reversible logic with the assistance of two helpful tools, namely, IBM Quantum (IBMQ) and QCADesigner. The encoder and decoder circuits for the Vigenere cipher are therefore proposed in this work in QCADesigner by utilizing Peres and DG gates in quantum-dot cellular automata (QCA) that consist of a single layer with 42 cells for encryption and 47 cells for decryption. The proposed circuit outperforms the existing ones concerning area, cell count and latency. Given that the layouts’ energy consumption is assessed, it is guaranteed that the QCA nanodevice might serve as a stand-in platform for the creation of reversible circuits. The same simulation outcome was also obtained while building the identical circuits in a quantum presentation using IBMQ. The two applications are closely connected and both rely on quantum concepts. The outcomes are therefore verified for each of the two situations. The reversible Vigenere cipher technique enhances data security. Further sophisticated low-power nanoscale lossless nanocommunication architecture may be created with the help of the suggested circuits.

Shallow unitary decompositions of quantum Fredkin and Toffoli gates for connectivity-aware equivalent circuit averaging

The controlled-swap and controlled-controlled-not gates are at the heart of the original proposal of reversible classical computation by Fredkin and Toffoli. Their widespread use in quantum computation, both in the implementation of classical logic subroutines of quantum algorithms and in quantum schemes with no direct classical counterparts, has made it imperative early on to pursue their efficient decomposition in terms of the lower-level gate sets native to different physical platforms. Here, we add to this body of literature by providing several logically equivalent circuits for the Toffoli and Fredkin gates under all-to-all and linear qubit connectivity, the latter with two different routings for control and target qubits. Besides achieving the lowest cnot counts in the literature for all these configurations, we also demonstrate the remarkable effectiveness of the obtained decompositions at mitigating coherent errors on near-term quantum computers via equivalent circuit averaging. We first quantify the performance of the method in silico with a coherent-noise model before validating it experimentally on a superconducting quantum processor. In addition, we consider the case where the three qubits on which the Toffoli or Fredkin gates act nontrivially are not adjacent, proposing a novel scheme to reorder them that saves one cnot for every swap. This scheme also finds use in the shallow implementation of long-range cnots. Our results highlight the importance of considering different entangling gate structures and connectivity constraints when designing efficient quantum circuits.

Migration, ethnic otherness and the ‘refugee crisis’ in Germany: Why more conflict is better integration, and how this reconfigures positive cross-cultural management scholarship

Otherness in contemporary cross-cultural management (CCM) studies often emerges from migration and refugee movements, with ensuing integration challenges. In this context, ‘difference’ is perceived as being more problematic than enriching, and this makes it difficult to contribute to integration via a Positive Organizational Scholarship. Introducing the sociology of conflict, I propose that the success of a positive cross-cultural management engagement with Otherness should not be measured in terms of the degree to which difference is overcome and integrated, but in terms of the degree to which more parties engage more deeply with relevant conflict and friction. Investigating Otherness by means of a sociology of conflict approach thus radically changes the assumptions, research agendas, practices, presumed goals and potential responsibilities of a contemporary cross-cultural management theory and practice: deeper conflict signifies better integration, and assuming otherwise is both unrealistic and mis-fitting. I exemplify this reverse logic, and how to employ it, with a discussion of the ‘refugee crisis’ and the dynamics of ‘migration background’ in Germany. Thus reconfigured, integration in Germany emerges as more successful than is commonly believed.

A new nano-design of configurable logic module based on coplanar reversible adder and modified Fredkin gates using quantum technology

