Quantum computing defines the use of quantum mechanics in the computation process. Given that Moore's law is about to reach its physical limits, it is natural to search for new technologies and computation models. The need for mechanisms and verification processes for infinite quantum computation will draw the attention of the research community. Potential applications of the proposed automata concern the verification of quantum systems and the design of appropriate quantum circuits. In the present work we define a quantum version of ω-automata, the periodic quantum automata that are able to efficiently recognize ω-languages of the form (amb)ω, where m is a finite number. We present our definitions through examples and figures. Even if our definition is simple, yet it has several interesting and useful properties. For example, they seem to be space efficient for periodic ω-languages of the form (amb)ω.Quantum computing defines the use of quantum mechanics in the computation process. Given that Moore's law is about to reach its physical limits, it is natural to search for new technologies and computation models. The need for mechanisms and verification processes for infinite quantum computation will draw the attention of the research community. Potential applications of the proposed automata concern the verification of quantum systems and the design of appropriate quantum circuits. In the present work we define a quantum version of ω-automata, the periodic quantum automata that are able to efficiently recognize ω-languages of the form (amb)ω, where m is a finite number. We present our definitions through examples and figures. Even if our definition is simple, yet it has several interesting and useful properties. For example, they seem to be space efficient for periodic ω-languages of the form (amb)ω.

International Conference on Information, Intelligence, Systems & Applications (IISA)Jul 1, 20159 citations

History and Definition of Quantum Computing Components

Siddhartha Bhattacharyya

IGI Global eBooksSep 7, 20160 citations

Quantum Representation for Deterministic Push-Down Automata

Varun Puram, K. M. George, Johnson P. Thomas

Abstract There are many papers presenting quantum computing models. The definitions parallel the classical definitions of finite state automata, push down automata, context-free grammars etc. Classical computing model definitions define languages precisely. We can state that a string belongs to a language or does not belong to it with no room for error. Quantum definitions do not possess this certainty. Sacrificing the certainty and adopting a quantum definition of a computing model does not appear to provide any concrete power to the model. Therefore, the path of this paper is to begin from the classical definition and end in a quantum circuit. In this paper we start from a Deterministic Push-Down Automaton (DPDA). We present circuit for state transition and stack operations. The circuits presented can be viewed as independent algorithms. As an example, the approach used to construct the circuit for state transition can be utilized to build the circuit for a function presented as a Boolean matrix.Abstract There are many papers presenting quantum computing models. The definitions parallel the classical definitions of finite state automata, push down automata, context-free grammars etc. Classical computing model definitions define languages precisely. We can state that a string belongs to a language or does not belong to it with no room for error. Quantum definitions do not possess this certainty. Sacrificing the certainty and adopting a quantum definition of a computing model does not appear to provide any concrete power to the model. Therefore, the path of this paper is to begin from the classical definition and end in a quantum circuit. In this paper we start from a Deterministic Push-Down Automaton (DPDA). We present circuit for state transition and stack operations. The circuits presented can be viewed as independent algorithms. As an example, the approach used to construct the circuit for state transition can be utilized to build the circuit for a function presented as a Boolean matrix.

ElectronicsNov 18, 20240 citations

Quantum computers and quantum computations

Kamil A. Valiev

Uspekhi Fizicheskih NaukJan 1, 200568 citations

A proposal for a conditional definition of the Swap Gate

P. C. Garcia Quijas, L. M. Arévalo Aguilar

In order to realize quantum logical operations, Quantum Computation (QC) requires that its basic tools and concepts obey the laws of physics. One of the fundamental concepts in QC is the conditional quantum dynamics \cite{barenco}, some times called controlled-unitary operation \cite{kumar}, which is established by the conditional "If-Then" sentence. The best know example is the c-not gate, which operates on the computational basis as follows: \textit{If the control qubit is set to $% |1>$ , then apply the single qubit quantum NOT gate on the target. Otherwise, if the control qubit is set to $|0>$ , then the target qubit is unchanged}. This gate represents the paradigm for the conditional quantum dynamics, where the flipping of the target qubit is conditioned to the state of the control qubit. Other gates have been defined in a similar way of conditional evolution; for instance, the control phase gates \cite{paulo1}. However, to the best of our knowledge, such conditional quantum dynamics has not been yet used to define the SWAP gate. Here we propose a possible conditional definition, in the form of If-Then sentence, to construct a SWAP gate in the case of two qubits. This definition suggests a classification in two classes, which depends upon the number of qubits that have to undergo a conditional quantum dynamics.In order to realize quantum logical operations, Quantum Computation (QC) requires that its basic tools and concepts obey the laws of physics. One of the fundamental concepts in QC is the conditional quantum dynamics \cite{barenco}, some times called controlled-unitary operation \cite{kumar}, which is established by the conditional "If-Then" sentence. The best know example is the c-not gate, which operates on the computational basis as follows: \textit{If the control qubit is set to $% |1>$, then apply the single qubit quantum NOT gate on the target. Otherwise, if the control qubit is set to $|0>$, then the target qubit is unchanged}. This gate represents the paradigm for the conditional quantum dynamics, where the flipping of the target qubit is conditioned to the state of the control qubit. Other gates have been defined in a similar way of conditional evolution; for instance, the control phase gates \cite{paulo1}. However, to the best of our knowledge, such conditional quantum dynamics has not been yet used to define the SWAP gate. Here we propose a possible conditional definition, in the form of If-Then sentence, to construct a SWAP gate in the case of two qubits. This definition suggests a classification in two classes, which depends upon the number of qubits that have to undergo a conditional quantum dynamics.

arXiv:0711.1917Nov 13, 20070 citations

% |1>

, then apply the single qubit quantum NOT gate on the target. Otherwise, if the control qubit is set to

|0>

, then the target qubit is unchanged}. This gate represents the paradigm for the conditional quantum dynamics, where the flipping of the target qubit is conditioned to the state of the control qubit. Other gates have been defined in a similar way of conditional evolution; for instance, the control phase gates \cite{paulo1}. However, to the best of our knowledge, such conditional quantum dynamics has not been yet used to define the SWAP gate. Here we propose a possible conditional definition, in the form of If-Then sentence, to construct a SWAP gate in the case of two qubits. This definition suggests a classification in two classes, which depends upon the number of qubits that have to undergo a conditional quantum dynamics.