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

AIP conference proceedings

Efficient Quantum Algorithm for NPC and EXPTIME Problems

Satoshi Iriyama, Makoto Ohya

Published Jan 1, 2011• 0 citations
Publisher

Abstract

We have studied a quantum algorithm for several years, and developed some applications for difficult problems, NPC problems and NP intermidiate problems. In order to discuss the computational complexity of quantum algorithm, we defined a generalized quantum Turing machine using a density operator on a Hilbert space and quantum channels on it. Since the properity of quantum channel, this mathematical model can describe not only unitary process of quantum algorithm but also measurement process and non‐linear dynamical process. Then we can calculate the computational complexity of quantum algorithm more regorously.In this paper, we review our results, and discuss why quantum algorithms are more effective than classical ones. Moreover, we propose a quantum algorotihm for EXPTIME problem.

DOI
10.1063/1.3567462

Related papers

Efficient Quantum Algorithm for NPC and EXPTIME Problems

Satoshi Iriyama, M. Ohya, Andrei Yu. Khrennikov +3 more

We have studied a quantum algorithm for several years, and developed some applications for difficult problems, NPC problems and NP intermidiate problems. In order to discuss the computational complexity of quantum algorithm, we defined a generalized quantum Turing machine using a density operator on a Hilbert space and quantum channels on it. Since the properity of quantum channel, this mathematical model can describe not only unitary process of quantum algorithm but also measurement process and non‐linear dynamical process. Then we can calculate the computational complexity of quantum algorithm more regorously.In this paper, we review our results, and discuss why quantum algorithms are more effective than classical ones. Moreover, we propose a quantum algorotihm for EXPTIME problem.

AIP conference proceedings•Jan 1, 2011•0 citations

Generalized quantum Turing machine and its use to find an algorithm solving NP-Complete problem

Satoshi Iriyama, Masanori Ohya

Ohya and Volovich found the quantum algorithm with a chaos dynamics, called the OV SAT algorithm which enabled to solve NP-Complete problem in polynomial time. It is proved that the unitary operator of the quantum algorithm can be constructed by a product of so called fundamental gates. To discuss the computational complexity rigorously, we introduced a generalized quantum Turing machine(GQTM) where the computational process is given by quantum channels including a dispative dynamics and the configuration is represented by density operators. In this paper, we explain the GQTM and the OV SAT algorithm, then we discuss the computational complexity of OV SAT algorithm. Finally, we introduce some resent results and topics by use of GQTM.

International Symposium on Applied Sciences in Biomedical and Communication Technologies•Nov 1, 2010•1 citation

Generalized Quantum Turing Machine and Its Use to Find an Algorithm Solving NP-Complete Problem (Invited Paper)

Satoshi Iriyama, Masanori Ohya

Ohya and Volovich found the quantum algorithm with a chaos dynamics, called the OV SAT algorithm which enabled to solve NP-Complete problem in polynomial time. It is proved that the unitary operator of the quantum algorithm can be constructed by a product of so called fundamental gates. To discuss the computational complexity rigorously, we intro- duced a generalized quantum Turing machine(GQTM) where the computational process is given by quantum channels including a dispative dynamics and the configuration is represented by density operators. In this paper, we explain the GQTM and the OV SAT algorithm, then we discuss the computational complexity of OV SAT algorithm. Finally, we introduce some resent results and topics by use of GQTM.

•Jan 1, 2010•0 citations

Mathematical characterization of quantum algorithm

Satoshi Iriyama, Masanori Ohya

We have studied quantum computation for many years, and defined the generalized quantum Turing machine by using completely positive channels and density operators on the Hilbert space. This mathematical model of quantum algorithm gives us the new language classes in which the class NP is included in a polynomial time class. It has also a possibility to expand the theory of computability which has philosophical significance. In this talk, we explain a definition of the model, the language classes, some theorems and applications.

International Conference on Applied Mathematics•Dec 14, 2009•1 citation

On Generalized Quantum Turing Machine and Its Applications

Satoshi Iriyama, Masanori Ohya

Ohya and Volovich discussed a quantum algorithm for the SAT problem with a chaos amplification process (OMV SAT algorithm) and showed that the number of steps it performed was polynomial in input size. In this paper, we define a generalized quantum Turing machine (GQTM) and related computational complexity. Then we show that there exists a GQTM which recognizes the SAT problem in polynomial time. Moreover, we discuss the problem of finding the quantum algorithm for a partial recursive function.

