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Quantum Search Algorithms

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Gems of Theoretical Computer Science

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Abstract

Widespread interest in quantum computation was sparked by an algorithm of P. Shor for factoring integers on a quantum computer. We investigate here a more recent quantum algorithm of L. Grover for searching a database. This algorithm demonstrates a proven speed-up against the best possible classical algorithm for the same task.

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References

  • P. Benioff: The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines, Journal of Statistical Physics 22 (1980), 563–591.

    Article  MathSciNet  Google Scholar 

  • E. Bernstein, U. Vazirani: Quantum Complexity Theory, Proceedings of the 25th Annual Symposium on Theory of Computing, ACM, 1993,11-20.

    Google Scholar 

  • D. Deutsch: Quantum Theory, the Church-Turing principle and the universal quantum computer, Proceedings of the Royal Society London Series A 400 (1985), 96–117.

    Article  MathSciNet  Google Scholar 

  • R.P. Feynman: Simulating physics with computers, International Journal of Theoretical Physics 21:6/7 (1981/82), 467–488.

    Article  MathSciNet  Google Scholar 

  • D. Deutsch, R. Jozsa: Rapid solutions of problems by quantum computation, Proceedings of the Royal Society of London, 1992, 553-558.

    Google Scholar 

  • D. Simon: On the power of Quantum Computation, SIAM Journal on Computing, 26:5 (1997), 1474–1483.

    Article  MATH  Google Scholar 

  • E. Biham, O. Biham, D. Biron, M. Grassl, D. Lidar: Exact solution of Grover’s quantum search algorithm for arbitrary initial amplitude distribution, LANL preprint quant-ph/9807027.

    Google Scholar 

  • M. Boyer, G. Brassard, P. H0yer, A. Tapp: Tight bounds on quantum searching, Proceedings of 4th Workshop on Physics and Computation, 1996, 36-43. Final version to appear in Fortschritte der Physik. Also LANL preprint quant-ph/9605034.

    Google Scholar 

  • G. Brassard, P. H0yer, A. Tapp: Quantum Counting, LANL preprint quant-ph/9805082.

    Google Scholar 

  • L. Grover: A fast quantum mechanical algorithm for database search, Proceedings of the 28th Annual Symposium on Theory of Computing, ACM, 1996, 212. Also LANL preprint quant-ph/9605043.

    Google Scholar 

  • L. Grover: A framework for quantum mechanical algorithms, Proceedings of the 30th Annual Symposium on Theory of Computing, ACM, 1998. Also LANL preprint quant-ph/9711043.

    Google Scholar 

  • P. Shor: Algorithms for quantum computation: Discrete log and factoring, Proceedings of the 35th Symposium on Foundations of Computer Science, IEEE, 1994, 124-134.

    Google Scholar 

  • A. Ekert, R. Jozsa: Quantum computation and Shor’s factoring algorithm, Reviews of Modern Physics 68 (1996), 733–753.

    Article  MathSciNet  Google Scholar 

  • P. Shor: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM Journal on Computing 26:5 (1997), 1484–1509. Also LANL preprint quant-ph/9508027.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • C. Bennett, E. Bernstein, G. Brassard, U. Vazirani: Strengths and weaknesses of quantum computing, SIAM Journal on Computing 26:5 (1997), 1510–1523.

    Article  MathSciNet  MATH  Google Scholar 

  • S. Fenner, F. Green, S. Homer, R. Pruim: Quantum NP is hard for PH, to appear in Proceedings of the 6th Italian Conference on Theoretical Computer Science, 1998.

    Google Scholar 

  • L. Fortnow, J. Rogers: Complexity limitations on quantum computation, Proceedings of the 13th IEEE Conference on Computational Complexity, IEEE, 1998, 202-209.

    Google Scholar 

  • J. Watrous: Relationships between quantum and classical space-bounded complexity classes, Proceedings of the 13th IEEE Conference on Computational Complexity, IEEE, 1998, 210-227.

    Google Scholar 

  • A. Berthiaume: Quantum Computation, chapter 2 in Complexity Retrospective II, Springer, 1997.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Abt. Theoretische Informatik, Universität Ulm, D-89069, Ulm, Germany

    Uwe Schöning

  2. Dept. of Mathematics and Statistics, Calvin College, Grand Rapids, MI, 49546, USA

    Randall Pruim

Authors
  1. Uwe Schöning
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  2. Randall Pruim
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© 1998 Springer-Verlag Berlin Heidelberg

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Schöning, U., Pruim, R. (1998). Quantum Search Algorithms. In: Gems of Theoretical Computer Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60322-8_27

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  • DOI: https://doi.org/10.1007/978-3-642-60322-8_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64352-1

  • Online ISBN: 978-3-642-60322-8

  • eBook Packages: Springer Book Archive

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