Quantum Computers and Quantum Automata

Kamil A. Valiev

Yumiko Murakami, Masaki Nakanishi, Shigeru Yamashita +1 more

Even though quantum computation is useful for solving certain problems, classical computation is more powerful in some cases. Thus, it is significant to compare the abilities of quantum computation and its classical counterpart, based on such a simple computation model as automata. In this paper we focus on the quantum pushdown automata which were defined by Golovkins in 2000, who showed that the class of languages recognized by quantum pushdown automata properly contains the class of languages recognized by finite automata. However, no one knows the entire relationship between the recognitive abilities of quantum and classical pushdown automata. As a part, we show a proposition that quantum pushdown automata can deterministically solve a certain problem that cannot be solved by any deterministic pushdown automata.

Stanley Gudder

Masaki Nakanishi

Quantum automata have been studied as simple quantum computation models. They can be considered models of small (or restricted)quantum computers. In this paper, we give descriptions of several kinds of quantum automata and show their power in comparison to their classical counterparts. We also give descriptions of quantum automata that have additional classical computational resources. Introducing classical computational resources can enhance the power of quantum automata, since this approach relaxes such restrictions as reversible state transitions.

Amandeep Singh Bhatia, Ajay Kumar

Quantum computing is concerned with computer technology based on the principles of quantum mechanics, with operations 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 light of the current state of quantum computation theory research, a systematic review of the literature seems timely. This article seeks to provide a comprehensive and systematic analysis of quantum finite automata models, quantum finite automata models with density operators and quantum finite automata models with classical states, interactive proof systems, quantum communication complexity and query complexity as described in the literature. The statistics of quantum finite automata related papers are shown and open problems are identified for more advanced research. The current status of quantum automata theory is distributed into various categories. This research work also highlights the previous research, current status and future directions of quantum automata models.

David Z. Albert