Quantum Dot Cellular Automata (QCA) and reversible logic have emerged as promising alternatives to conventional CMOS technology, offering several advantages, such as ultra-dense structures and ultra-low-power consumption. Among the crucial components of processors, the Arithmetic Logic Unit (ALU) has witnessed significant advancements in reversible computing, leading to energy-efficient and high-speed computing systems, particularly beneficial for Digital Signal Processing (DSP) applications. Conventional ALUs, reliant on irreversible logic, encounter energy inefficiencies due to information loss during computations, resulting in increased power consumption. Moreover, they may face limitations in processing speed, impacting real-time processing capabilities, especially for complex DSP tasks involving intensive arithmetic and logic operations. In response to these challenges, a research paper presents a pioneering approach, proposing a novel reversible ALU design using QCA nanotechnology. The proposed design ingeniously incorporates Modified Fredkin (MF) gates, and a coplanar reversible full adder based on the HNG gate, skillfully leveraging the unique features of QCA nanotechnology to optimize the ALU's energy-efficient and high-speed performance for DSP applications. This revolutionary QCA reversible ALU comprises 330 QCA cells arranged in a compact 0.41 μm2 area, skillfully realized through the coplanar clock-zone-based crossover approach. Its core computational elements, the three MF gates, and the innovative coplanar reversible full adder empower the ALU to execute a remarkable array of 20 distinct arithmetic and logic operations, showcasing its versatility in handling diverse DSP tasks. The proposed structure undergoes extensive simulations utilizing QCADesigner version 2.0.3 to confirm its performance. The evaluation results manifest substantial improvements compared to previous designs, boasting a 30% reduction in area occupancy, a 20% decrement in cell count, a 10% reduction in latency, and a 10% decrease in quantum cost compared to the best-known previous structure. These compelling outcomes solidify the potential of the proposed reversible ALU as a transformative advancement in energy-efficient and high-speed computing for DSP applications.

Optimized design and investigation of novel reversible toffoli and peres gates using QCA techniques

The QCA is a revolutionary dominating transistor-less computational nanotechnology based on quantum dots. As such, it might be used in the next generation of quantum computational nano-electronics devices. New molecular materials like QCA are being developed for use in nanoscale devices and cables. The major objective of this research is to optimize the design and investigate numerous properties of a QCA reversible logic circuit design. These locations include, limited Toffoli Gate (TG) and Peres Gate (PG). To address the key problems associated with the physical integration of digital circuits is power consumption and power dissipation which leads to synchronization issues, this research proposes a novel reversible logic gates (RLG-TG) a single layer coplanar approach. RLG designs with minimal design area, latency, and quantum cell count (QCA) are given and implemented using a Bijection functional method. Using the QD-E (Energy) tool, the first-order energy dissipation of the proposed shape and the impact of output bias cell temperature are also investigated. The proposed circuit designs were tested using the CVSE parameters, which had high clock signal saturation energies of 9.8e-22 d (Jules), recovery times for damping factors of 1e-15 s, and relative dielectric constants of 12.90 for GaAs and AlGaAs. The number of quantum cells used by the described new RLG-TG and RLG-PG designs is decreased by 38.23 % and 21.14 %, respectively, when compared to the optimal RLG designs employed in the state-of-the-art RLG designs. In this investigation of the proposed four-bit EPG and OPG circuits occupies 18.91 % and 38.27 % less design area, requires 46.15 % and 46.25 % less number of cells, and both designs has been 66.66 % improvement in delay.

Reversible debugging of concurrent Erlang programs: Supporting imperative primitives

Reversible computing is a programming paradigm allowing one to execute programs both in the standard, forward direction as well as backwards, recovering past states. A relevant application of reversible computing is causal-consistent reversible debugging, which allows one to explore concurrent computations backwards and forwards to find a bug. The basic idea is that any action can be undone, provided that its consequences are undone beforehand. This approach has been put into practice in CauDEr, a Causal-consistent reversible Debugger for the Erlang programming language. CauDEr provides the ability to explore a concurrent computation back and forward in a step-by-step way as well as to undo an action far in the past including all and only its consequences (rollback), and to replay an action from a log, together with its causes. CauDEr supports the functional, concurrent and distributed fragment of Erlang. However, Erlang also includes imperative primitives to manage a map (shared among all the processes of a same node) associating process identifiers to names. Here we extend CauDEr and the related theory, including rollback and replay, to support such imperative primitives. From a theoretical point of view, the imperative primitives create different causal structures to those derived from the concurrent Erlang fragment previously handled in CauDEr, yet we show that the main results proved for previous versions of CauDEr are still valid. From a practical point of view, this allows one to debug a larger subset of Erlang programs, as shown with a small case study of a server providing mathematical functionalities.

An Ultra-Energy-Efficient Reversible Quantum-Dot Cellular Automata 8:1 Multiplexer Circuit

Energy efficiency considerations in terms of reduced power dissipation are a significant issue in the design of digital circuits for very large-scale integration (VLSI) systems. Quantum-dot cellular automata (QCA) is an emerging ultralow power dissipation approach, distinct from traditional, complementary metal-oxide semiconductor (CMOS) technology, for building digital computing circuits. Developing fully reversible QCA circuits has the potential to significantly reduce energy dissipation. Multiplexers are fundamental elements in the construction of useful digital circuits. In this paper, a novel, multilayer, fully reversible QCA 8:1 multiplexer circuit with ultralow energy dissipation is introduced. The power dissipation of the proposed multiplexer is simulated using the QCADesigner-E version 2.2 tool, describing the microscopic physical mechanisms underlying the QCA operation. The results show that the proposed reversible QCA 8:1 multiplexer consumes 89% less energy than the most energy-efficient 8:1 multiplexer circuit previously presented in the literature.

