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Quantum Finite Automata: A Modern Introduction

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Computing with New Resources

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8808))

Abstract

We present five examples where quantum finite automata (QFAs) outperform their classical counterparts. This may be useful as a relatively simple technique to introduce quantum computation concepts to computer scientists. We also describe a modern QFA model involving superoperators that is able to simulate all known QFA and classical finite automaton variants.

Some parts of the material are based on the lectures given by the second author during his visits to Kazan Federal University, Ural Federal University, and Boğaziçi University in 2013.

Yakaryılmaz was partially supported by CAPES with grant 88881.030338/2013-01, ERC Advanced Grant MQC, and FP7 FET project QALGO.

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References

  1. Adleman, L.M., DeMarrais, J., Huang, M.-D.A.: Quantum computability. SIAM Journal on Computing 26(5), 1524–1540 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ambainis, A., Watrous, J.: Two-way finite automata with quantum and classical states. Theoretical Computer Science 287(1), 299–311 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  3. Ambainis, A., Beaudry, M., Golovkins, M., Ķikusts, A., Mercer, M., Thérien, D.: Algebraic results on quantum automata. Theory of Computing Systems 39(1), 165–188 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  4. A. Ambainis, Freivalds, R.: 1-way quantum finite automata: strengths, weaknesses and generalizations. In: FOCS 1998, pp. 332–341 (1998). http://arxiv.org/abs/quant-ph/9802062

  5. Ambainis, A., Nahimovs, N.: Improved constructions of quantum automata. Theoretical Computer Science 410(20), 1916–1922 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ambainis, A., Yakaryılmaz, A.: Automata: from Mathematics to Applications, chapter Automata and quantum computing (in preparation)

    Google Scholar 

  7. Ambainis, A., Yakaryılmaz, A.: Superiority of exact quantum automata for promise problems. Information Processing Letters 112(7), 289–291 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Bertoni, A., Carpentieri, M.: Analogies and differences between quantum and stochastic automata. Theoretical Computer Science 262(1–2), 69–81 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bertoni, A., Mereghetti, C., Palano, B.: Quantum computing: 1-way quantum automata. In: Èsik and Z. Fülöp (eds.): DLT 2003. LNCS, vol. 2710, pp. 1–20. Springer, Heidelberg (2003)

    Google Scholar 

  10. Dwork, C., Stockmeyer, L.: A time complexity gap for two-way probabilistic finite-state automata. SIAM Journal on Computing 19(6), 1011–1123 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  11. Geffert, V., Yakaryılmaz, A.: Classical Automata on Promise Problems. In: Jürgensen, H., Karhumäki, J., Okhotin, A. (eds.) DCFS 2014. LNCS, vol. 8614, pp. 126–137. Springer, Heidelberg (2014)

    Google Scholar 

  12. Golovkins, M., Kravtsev, M., Kravcevs, V.: Quantum Finite Automata and Probabilistic Reversible Automata: R-trivial Idempotent Languages. In: Murlak, F., Sankowski, P. (eds.) MFCS 2011. LNCS, vol. 6907, pp. 351–363. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  13. Gruska, J.: Quantum Computing. McGraw-Hill (1999)

    Google Scholar 

  14. Gruska, J., Qiu, D., Zheng, S.: Generalizations of the distributed Deutsch-Jozsa promise problem. Technical report (2014). arXiv:1402.7254

  15. Gruska, J., Qiu, D., Zheng, S.: Potential of quantum finite automata with exact acceptance. Technical Report (2014). arXiv:1404.1689

  16. Hirvensalo, M.: Quantum automata with open time evolution. International Journal of Natural Computing 1(1), 70–85 (2010)

    Article  Google Scholar 

  17. Klauck, H.: On quantum and probabilistic communication: Las vegas and one-way protocols. In: STOC 2000, pp. 644–651 (2000)

    Google Scholar 

  18. Kondacs, A., Watrous, J.: On the power of quantum finite state automata. In: FOCS 1997, pp. 66–75 (1997)

    Google Scholar 

  19. Li, L., Qiu, D., Zou, X., Li, L., Lihua, W., Mateus, P.: Characterizations of one-way general quantum finite automata. Theoretical Computer Science 419, 73–91 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  20. Moore, C., Crutchfield, J.P.: Quantum automata and quantum grammars. Theoretical Computer Science 237(1–2), 275–306 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  21. Paz, A.: Introduction to Probabilistic Automata. Academic Press, New York (1971)

    MATH  Google Scholar 

  22. Qiu, D., Li, L., Mateus, P., Gruska, J.: Quantum finite automata. Discrete Mathematics and Its Applications. In: Handbook on Finite State based Models and Applications. Chapman and Hall/CRC (2012)

    Google Scholar 

  23. Rabin, M.O.: Probabilistic automata. Information and Control 6, 230–243 (1963)

    Article  MATH  Google Scholar 

  24. Rashid, J., Yakaryılmaz, A.: Implications of Quantum Automata for Contextuality. In: Holzer, M., Kutrib, M. (eds.) CIAA 2014. LNCS, vol. 8587, pp. 318–331. Springer, Heidelberg (2014)

    Google Scholar 

  25. Shur, A.M., Yakaryılmaz, A.: Quantum, Stochastic, and Pseudo Stochastic Languages with Few States. In: Ibarra, O.H., Kari, L., Kopecki, S. (eds.) UCNC 2014. LNCS, vol. 8553, pp. 327–339. Springer, Heidelberg (2014)

    Google Scholar 

  26. Yakaryılmaz, A., Cem Say, A. C.: Languages recognized by nondeterministic quantum finite automata. Quantum Information and Computation 10(9&10), 747–770 (2010)

    Google Scholar 

  27. Yakaryılmaz, A., Cem Say, A.C.: Unbounded-error quantum computation with small space bounds. Information and Computation 279(6), 873–892 (2011)

    Google Scholar 

  28. Zheng, S., Gruska, J., Qiu, D.: On the State Complexity of Semi-quantum Finite Automata. In: Dediu, A.-H., Mart\’ın-Vide, C., Sierra-Rodr\’ıguez, J.-L., Truthe, B. (eds.) LATA 2014. LNCS, vol. 8370, pp. 601–612. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  29. Zheng, S., Qiu, D., Li, L., Gruska, J.: One-Way Finite Automata with Quantum and Classical States. In: Bordihn, H., Kutrib, M., Truthe, B. (eds.) Languages Alive. LNCS, vol. 7300, pp. 273–290. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Engineering, Boğaziçi University, 34342, Bebek, İstanbul, Turkey

    A.C. Cem Say

  2. National Laboratory for Scientific Computing, Petrópolis, RJ, 25651-075, Brazil

    Abuzer Yakaryılmaz

Authors
  1. A.C. Cem Say
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  2. Abuzer Yakaryılmaz
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Correspondence to Abuzer Yakaryılmaz .

Editor information

Editors and Affiliations

  1. Department of Computer Science, The University of Auckland, Auckland, New Zealand

    Cristian S. Calude

  2. University of Latvia, Riga, Latvia

    Rūsiņš Freivalds

  3. School of Informatics, Kyoto University, Kyoto, Japan

    Iwama Kazuo

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Say, A., Yakaryılmaz, A. (2014). Quantum Finite Automata: A Modern Introduction. In: Calude, C., Freivalds, R., Kazuo, I. (eds) Computing with New Resources. Lecture Notes in Computer Science(), vol 8808. Springer, Cham. https://doi.org/10.1007/978-3-319-13350-8_16

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  • DOI: https://doi.org/10.1007/978-3-319-13350-8_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13349-2

  • Online ISBN: 978-3-319-13350-8

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