On Some Aspects of Quantum Computational Models

Abstract

Quantum computing is concerned with computer technology based on the principles of quantum mechanics, in which operations are performed at the quantum level. Quantum computational models make it possible to analyze the resources required for computations. Quantum automata can be classified thusly: quantum finite automata, quantum sequential machine, quantum pushdown automata, quantum Turing machine, and orthomodular lattice-valued automata. These models are useful for determining the expressive power and boundaries of various computational features. In many cases, quantum models are more superior to classical models in terms of language recognition. Thus, mathematical models of quantum computation can be view as generalizations of its physical models. Motivated from the above-mentioned facts, we proposed a variant of two-way quantum finite automata named two-way multihead quantum finite automata and determined its language recognition capability. Moreover, we have proposed a quantum analogue of classical queue automata by using the definition of the quantum Turing machine and quantum finite-state automata. Further, we have also introduced a generalization of real-time deterministic queue automata, the real-time quantum queue automata which work in real-time i.e., the input head can move towards the right direction only and takes precisely one step per input symbol. We have proved that real-time quantum queue automaton is more superior than its real-time classical variants by using quantum transitions. Classical systems are not robust and capable of describing quantum systems. Some tasks that are impossible in classical systems can be realized in quantum systems. The most significant property entanglement separates the classical world from the quantum world. It is one of the most central topics in quantum information theory. In fact, quantum many-body systems cannot be simulated by classical systems because of the increase in size of Hilbert space.