Frequency encoded tristate Pauli X-gate using SOA assisted photonic band gap crystal

The quantum optical tristate Pauli-X gate can broadly be used due to its very fast speed of operation up to THz order, very fast information processing rate, and a wide domain of application. This Pauli X-gate is also important as it can undergo inversion operation. In this proposed scheme, the quantum tristate Pauli-X logic gate has been constructed by a closely packed square lattice of 2D air photonic band gap crystal (PhCs) composed of GaAsInP-dopped rods. The photonic band gap crystal-based tristate Pauli-X gate is performed also as an all-optical reversible quantum logic gate which has the character of low-powered output, very fast speed and a densely packed design structure. This photonic crystal-based structure is also verified by simulation experiment that this proposed scheme performs as the path of two input signals are cross-exchanged to one another at the output, retaining the path of the other input signal same. In this paper, the frequency encoding technique is used in all the designs to establish the logic of all-optical tristate Pauli X-gate towards the need of obtaining a three-input-three-output inversion system. The frequency encoding technique and the photonic crystal-based three Semiconductor Optical Amplifiers (pc-SOAs) are used here in all the schemes to establish the logic of the tristate Pauli-X gate scheme. Tristate Pauli-X gates have been designed and analyzed by Finite-Difference Time-Domain (FDTD) and Plane Wave Expansion (PWE) techniques. The Plane Wave Expansion (PWE) technique is used here in each system for determining the frequency range of band gap structure of transverse electric (TE) mode in the units of μm-1. All of these devices perform within the frequency range 0.629818≤ω2πc≤0.888037 and 1.17551≤ω2πc ≤ 1.34921 μm-1. The wafer dimension of each photonic band gap crystal-based device is 19.20 μm (length) × 16.20 μm (width) providing a very fast response time and very fast information handling (bit rate) capacity, which is found good for these THz Photonic crystal devices. Simulation results show that the proposed gate provides a response period of 0.291 ps and a bit rate of 3.44 Tbps, operating with a low input power of 3.45 mW. The reversible gate exhibits a response period of 0.289 ps and a bit rate of 3.46 Tbps, operating also with a low input power of 2.70 mW. Additionally, the alternative Pauli-X gate demonstrates a response time of 0.291 ps and a bit rate of 3.44 Tbps, operating with a low input power of 2.83 mW.

With a Few Square Roots, Quantum Computing Is as Easy as Pi

Rig groupoids provide a semantic model of Π, a universal classical reversible programming language over finite types. We prove that extending rig groupoids with just two maps and three equations about them results in a model of quantum computing that is computationally universal and equationally sound and complete for a variety of gate sets. The first map corresponds to an 8th root of the identity morphism on the unit 1. The second map corresponds to a square root of the symmetry on 1+1. As square roots are generally not unique and can sometimes even be trivial, the maps are constrained to satisfy a nondegeneracy axiom, which we relate to the Euler decomposition of the Hadamard gate. The semantic construction is turned into an extension of Π, called √Π, that is a computationally universal quantum programming language equipped with an equational theory that is sound and complete with respect to the Clifford gate set, the standard gate set of Clifford+T restricted to ≤2 qubits, and the computationally universal Gaussian Clifford+T gate set.

Efficient Nano-Scale Design of TIEO Based Reversible Logic Toffoli Gate Priority Encoder in Quantum-Dot Cellular Automata

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.

Efficient design and implementation of a reversible switched network in quantum cellular automata technology

Nano-communication networks have critical roles in future worldwide communications, which provide efficient data transmission at ultra-high speeds employing nano-circuits that operate with ultra-low power. The quantum cellular automata (QCA) paradigm enables designing molecular-scale devices operating at terahertz frequencies with negligible power consumption. Moreover, reversible logic aids in reducing thermodynamic power dissipation significantly. In this paper, we design and implement a single-layer Fredkin gate and use it to implement reversible QCA devices, including the crossbar switch, multiplexer, demultiplexer, transmitter, and receiver. These devices are then used to implement a reversible switched network in QCA technology. The proposed circuits employ standard 90-degree QCA cells and coplanar crossovers. The results show that the area-time complexity and power dissipation of the designed reversible switched network have been reduced significantly compared to previous designs.