Open Systems & Information Dynamics•Aug 13, 2009•0 citations

Using quantum computing to create efficient algorithms

Ирина Николаевна Балаба, Galina Deryabina, I. Pinchuk +2 more

Abstract The article presents a historical overview of the development of the mathematical idea of a quantum computing model - a new computational strategy based on the postulates of quantum mechanics and having advantages over the traditional computational model based on the Turing machine; clarified the features of the operation of multi-qubit quantum systems, which ensure the creation of efficient algorithms; the principles of quantum computing are outlined and a number of efficient quantum algorithms are described that allow solving the problem of exponential growth of the complexity of certain problems.

Journal of Physics Conference Series•Oct 1, 2021•0 citations
We have studied a quantum algorithm for several years, and developed some applications for difficult problems, NPC problems and NP intermidiate problems. In order to discuss the computational complexity of quantum algorithm, we defined a generalized quantum Turing machine using a density operator on a Hilbert space and quantum channels on it. Since the properity of quantum channel, this mathematical model can describe not only unitary process of quantum algorithm but also measurement process and non‐linear dynamical process. Then we can calculate the computational complexity of quantum algorithm more regorously.In this paper, we review our results, and discuss why quantum algorithms are more effective than classical ones. Moreover, we propose a quantum algorotihm for EXPTIME problem.
We have studied a quantum algorithm for several years, and developed some applications for difficult problems, NPC problems and NP intermidiate problems. In order to discuss the computational complexity of quantum algorithm, we defined a generalized quantum Turing machine using a density operator on a Hilbert space and quantum channels on it. Since the properity of quantum channel, this mathematical model can describe not only unitary process of quantum algorithm but also measurement process and non‐linear dynamical process. Then we can calculate the computational complexity of quantum algorithm more regorously.In this paper, we review our results, and discuss why quantum algorithms are more effective than classical ones. Moreover, we propose a quantum algorotihm for EXPTIME problem.
Ohya and Volovich found the quantum algorithm with a chaos dynamics, called the OV SAT algorithm which enabled to solve NP-Complete problem in polynomial time. It is proved that the unitary operator of the quantum algorithm can be constructed by a product of so called fundamental gates. To discuss the computational complexity rigorously, we introduced a generalized quantum Turing machine(GQTM) where the computational process is given by quantum channels including a dispative dynamics and the configuration is represented by density operators. In this paper, we explain the GQTM and the OV SAT algorithm, then we discuss the computational complexity of OV SAT algorithm. Finally, we introduce some resent results and topics by use of GQTM.
Ohya and Volovich found the quantum algorithm with a chaos dynamics, called the OV SAT algorithm which enabled to solve NP-Complete problem in polynomial time. It is proved that the unitary operator of the quantum algorithm can be constructed by a product of so called fundamental gates. To discuss the computational complexity rigorously, we intro- duced a generalized quantum Turing machine(GQTM) where the computational process is given by quantum channels including a dispative dynamics and the configuration is represented by density operators. In this paper, we explain the GQTM and the OV SAT algorithm, then we discuss the computational complexity of OV SAT algorithm. Finally, we introduce some resent results and topics by use of GQTM.
We have studied quantum computation for many years, and defined the generalized quantum Turing machine by using completely positive channels and density operators on the Hilbert space. This mathematical model of quantum algorithm gives us the new language classes in which the class NP is included in a polynomial time class. It has also a possibility to expand the theory of computability which has philosophical significance. In this talk, we explain a definition of the model, the language classes, some theorems and applications.
Abstract The article presents a historical overview of the development of the mathematical idea of a quantum computing model - a new computational strategy based on the postulates of quantum mechanics and having advantages over the traditional computational model based on the Turing machine; clarified the features of the operation of multi-qubit quantum systems, which ensure the creation of efficient algorithms; the principles of quantum computing are outlined and a number of efficient quantum algorithms are described that allow solving the problem of exponential growth of the complexity of certain problems.