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.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/0112023Dec 4, 20010 citations

On the logic of pairs of quantum systems

Allen Stairs

SyntheseJul 1, 198314 citations

Quantum logical description of two-particle systems

Andrey Anatoljevich Grib, Romàn R. Zapatrin

International Journal of Theoretical PhysicsJul 1, 19917 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.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/0312131Journal of Physics A Mathematical and GeneralJun 14, 200265 citations

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.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 eBooksAug 29, 20230 citations

A Logic for Probability in Quantum Systems

Ron van der Meyden, Manas K. Patra

Lecture notes in computer scienceJan 1, 200318 citations

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.