Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Natural Science Journal of Xiangtan University

Four-Valued Quantum Logic

Ang Jian-quan

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

Quantum computing,which is based on quantum physical,is a novel computing model.As multiple-valued logic is an extension to two-valued logic,we introduce multiple-valued logic to the research of four-valued quantum logic.This paper illustrates the concept of four valued quantum qubit and four valued quantum logic based on Galois field.

Related papers

Multiple-Valued Logic Operations in Quantum Computing

Hafiz Md. Hasan Babu

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.

CRC Press eBooks•Aug 29, 2023•0 citations

Multiple-Valued Quantum Arithmetic Operations

Hafiz Md. Hasan Babu

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.

CRC Press eBooks•Aug 29, 2023•0 citations

Quantum computer with mixed states and four-valued logic

Vasily Evgenevich Tarasov

In this paper we discuss a model of quantum computer in which a state is an operator of density matrix and gates are general quantum operations, not necessarily unitary. A mixed state (operator of density matrix) of n two-level quantum systems is considered as an element of 4 n -dimensional operator Hilbert space (Liouville space). It allows us to use a quantum computer model with four-valued logic. The gates of this model are general superoperators which act on n -ququat state. Ququat is a quantum state in a four-dimensional (operator) Hilbert space. Unitary two-valued logic gates and quantum operations for an n -qubit open system are considered as four-valued logic gates acting on n -ququats. We discuss properties of quantum four-valued logic gates. In the paper we study universality for quantum four-valued logic gates.

arXiv:quant-ph/0312131•Journal of Physics A Mathematical and General•Jun 14, 2002•65 citations

Open n-Qubit System as a Quantum Computer with Four-Valued Logic

Vasily Evgenevich Tarasov

In this paper we generalize the usual model of quantum computer to a model in which the state is an operator of density matrix and the gates are general superoperators (quantum operations), not necessarily unitary. A mixed state (operator of density matrix) of n two-level quantum system (open or closed n-qubit system) is considered as an element of $4^{n}$-dimensional operator Hilbert space (Liouville space). It allows to use quantum computer (circuit) model with 4-valued logic. The gates of this model are general superoperators which act on n-ququats state. Ququat is quantum state in a 4-dimensional (operator) Hilbert space. Unitary two-valued logic gates and quantum operations for n-qubit open system are considered as four-valued logic gates acting on n-ququats. We discuss properties of quantum 4-valued logic gates. In the paper we study universality for quantum four-valued logic gates.

arXiv:quant-ph/0112023•Dec 4, 2001•0 citations

Multiple-Valued Computing in Quantum Molecular Biology

Hafiz Md. Hasan Babu

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.

CRC Press eBooks•Aug 29, 2023•3 citations

APPLICATION OF DECISION DIAGRAMS TO DESIGN QUANTUM LOGIC CIRCUITS

Joyshree Nath, Asoke Nath

Quantum computing is the theory of quantum bits, or qubits, and their associated linear transformations. A quantum computer is more powerful than classical computers, with the problems being solvable. Quantum computing is expected to play an increasingly important role in building more compact and less power-consuming computers. Quantum Computing has emerged to be a very effective field where numerous scientists are doing research in this area. It is true that quantum computing system is now in its initial theoretical state, a lot of aspects of this logic has been proposed by scientists over the years. Quantum computing promises to compute a whole set of intractable problems easily and within a very small amount of time. From binary to multi-valued logic quantum computing systems have a lot of properties to be explored, but mainly theoretically and not in a form of some tangible hardware logic. In the present study the authors have made a thorough study of the properties of binary and multi-valued quantum logic along with the impact of Quantum Information Decision Diagram (QUIDD), Quantum Multi-Valued Decision Diagrams in quantum logic.

Journal of Global Research in Computer Sciences•Apr 7, 2012•0 citations
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.
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.
In this paper we discuss a model of quantum computer in which a state is an operator of density matrix and gates are general quantum operations, not necessarily unitary. A mixed state (operator of density matrix) of n two-level quantum systems is considered as an element of 4 n -dimensional operator Hilbert space (Liouville space). It allows us to use a quantum computer model with four-valued logic. The gates of this model are general superoperators which act on n -ququat state. Ququat is a quantum state in a four-dimensional (operator) Hilbert space. Unitary two-valued logic gates and quantum operations for an n -qubit open system are considered as four-valued logic gates acting on n -ququats. We discuss properties of quantum four-valued logic gates. In the paper we study universality for quantum four-valued logic gates.
In this paper we generalize the usual model of quantum computer to a model in which the state is an operator of density matrix and the gates are general superoperators (quantum operations), not necessarily unitary. A mixed state (operator of density matrix) of n two-level quantum system (open or closed n-qubit system) is considered as an element of 4n4^{n}4n-dimensional operator Hilbert space (Liouville space). It allows to use quantum computer (circuit) model with 4-valued logic. The gates of this model are general superoperators which act on n-ququats state. Ququat is quantum state in a 4-dimensional (operator) Hilbert space. Unitary two-valued logic gates and quantum operations for n-qubit open system are considered as four-valued logic gates acting on n-ququats. We discuss properties of quantum 4-valued logic gates. In the paper we study universality for quantum four-valued logic gates.
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.
Quantum computing is the theory of quantum bits, or qubits, and their associated linear transformations. A quantum computer is more powerful than classical computers, with the problems being solvable. Quantum computing is expected to play an increasingly important role in building more compact and less power-consuming computers. Quantum Computing has emerged to be a very effective field where numerous scientists are doing research in this area. It is true that quantum computing system is now in its initial theoretical state, a lot of aspects of this logic has been proposed by scientists over the years. Quantum computing promises to compute a whole set of intractable problems easily and within a very small amount of time. From binary to multi-valued logic quantum computing systems have a lot of properties to be explored, but mainly theoretically and not in a form of some tangible hardware logic. In the present study the authors have made a thorough study of the properties of binary and multi-valued quantum logic along with the impact of Quantum Information Decision Diagram (QUIDD), Quantum Multi-Valued Decision Diagrams in quantum logic.