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Exact Results for Accepting Probabilities of Quantum Automata

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Mathematical Foundations of Computer Science 2001 (MFCS 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2136))

Abstract

One of the properties of Kondacs-Watrous model of quantum finite automata (QFA) is that the probability of the correct answer for a QFA cannot be amplified arbitrarily. In this paper, we determine the maximum probabilities achieved by QFAs for several languages. In particular, we show that any language that is not recognized by an RFA (reversible finite automaton) can be recognized by a QFA with probability at most 0.7726....

Research supported by Berkeley Fellowship for Graduate Studies, Microsoft Research Fellowship and NSF Grant CCR-9800024.

Research supported by Grant No.01.0354 from the Latvian Council of Science and European Commission, contract IST-1999-11234.

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References

  1. Andris Ambainis, Richard Bonner, Rũsiņš Freivalds, Arnolds Ķikusts. Probabilities to accept languages by quantum finite automata. Proceedings of COCOON’99, p. 174–183. Also quant-ph/9904066.

    Google Scholar 

  2. Andris Ambainis, Rũsiņš Freivalds. 1-way quantum finite automata: strengths, weaknesses and generalizations. Proceedings of FOCS’98, p. 332–341. Also quant-ph/9802062.

    Google Scholar 

  3. Andris Ambainis, Arnolds Ķikusts, Mãris Valdats. On the class of languages recognizable by 1-way quantum finite automata. Proceedings of STACS’01, p. 75–86. Also quant-ph/0009004.

    Google Scholar 

  4. Andris Ambainis, John Watrous. Quantum automata with mixed states. In preparation, 2001.

    Google Scholar 

  5. Ethan Bernstein, Umesh Vazirani, Quantum complexity theory. SIAM Journal on Computing, 26:1411–1473, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  6. Alex Brodsky, Nicholas Pippenger. Characterizations of 1-way quantum finite automata. quant-ph/9903014.

    Google Scholar 

  7. M. Pica Ciamarra. Quantum reversibility and a new type of quantum automaton. Proceedings of FCT’01, to appear.

    Google Scholar 

  8. Jozef Gruska. Descriptional complexity issues in quantum computing. Journal of Automata, Languages and Combinatorics, 5:191–218, 2000.

    MATH  MathSciNet  Google Scholar 

  9. Arnolds Ķikusts, Zigmãrs Rasščevskis. On the accepting probabilities of 1-way quantum finite automata. Proceedings of the workshop on Quantum Computing and Learning, 2000, p. 72–79.

    Google Scholar 

  10. J. Kemeny, J. Snell. Finite Markov Chains. Springer-Verlag, 1976.

    Google Scholar 

  11. Arnolds Ķikusts. A small 1-way quantum finite automaton. quant-ph/9810065.

    Google Scholar 

  12. Attila Kondacs and John Watrous. On the power of quantum finite state automata. In Proceedings of FOCS’97, p. 66–75.

    Google Scholar 

  13. C. Moore, J. Crutchfield. Quantum automata and quantum grammars. Theoretical Computer Science, 237:275–306, 2000. Also quant-ph/9707031.

    Article  MATH  MathSciNet  Google Scholar 

  14. Ashwin Nayak. Optimal lower bounds for quantum automata and random access codes. Proceedings of FOCS’99, p. 369–376. Also quant-ph/9904093.

    Google Scholar 

  15. Katrin Paschen. Quantum finite automata using ancilla qubits. University of Karlsruhe technical report.

    Google Scholar 

  16. John Watrous. Relationships between quantum and classical space-bounded complexity classes. Proceedings of Complexity’98, p. 210–227.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Computer Science Division, University of California, Berkeley, CA, 94720, USA

    Andris Ambainis

  2. Institute of Mathematics and Computer Science, University of Latvia, Raīga bulv. 29, Rĩga, Latvia

    Arnolds Ķikusts

Authors
  1. Andris Ambainis
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  2. Arnolds Ķikusts
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Editor information

Editors and Affiliations

  1. Mathematical Institute, AS CR, Žitná 25, 115 67, Praha 1, Czech Republic

    Jiří Sgall

  2. Faculty of Mathematics and Physics Institute for Theoretical Computer Science (ITI), Charles University, Malostranské náměstí 25, 118 00, Praha 1, Czech Republic

    Aleš Pultr  & Petr Kolman  & 

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© 2001 Springer-Verlag Berlin Heidelberg

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Ambainis, A., Ķikusts, A. (2001). Exact Results for Accepting Probabilities of Quantum Automata. In: Sgall, J., Pultr, A., Kolman, P. (eds) Mathematical Foundations of Computer Science 2001. MFCS 2001. Lecture Notes in Computer Science, vol 2136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44683-4_13

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  • DOI: https://doi.org/10.1007/3-540-44683-4_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42496-3

  • Online ISBN: 978-3-540-44683-5

  • eBook Packages: Springer Book Archive

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