arXiv:1901.07992

Quantum finite automata: survey, status and research directions

Amandeep Singh Bhatia, Ajay Kumar

Published Jan 23, 2019• 9 citations

Abstract

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.

DOI: 10.48550/arxiv.1901.07992

Related papers

Computational Power of the Quantum Turing Automata

Sina Jafarpour, Mohammad Ghodsi, Keyvan Sadri +1 more

Lots of efforts in the last decades have been done to prove or disprove whether the set of polynomially bounded problems is equal to the set of polynomially verifiable problems. This paper will present an overview of the current beliefs of quantum complexity theorists and discussion detail the impacts these beliefs may have on the future of the field. We introduce a new form of Turing machine based on the concepts of quantum mechanics and investigate the domain of this novel definition for computation. The main object is to show the domain of these computation machines and the new definition of algorithms using these automata. In section one we give a brief fundamental overview of classical complexity theory, Turing machine and all the fundamental concepts required for the next chapters. In section two we describe various classes of classical complexity automata. In next chapter we introduce quantum complexity featuring quantum Turing machines and discuss its relationship to classical complexity. Section four presents a relationship between quantum complexity classes based on the quantum Turing machines and quantum oracles, and their relationship with corresponding classical complexity classes. And section five presents a discussion on the practical phenomena in problem solving using quantum computers. Finally in section five we speculate briefly on the direction we believe the field to be headed, and what might reasonably be expected in the future

Apr 1, 20070 citations

Automata and quantum computing

Andris Ambainis, Abuzer Yakaryılmaz

Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted models such as quantum versions of finite automata have been studied. In this paper, we survey various models of quantum finite automata and their properties. We also provide some open questions and new directions for researchers. Keywords: quantum finite automata, probabilistic finite automata, nondeterminism, bounded error, unbounded error, state complexity, decidability and undecidability, computational complexity

EMS Press eBooksSep 13, 202133 citations

Automata and Quantum Computing

Andris Ambainis, Abuzer Yakaryılmaz

arXiv:1507.01988Jul 7, 201516 citations

A Taxonomy of Quantum Computing Algorithms

Lopamudra Hota, Prasant Kumar Dash

Quantum computing exploits quantum-mechanical principles such as entanglement and superposition to offer significant computational advantages over conventional classical computing. Many complex and computationally challenging problems are expected to be solved by quantum computing in a number of fields, such as data science, industrial chemistry, smart energy, finance, secure communications, and many others. In order to understand the current status of quantum computing and identify its challenges, a systematic review of the existing literature will be valuable. An overview of quantum computing literature and its taxonomy is presented in this chapter. Further, the proposed taxonomy aims to identify research gaps by mapping various related studies. There is a detailed analysis of quantum technologies with the most current state of the art. Finally, the chapter presents a highlight of open challenges and future research directions.

Advances in systems analysis, software engineering, and high performance computing book seriesJan 1, 20220 citations

Quantum automata and quantum computing

Marats Golovkins

Quantum finite automata were introduced by C.Moore and J.P.Crutchfield in [MC 97] and by A.Kondacs and J.Watrous in [KW 97]. This notion is not a generalization of the deterministic finite automata, but rather a generalization of deterministic reversible (permutation) automata. In [AF 98] A.Ambainis and R.Freivalds raised the question what kind of probabilistic automata can be viewed as a special case of quantum finite automata. To answer that question and study relationship between quantum finite automata and probabilistic finite automata, we introduce a notion of probabilistic reversible automata (PRA, or doubly stochastic automata). We give the necessary condition for a language to be recognized by PRA. We find that there is a strong relationship between different possible models of PRA and corresponding models of quantum finite automata. In these thesis we regard quantum automata, probabilistic reversible and deterministic reversible automata as reversible automata. At least two non-equivalent definitions of language recognition are used for one-way reversible finite automata in various papers. Both of these definitions have their own advantages and disadvantages, summarized in our classification of one-way reversible automata. Further, we introduce a notion of quantum finite multitape automata and prove that there is a language recognized by a quantum finite multitape automaton but not by deterministic finite multitape automata. Additionally we discover unexpected probabilistic automata recognizing complicated languages. Finally, we revise the concept of quantum pushdown automata (QPA), first introduced by C.Moore and J.P.Cruthchfield in [MC 97]. We give the definition of QPA in a non-equivalent way, including unitarity criteria, by using the definition of quantum finite automata of [KW 97]. It is established that the unitary criteria of QPA are not equivalent to the corresponding unitary criteria of quantum Turing machines [BV 97]. We show that QPA can recognize every regular language. We also present some simple non-context-free languages recognized by QPA (hence not recognizable by deterministic and nondeterministic pushdown automata).

Jan 1, 20020 citations

Automata and quantum computing

Andris Ambainis, Abuzer Yakaryılmaz

Quantum computing is a new model of computation, based on quantum physics.Quantum computers can be exponentially faster than conventional computers for problems such as factoring.Besides full-scale quantum computers, more restricted models such as quantum versions of finite automata have been studied.In this paper, we survey various models of quantum finite automata and their properties.We also provide some open questions and new directions for researchers.

Aug 6, 20212 citations