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.
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.
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.
This book focuses on the design methodologies of various quantum circuits, DNA circuits, DNA-quantum circuits and quantum-DNA circuits. It considers the merits and challenges of multivalued logic circuits in quantum, DNA, quantum-DNA and DNA-quantum computing. Multiple-Valued Computing in Quantum Molecular Biology: Arithmetic and Combinational Circuits is Volume 1 of a two-volume set. From fundamentals to advanced levels, this book discusses different multiple-valued logic DNA-quantum and quantum-DNA circuits. The text consists of four parts. Part I introduces multiple-valued quantum computing and DNA computing. It contains the basic understanding of multiple-valued quantum computing, multiple-valued DNA computing, multiple-valued quantum-DNA computing and multiple-valued DNA-quantum computing. Part II examines heat calculation, speed calculation, heat transfer, data conversion and data management in multi-valued quantum, DNA, quantum-DNA and DNA-quantum computing. Part III discusses multiple-valued logic operations in quantum and DNA computing such as ternary AND, NAND, OR, NOR, XOR, XNOR and multiple-valued arithmetic operations such as adder, multiplier, divider and more. Quantum-DNA and DNA-quantum multiple-valued arithmetic operations are also explained in this section. Part IV explains multiple-valued quantum and DNA combinational circuits such as multiple-valued DNA-quantum and quantum-DNA multiplexer, demultiplexer, encoder and decoder. This book will be of great help to researchers and students in quantum computing, DNA computing, quantum-DNA computing and DNA-quantum computing researchers.
Multi-Valued quantum computing is a challenging field for researchers. Two-valued quantum computing is not so old, but multi-valued quantum computing is a new topic to discuss. Designing with multiple-valued logic has obtained a lot of attention in the previous three decades. Multiple-valued logic emerged as a separate study in the early 1920s, thanks to a Polish philosopher named Lukasiewicz, his goal was to add a third value to the binary system. The Lukasiewicz system is the result of this investigation. This chapter explores the quantum world with multiple-valued logic systems. All operations will be covered that learned before in the binary quantum logic system. The basic operations of quantum computing in the ternary logic system will be implemented. In the two-valued quantum computing, several quantum fundamental gates for reversible logic are learned which include - the Pauli gate, Pauli-X gate, Hadamard gate, Toffoli gate, Fredkin gate, Deutsch gate, and Swap gate.
The combination of quantum computing and DNA computing is a new creation that is introduced in this book with multi-valued logic. This is actually the combination of quantum physics and molecular biology. So, it can be said that the combination is actually quantum molecular biology. In the multiple-valued logic system, the general organization of the Quantum-DNA cross-platform for the multiple-valued logic system is depicted. A Multi-Valued half adder is a type of adder or electronic circuit that performs ternary number addition. A Multiple-Valued Quantum-DNA full adder removes the drawback of a Multiple-Valued Quantum-DNA half adder as it includes carry bit in the addition operation. A ternary half subtractor is a type of subtractor, an electronic circuit that performs the subtractions of ternary numbers. Multi-Valued full subtractor performs subtraction operation taking borrow qubit in consideration, thus it solves the problem that half subtractor cannot overcome.
This book mainly focuses on the design methodologies of various quantum circuits, DNA circuits, DNA-quantum circuits, and quantum-DNA circuits. In this text, the author has compiled various design aspects of multiple-valued logic DNA-quantum and quantum-DNA sequential circuits, memory devices, programmable logic devices, and nanoprocessors. Multiple-Valued Computing in Quantum Molecular Biology: Sequential Circuits, Memory Devices, Programmable Logic Devices, and Nanoprocessors is Volume 2 of a two-volume set, and consists of four parts. This book presents various design aspects of multiple-valued logic DNA-quantum and quantum-DNA sequential circuits, memory devices, programmable logic devices, and nanoprocessors. Part I discusses multiple-valued quantum and DNA sequential circuits such as D flip-flop, SR latch, SR flip-flop, JK flip-flop, T flip-flop, shift register, ripple counter, and synchronous counter, which are described, respectively, with the applications and working procedures. After that, multiple-valued quantum-DNA and DNA-quantum sequential circuits such as D flip-flop, SR flip-flop, JK flip-flop, T flip-flop, shift register, ripple counter and synchronous counter circuits are explained with working procedures and architecture. Part II discusses the architecture and design procedure of memory devices such as random access memory (RAM), read-only memory (ROM), programmable read-only memory (PROM), and cache memory, which are sequentially described in multiple-valued quantum, DNA, quantum-DNA, and DNA-quantum computing. In Part III, the author examines the architectures and working principles of programmable logic devices such as programmable logic array (PLA), programmable array logic (PAL), field programmable gate array (FPGA), and complex programmable logic device (CPLD) in multiple-valued quantum, DNA, quantum-DNA, and DNA-quantum computing. Multiple-valued quantum, DNA, quantum-DNA, and DNA-quantum nanoprocessors are designed with algorithms in Part IV. Furthermore, the basic components of ternary nanoprocessors such as T-RAM, ternary instruction register, ternary incrementor circuit, ternary decoder, ternary multiplexer, ternary accumulator in quantum, DNA, quantum-DNA, and DNA-quantum computing are also explained in detail. This book will be of great help to researchers and students in quantum computing, DNA computing, quantum-DNA computing, and DNA-quantum computing.
Abstract—Multiple-valued quantum circuits are promising choices for future quantum computing technology, since the multiple-valued quantum system is more compact than the corresponding binary quantum system. Grover’s quantum search algorithm requires a sub-circuit called oracle, which takes a set of inputs and gives an output stating whether a given search condition on the inputs is satisfied or not. Equality, less-than, and greater-than comparisons are widely used as search conditions. In this paper, we show design of quantum ternary equality, less-than, and greater-than comparators on the top of ion-trap realizable 1-qutrit gates and 2-qutrit Muthukrishnan-Stroud gates. Index Terms—Multiple-valued logic, quantum logic, reversible logic, ternary comparators, ternary logic I.