Abstract
Quantum computation is a most challenging project involving research both by physicists and computer scientists. The principles of quantum computation differ from the principles of classical computation very much. When quantum computers become available, the public-key cryptography will change radically. It is no exaggeration to assert that building a quantum computer means building a universal code-breaking machine. Quantum finite automata are expected to appear much sooner. They do not generalize deterministic finite automata. Their capabilities are incomparable.
Research supported by Grant No.96.0282 from the Latvian Council of Science
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Andris Ambainis and Rusin Freivalds, “1-way quantum finite automata: strengths, weaknesses and generalizations”, Proc. 39th FOCS,1998, http://www.lanl.gov/abs/quant-ph/9802062
Andris Ambainis, Ashwin Nayak, Amnon Ta-Shma and Umesh Vazirani, “Dense Quantum Coding and a Lower Bound for 1-way Quantum Automata”, http://www.lanl.gov/abs/quant-ph/9804043
Andris Ambainis, Rūsinš Freivalds and Marek Karpinski, “Multi-tape quantum finite automata”, http://www.lanl.gov/abs/quant-ph/9905026
D. Angluin, “Inference of reversible languages”, Journal of the ACM, 29, 1982, 741–765.
Paul Benioff, “Quantum mechanical Hamiltonian models of Turing machines”, J. Statistical Physics, 29, 1982, 515–546.
Ethan Bernstein and Umesh Vazirani, “Quantum complexity theory”, SIAM Journal on Computing, 26, 1997, 1411–1473.
Daniel Danin, Inevitability of the strange world, Molodaya Gvardiya, Moscow, 1962 (in Russian).
Daniel Danin, Probabilities of the quantum world, Mir Publishers, Moscow, 1983.
David Deutsch, “Quantum theory, the Church-Turing principle and the universal quantum computer”, Proc. Royal Society London, A400, 1989, 96–117.
Rúsins Freivalds, “Fast probabilistic algorithms”, Lecture Notes in Computer Science, 74, 1979, 57–69.
Richard Feynman, “Simulating physics with computers”, International Journal of Theoretical Physics,21, 6/7, 1982, 467–488.
Felix Gantmacher, Theory of matrices. Nauka, Moscow, 1967 (in Russian).
Jozef Gruska, Quantum Computing. World Scientific, Singapore, 1999.
Arnolds Kikusts, “A small 1-way quantum finite automaton”, http://www.lanl.gov/abs/quant-ph/9810065
Attila Kondacs and John Watrous, “On the power of quantum finite state automata”, Proc. 38th FOCS, 1997, 66–75.
K. de Leeuw, E.F. Moore, C.E. Shannon and N. Shapiro, “Computability by probabilistic machines”,Automata Studies, C.E. Shannon and J. McCarthy, Eds., Princeton University Press, Princeton, NJ, 1955, 183–212.
Yuri I. Manin, The provable and not provable, Sovetskoye Radio, Moscow, 1979, (in Russian).
Yuri I. Manin, The computable and not computable, Sovetskoye Radio, Moscow, 1980, (in Russian).
Cristopher Moore, James P. Crutchfield, “Quantum automata and quantum grammars”, Manuscript available at http://www.lanl.gov/abs/quant-ph/9707031
Max Planck, “Über eine Verbesserung der Wien’schen Spectralgleichung”, Verhandlungen der deutschen physikalischen Gesellschaft 2 1900, S. 202.
Jean-Eric Pin, “On reversible automata”, Lecture Notes in Computer Science, 583, 401–415.
R. P. Poplayskiy, “Thermodynamical models of information processes”, Uspekhi Fizicheskikh Nauk, 115, No. 3, 1975, 465–501 (in Russian).
Michael Rabin, “Probabilistic automata”, Information and Control, 6, 1963, 230–245.
Peter W. Shor, “Algorithms for quantum computation: discrete logarithms and factoring”, Proc. 35th FOCS, 1994, 124–134.
Daniel R. Simon, “On the power of Quantum Computation”, Proc. 35th FOCS, 1994, 116–123.
Andrew Chi-Chill Yao, “Quantum circuit complexity”, Proc. 34th FOCS, 1993, 352–361.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media New York
About this chapter
Cite this chapter
Freivalds, R. (2000). Quantum Computers and Quantum Automata. In: Althöfer, I., et al. Numbers, Information and Complexity. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6048-4_44
Download citation
DOI: https://doi.org/10.1007/978-1-4757-6048-4_44
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4967-7
Online ISBN: 978-1-4757-6048-4
eBook Packages: Springer Book Archive