Ternary Toffoli Research Articles

A Study of q-Deformed Bosons, and Their Implications to Quantum Optics

In this study, we investigate three types of q-deformed boson oscillators, focusing on their mathematical frameworks and thermodynamic properties. We calculate key thermodynamic quantities, such as internal energy and entropy, as functions of the deformation parameter q. Our results reveal that these oscillators are eigenstates of specific deformed boson annihilation operators. We also analyze their unique characteristics and implications in deformed quantum optics. Furthermore, we examine the impact of q-deformation on qutrit logic gates, including cycle, self-shift, controlled cycle, controlled self-shift, Feynman, ternary Toffoli, and Fredkin gates, highlighting their altered computational properties. This research contributes to a deeper understanding of q-deformed systems and their applications in quantum computing. Overall, it opens new avenues for exploring the interplay between deformation parameters and quantum information processing.

Mixed Multi-Chaos Quantum Image Encryption Scheme Based on Quantum Cellular Automata (QCA)

The advent of quantum computers could enable the resolution of complex computational problems that conventional cryptographic protocols find challenging. As a result, the formidable computing capabilities of quantum computers may render all present-day cryptographic schemes that rely on computational complexity ineffectual. Inspired by these possibilities, the primary purpose of this paper is to suggest a quantum image encryption scheme based on quantum cellular automata with mixed multi-chaos hybrid maps and a hyperchaotic system with quantum operations. To achieve desirable encryption outcomes, we designed an encryption scheme involving two main operations: (1) pixel-level diffusion and (2) pixel-level permutation. Initially, the secret keys generated using the hyperchaotic system were closely tied to the original image. During the first phase, the establishment of correlations among the image pixels, in addition to the three chaotic sequences obtained from the hyperchaotic system, was achieved with the application of a quantum-state superposition and measurement principle, wherein the color information of a pixel is described using a single qubit. Therefore, the three channels of the plain image were subjected to quantum operations, which involve Hadamard transformation and the quantum-controlled NOT gate, before the diffusion of each color channel with the hyperchaotic system. Subsequently, a quantum ternary Toffoli gate was used to perform the diffusion operation. Next, the appropriate measurement was performed on the three diffused channels. To attain the confusion phase, a blend of mixed multi-chaos hybrid maps and a two-dimensional quantum cellular automaton was used to produce random and chaotic sequence keys. Subsequently, the circular shift was utilized to additionally shuffle the rows and columns of the three diffused components, in order to alter the positions of their pixel values, which significantly contributes to the permutation process. Lastly, the three encoding channels, R, G, and B, were merged to acquire the encrypted image. The experimental findings and security analyses established that the designed quantum image encryption scheme possesses excellent encryption efficiency, a high degree of security, and the ability to effectively withstand a diverse variety of statistical attacks.

Optically Driven Both Classical and Quantum Unary, Binary, and Ternary Logic Gates on Co-Decorated Graphene Nanoflakes.

Nanospintronics holds great potential for providing high-speed, low-power, and high-density logic and memory elements in future computational devices. Here, using ab initio many-body theory, we suggest a nanoscale framework for building quantum computation elements, based on individual magnetic atoms deposited on graphene nanoflakes. We show the great possibilities of this proposal by exemplarily presenting four quantum gates, namely, the unary Pauli-X, Pauli-Y, Pauli-Z, and Hadamard gates, as well as the universal classical ternary Toffoli gate, which preserves information entropy and is therefore fully reversible and minimally energy consuming. All our gates operate within the subpicosecond time scale and reach fidelities well above 90%. We demonstrate the ability to control the spin direction and localization, as well as to create superposition states and to control the quantum phase of states, which are indispensable ingredients of quantum computers. Additionally, being optically driven, their predicted operating speed by far beats that of modern quantum computers.

Quantum Ternary Multiplication Gate (QTMG): Toward Quantum Ternary Multiplier and a New Realization for Ternary Toffoli Gate

The designs using ternary logic exploit its logarithmic reduction in the number of qudits compared with the binary circuits. In this paper, we propose quantum ternary multiplication gate. We term it as QTMG. Then we present the symbol and the realization of QTMG. Researchers will be able to use this gate as well as its symbol and realizations in their future studies. We also present a new realization of ternary Toffoli gate in specific state. Moreover, in this paper, we propose 1-qutrit multiplier circuit. The symbol and the realization of the proposed 1-qutrit multiplier circuit are also provided. Afterward, we proposed ternary partial products generation circuit (TPPG) and summation network circuit in order to design quantum ternary 2-qutrit multiplier circuit. Overall, the proposed design of QTMG in this paper is suggested for the first time. In addition, the proposed realization of ternary Toffoli gate, TPPG, summation network and 2-qutrit multiplier circuits are compared with the existing designs and the improvements are reported. The proposed gate and circuits are realized using macro-level ternary gates which are built on the top of the ion-trap realizable 1-qutrit gates and 2-qutrit Muthukrishnan–Stroud gates.