Reversible Computations of One-Way Counter Automata

Deterministic one-way time-bounded multi-counter automata are studied with respect to their ability to perform reversible computations, which means that the automata are also backward deterministic and, thus, are able to uniquely step the computation back and forth. We study the computational capacity of such devices and obtain separation results between irreversible and reversible k-counter automata for polynomial and superpolynomial time. For polynomial time and exponential time we obtain moreover infinite and tight hierarchies with respect to the number of counters. These hierarchies are shown with Kolmogorov complexity and incompressibility arguments. In this way, on passing we can prove these hierarchies also for ordinary counter automata. This improves the known hierarchies for ordinary counter automata in the sense that we consider here a weaker acceptance condition. Then, it turns out that k +1 reversible counters are not better than k ordinary counters and vice versa. Finally, almost all usually studied decidability questions turn out to be undecidable and not even semidecidable for reversible multi-counter automata, if at least two counters are provided. In case of reversible one-counter automata, it is possible to show that the inclusion problem is also not even semidecidable.

The Complexity of Iterated Reversible Computation

We study a class of functional problems reducible to computing $f^{(n)}(x)$ for inputs $n$ and $x$, where $f$ is a polynomial-time bijection. As we prove, the definition is robust against variations in the type of reduction used in its definition, and in whether we require $f$ to have a polynomial-time inverse or to be computible by a reversible logic circuit. These problems are characterized by the complexity class $\mathsf{FP}^{\mathsf{PSPACE}}$, and include natural $\mathsf{FP}^{\mathsf{PSPACE}}$-complete problems in circuit complexity, cellular automata, graph algorithms, and the dynamical systems described by piecewise-linear transformations.

Compact hybrid silicon nitride and lithium niobate nano-film photoelectronic reversible logic gate

Photoelectronic hybrid logic operation improves digit circuit efficiency without any additional photoelectric conversion, especially a photoelectronic reversible logic gate may reduce energy dissipation. In this paper, a compact photoelectronic reversible logic gate is proposed based on a hybrid silicon nitride and lithium niobate nano-film waveguide. Tow Mach-Zehnder modulators are cascaded together to construct the main part of the compact photoelectronic reversible logic gate. The whole length of the gate is only 4.4mm, one hundredth of the length of the common proton exchange lithium niobate modulator. By operating at the wavelength of 1.55μm, the proposed Mach-Zehnder modulator only requires 4.9V voltage to complete a full cross-coupling, which is well compatible with CMOS technology. It is demonstrated that at the wavelength range of 1.4μm to 1.6μm, the average insertion loss is 0.6dB, the minimum crosstalk is -47dB, and the maximum extinction ratio is 41dB; in the voltage range of 4V to 6V, the average insertion loss is 0.63dB, the minimum crosstalk is -26dB, and the maximum extinction ratio is 22dB. These features indicate that the photoelectronic reversible logic gates have good performances, bringing the photoelectronic logic gates into a new design parameter space and providing a possible solution for easing the electronic bottleneck.

A novel re-entry trajectory design strategy enforcing inequality and terminal constraints in height-velocity plane

A novel re-entry trajectory design approach for a winged reusable launch vehicle that satisfies path and terminal state constraints in the height velocity plane is proposed in this paper. A two-phase re-entry trajectory is proposed. A height-velocity plane entry corridor is designed using all path and quasi-equilibrium glide constraints. The proposed method creates the reference trajectory inside the re-entry corridor using three piecewise polynomials, such as linear and logarithmic. A two-parameter search optimization problem minimizes terminal range-to-go error for this reference trajectory generation problem. Improved Search Space Reduction solves this optimization problem. The Improved Search Space Reduction algorithm is compared to the Grey Wolf Optimizer and Particle Swarm Optimisation algorithms to prove its efficacy and superiority. The reference bank angle is modified using feedback linearization and bank reversal logic to create an entry trajectory that meets all path and terminal constraints. The effectiveness of the proposed method has been validated through Monte Carlo simulations that incorporate uncertainties such as variations in initial state, uncertainties in aerodynamics, and atmospheric perturbations. The controller OPAL-RT OP4510 provides bank angle command at every instant based on the current state of the vehicle parameters associated with real-time simulator OP4510. The real-time hardware-in-loop simulation results show that the obtained re-entry trajectory satisfies all path and terminal constraints.