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Evolution of a human-competitive quantum fourier transform algorithm using genetic programming

Published: 25 June 2005 Publication History

Abstract

In this paper, we show how genetic programming (GP) can be used to evolve system-size-independent quantum algorithms, and present a human-competitive Quantum Fourier Transform (QFT) algorithm evolved by GP.

References

[1]
H. Barnum, H. J. Bernstein, L. Spector. Quantum circuits for OR and AND of ORs. J. Physics A: Mathematical and General, 33(45):8047--8057, November 2000]]
[2]
H. Barnum, H. J. Bernstein, L, Spector. A quantum circuit for OR. quant-ph/990756]]
[3]
G. Brassard. Teleportation as Quantum Computation. In Proc. 4th Workshop on Physics and Computation, New England Complex Systems Institute 1996. Also as quant-ph/9605035, 1996]]
[4]
D. Deutsch. Quantum Theory, the Church-Turing Thesis, and the Universal Quantum Computer, Proc. Royal Society of London, series A, vol. 400, p97, 1985]]
[5]
N. A. Gershenfeld, I. L. Chuang. Bulk Spin-Resonance Quantum Computing. Science 275, 350--356, January 1997]]
[6]
L. K. Grover. A fast quantum mechanical algorithm for database search. Proc. 28th Ann. ACM Symp. on the Theory of Computing (STOC), 212--219, 1996]]
[7]
A. Leier, W. Banzhaf. Evolving Hogg's Quantum Algorithm Using Linear-Tree GP. GECCO 2003, 390--400. LNCS 2723, Springer, 2003]]
[8]
A. Leier, W. Banzhaf. Exploring the search space of quantum programs. CEC 2003, 170--177. IEEE Press, 2003]]
[9]
A. Leier, W. Banzhaf. Comparison of Selection Strategies for Evolutionary Quantum Circuit Design. GECCO 2004, 557--568. LNCS 3103, Springer, 2004]]
[10]
M. A. Nielsen, I. L. Chuang. Quantum Computation and Quantum Information. CUP, 2000]]
[11]
P. Massey, J. A. Clark, S. Stepney. Evolving Quantum Programs and Circuits through Genetic Programming, GECCO 2004, 569--580. LNCS 3103, Springer, 2004]]
[12]
M. J. Rethinam, A. K. Javali, E.C. Behrman, J.E. Steck, S. R. Skinner. A genetic algorithm for finding pulse sequences for NMR quantum computing. Available as quant-ph/0404170, April 2004]]
[13]
E. Rieffel, W. Polak. An Introduction to Quantum Computing for non-Physicists. Available as quant-ph/9809016, 1998]]
[14]
P. Shor. Algorithms for Quantum Computation : Discrete Logarithms and Factoring, Proc. 35th IEEE Symposium on the Foundations of Computer Science, p124, 1994]]
[15]
P. Shor. Polynomial Time Algorithms for Prime-Factorisation and Discrete Logarithms on a Quantum Computer, SIAM Journal of Computing, 26, p1484, 1997]]
[16]
L. Spector, H. Barnum, H. J. Bernstein, N. Swamy. Genetic Programming for Quantum Computers. In Genetic Programming 1998, 365--374. Morgan Kauffman, 1998]]
[17]
L. Spector, H. Barnum, H. J. Bernstein, N. Swamy. Finding a Better-than-Classical Quantum AND/OR Algorithm using Genetic Programming. CEC 1999, 2239--2246. IEEE, 1999]]
[18]
L. Spector, H. Barnum, H. J Bernstein, N. Swamy. Quantum Computing Applications of Genetic Programming. In L. Spector, W. B. Langdon, U.-M. O'Reilly, P. J. Angeleine, eds, Advances in Genetic Programming 3, chapter 7, pp 135--160. MIT Press, 1999]]
[19]
L. Spector. Automatic Quantum Computer Programming: a genetic programming approach. Kluwer, 2004]]
[20]
L. Spector, H. J. Bernstein. Communication Capacities of some Quantum Gates, discovered in part through Genetic Programming. In Proc. 6th Int. Conf. Quantum Communication, Measurement, and Computing (QCMC), pp. 500--503, 2003]]
[21]
S. Stepney, J. A. Clark. Evolving Quantum Algorithms and Protocols. In M. Rieth, W. Schommers, eds. Handbook of Theoretical and Computational Nanotechnology, American Scientific Publishers, 2005 (in press)]]
[22]
R. Van Meter, K. Binkley. Compiling Quantum programs Using Genetic Algorithms. In The Wild and Crazy Idea Session IV, abstracts, part of 11th Intl. Conf. Architectural Support for Programming Languages and Operating Systems, October 2004]]
[23]
M. Wall. GALib, a C++ Library for Genetic Algorithms, available from http://lancet.mit.edu/ga/]]
[24]
C. P. Williams, A. G. Gray. Automated Design of Quantum Circuits. In Quantum Computing and Communications: First NASA Conference, QCQC'98, 113--125. LNCS 1509, Springer, 1999]]
[25]
T. Yabuki, H. Iba. Genetic algorithms for quantum circuit design - evolving a simpler teleportation circuit. In Late Breaking Papers at GECCO 2000, pp. 425--430, 2000]]

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      cover image ACM Conferences
      GECCO '05: Proceedings of the 7th annual conference on Genetic and evolutionary computation
      June 2005
      2272 pages
      ISBN:1595930108
      DOI:10.1145/1068009
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      Published: 25 June 2005

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      Author Tags

      1. evolutionary computing
      2. genetic algorithms
      3. genetic programming
      4. quantum computing
      5. quantum fourier transform

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