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CRC Press eBooks

Multiple-Valued Quantum Combinational Circuits

Hafiz Md. Hasan Babu

Published Aug 29, 2023• 0 citations
Publisher

Abstract

The qutrit is the information unit of a three-valued quantum system (ternary quantum system). One of the most vital block designs in a binary digital system is the multiplexer. It is a device that allows only one input signal from a group of input signals, and the input signal selected by the multiplexer is transmitted into a single medium. Multiplexers, in fact, help to improve the efficiency of the communication system. It enables the transmission of data such as audio, video, and so on from various channels via cables. This circuit is useful for creating multi-valued arithmetic circuits. Demultiplexer circuits are among the most important circuits in the design of complex hardware. It maps a single input to multiple outputs. Multi-Valued Quantum Encoder is a combinational logic circuit which acts as a multi inputs and multi outputs device as it has 3 n input lines and n output lines.

DOI
10.1201/9781003381938-16

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CRC Press eBooks•Aug 29, 2023•0 citations
The qutrit is the information unit of a three-valued quantum system (ternary quantum system). One of the most vital block designs in a binary digital system is the multiplexer. It is a device that allows only one input signal from a group of input signals, and the input signal selected by the multiplexer is transmitted into a single medium. Multiplexers, in fact, help to improve the efficiency of the communication system. It enables the transmission of data such as audio, video, and so on from various channels via cables. This circuit is useful for creating multi-valued arithmetic circuits. Demultiplexer circuits are among the most important circuits in the design of complex hardware. It maps a single input to multiple outputs. Multi-Valued Quantum Encoder is a combinational logic circuit which acts as a multi inputs and multi outputs device as it has 3 n input lines and n output lines.
Quantum computers might be built directly from the physical properties of the DNA molecule. Multi-Valued logic enhances the advantages of this combination. The combination of this quantum computing and DNA computing is called quantum molecular biology. This chapter describes the combinational circuits in multi-valued quantum-DNA computing. A balanced multiplexer is an essential component of a digital system that converts multiple inputs to a single output. This circuit is useful for building multi-valued arithmetic circuits. Demultiplexer circuits are among the most important circuits in the design of complex hardware. It maps a single input to multiple outputs. The Multi-Valued Encoder is a combinational logic circuit with 3 n input lines and n output lines that functions as a multi-input and multi-output device. An encoder is a critical component of a digital computer. A Quantum-DNA decoder first performs some Quantum operation on its inputs, then proceeds to the DNA operations after converting the qubit to its corresponding DNA molecule.
Both DNA computing and quantum computing have the potential to outperform ordinary digital computers, but considerable technical hurdles must be overcome first. Because of their coherent superposition of states, quantum computers are more powerful than traditional turing machines. DNA computers can be evolved via biotechnology techniques. Combining DNA and quantum computers could capture both of these properties. With this in mind, this chapter is devoted to DNA-Quantum Computing, which combines two distinct technologies. It discusses multi-valued DNA-Quantum multiplexer, demultiplexer, encoder and decoder. A balanced multiplexer is an essential component of a digital system that converts multiple inputs to a single output. This circuit is useful for building multi-valued arithmetic circuits. Demultiplexer circuits are among the most important circuits in the design of complex hardware. It maps a single input to multiple outputs. The Multi-Valued Encoder is a combinational logic circuit with 3 n input lines and n output lines that functions as a multi-input and multi-output device.
Quantum computing is a new and challenging field in research and arithmetic circuits in multi-valued quantum computing are a recent attraction for all. It is a speedy technology in modern science. Multiple-valued logic circuits are a type of circuit that offer several potential opportunities for the improvement of present VLSI circuit designs. Multiple-valued logic has a wide range of applications in addition to providing a better understanding of binary difficulties. They can be divided into two categories. To handle binary issues more quickly, the first group use a multiple-valued logic domain. The second group focuses on electrical circuits that use more than two discrete levels of signals, such as multiple-valued memory, arithmetic circuits, and Field Programmable Gate Arrays. In quantum multiple valued parallel adder, it is required to add two qutrits (the addend and the augend) which are only single-qutrit input. The procedures are the same, the only difference is the logical operation will be in the ternary system.
Abstract Designing conventional circuits present many challenges, including minimizing internal power dissipation. An approach to overcoming this problem is utilizing quantum technology, which has attracted significant attention as an alternative to Nanoscale CMOS technology. The reduction of energy dissipation makes quantum circuits an up-and-coming emerging technology. Ternary logic can potentially diminish the quantum circuit width, which is currently a limitation in quantum technologies. Using qutrit instead of qubit could play an essential role in the future of quantum computing. First, we propose two approaches for quantum ternary decoder circuit in this context. Then, we propose a quantum ternary multiplexer and quantum ternary demultiplexer to exploit the constructed quantum ternary decoder circuit. Techniques to achieve lower quantum cost are of importance. We considered two types of circuits, one in which the output states are always restored to the initial input states and the other in which the states of the output are irrelevant. We compare the proposed quantum ternary circuits with their existing counterparts and present the improvements. It is possible to realize the proposed designs using macro-level ternary gates that are based on the ion-trap realizable ternary 2-qutrit Muthukrishnan–Stroud and 1-qutrit permutation gates.
Abstract In recent years, ternary reversible logic has become a promising paradigm for advancing low-power, high-performance quantum digital systems that preserve information and are energy efficient. This paper focuses on two primary objectives: first, the efficient realization of ternary reversible 3×13 \times 13×1 3 × 1 multiplexers and 1×31 \times 31×3 1 × 3 demultiplexers using quantum gates, specifically 1-qutrit Shift and 3-qutrit Controlled Feynman gates, and second, the design of generalized n×1n \times 1n×1 n × 1 multiplexers and 1×n1 \times n1×n 1 × n demultiplexers. The proposed 9×19 \times 19×1 9 × 1 multiplexer we propose in this study has demonstrated notable improvements in terms of quantum cost (20%), depth (18%), number of constant inputs (60%), and garbage outputs (30%), while the proposed 1×91 \times 91×9 1 × 9 demultiplexer shows a 20% reduction in quantum cost, a 18% reduction in depth, a 33% reduction in constant inputs, and a 50% reduction in garbage outputs, compared to the most efficient existing designs. These optimizations represent an important step forward in the development of more efficient ternary and quantum reversible logic circuits, advancing the scalability of quantum systems.
In multiple-valued DNA-Quantum computing FPGA design, DNA sequences will work as input for the programmable logic devices. Ternary D Flip-Flop is a sequential circuit that consists of four ternary NAND operations and one NOT operation. In multiple-valued DNA-Quantum computing CPLD design, DNA sequences will work as input for the programmable logic devices. DNA part consists of DNA operation of the logic function, Flip-flop and 3 and operation of the multiplexer. The D Flip-Flop is a sequential circuit that consists of four Quantum NAND operations and one DNA NOT operation. Quantum part consists of Quantum operation of Multiplexer OR operations. Multi-Valued DNA to Quantum CPLD functional block is designed by connecting DNA circuit and Quantum circuit. Ternary CPLD functional block is designed by connecting Flip-Flops, logic function and Multiplexers. This chapter presents four PLDs in details. The PLA, PAL, FPGA, CPLD are explained with their working principles and circuit architectures.