A Ternary Decision Diagram (TDD)-Based Synthesis Approach for Ternary Logic Circuits

Ternary reversible logic synthesis has started gaining the attention of researchers in recent years because of its distinct advantages over binary reversible logic synthesis. However, the existing methods for the synthesis of ternary reversible logic circuits are applicable only to smaller benchmarks. The present paper proposes an efficient synthesis approach in this regard using ternary decision diagrams (TDDs). A TDD is first generated for the function that is to be synthesized. Then, using a gate library of ternary reversible gates, each TDD node is mapped to a sequence of ternary reversible gates that are finally merged together to form the required netlist. The ternary gate library consists of ternary reversible gates such as multi-polarity ternary Feynman gate and multi-polarity ternary Toffoli gate. To estimate the quantum cost, we propose a decomposition approach to represent a ternary reversible gate in terms of ternary elementary gates. We have carried out experimental evaluation on two types of benchmarks. The first type consists of binary reversible benchmarks converted into ternary reversible benchmarks using a transformation approach. The second type is based on ternary non-reversible benchmarks. We have reported the results for benchmarks with up to 13 inputs with a longest runtime of 7 min, which compares favourably with the existing works in the literature.

Realization of Ternary Reversible Circuits Using Improved Gate Library

Ternary logic has some distinct advantage over binary logic. In this paper we propose a synthesis approach for ternary reversible circuits using ternary reversible gates. Our method takes a boolean function as input. The input is provided as .pla file. The .pla file is first converted into ternary logic function, which can be represented as permutation. The gate library used for synthesis is Ternary Not, Ternary Toffoli and Ternary Toffoli+ (NT ,TT ,TT+). The proposed constructive method, generates 3-cycles from the permutation, and then each 3-cycle is mapped to (NT ,TT ,TT+) gate library. Experimental results show that the method generates lesser number of gates for some circuits compared to previously reported works.

Design of New Quantum/Reversible Ternary Subtractor Circuits

Ternary quantum circuits play a significant role in future quantum computing technology because they have many advantages over binary quantum circuits. Subtraction is considered as being one of the key arithmetic operations; hence, subtractors are very essential for the construction of various computational units of quantum computers and other complex computational systems. In this paper, we have proposed the realization of a quantum reversible ternary half-subtractor circuit using a generalized ternary gate, a ternary Toffoli gate, and a ternary C2NOT gate. Based on the realization of the ternary half-subtractor, we proposed the realization of a ternary full-subtractor.

Logic Synthesis of Ternary Quantum Circuits with Minimal Qutrits

This paper investigates a universal approach of synthesizing arbitrary ternary logic circuits in quantum computation based on the truth table technology. It takes into account of the relationship of classical logic and quan-tum logic circuits. By adding inputs with constant value and garbage outputs, the classical non-reversible logic can be transformed into reversible logic. Combined with group theory, it provides an algorithm using the ternary Swap gate, ternary NOT gate and ternary Toffoli gate library. Simultaneously, the main result shows that the numbers of qutrits we use are minimal compared to other methods. We also illustrate with two examples to test our approach.

Design and Analysis of a Compact Reversible Ternary Systolic Array

Multi-valued logic synthesis is a very promising and affluent research area at present because of allowing designers to build much more efficient computers than the existing classical ones. In this regard, research on ternary logic synthesis has got impetus in the recent years. Many existing literature are mainly perceptive to the realization of efficient ternary reversible processors. This research is based on the design of a reversible systolic array, one of the best examples of the parallel processing, using micro level ternary Toffoli gate. General architecture of the ternary reversible systolic array multiplier is shown along with example. Lower bound for the quantum cost and the garbage outputs in terms of entire circuit entire circuit is calculated here to establish the compactness of the design. Finally, comparative result shown that the proposed circuit outperforms the existing one both in terms of number of gates and Quantum cost analysis.

Realizing ternary quantum switching networks without ancilla bits

This paper investigates the synthesis of quantum networks built to realize ternary switching circuits in the absence of ancilla bits. The results we established are twofold. The first shows that ternary Swap, ternary Not and ternary Toffoli gates are universal for the realization of arbitrary $n\times n$ ternary quantum switching networks without ancilla bits. The second result proves that all $n\times n$ quantum ternary networks can be generated by Not, Controlled-Not, Multiply-Two, and Toffoli gates. Our approach is constructive. key words: ternary quantum logic synthesis, quantum circuit optimization, group theory.