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Evolving blackbox quantum algorithms using genetic programming

Published online by Cambridge University Press:  12 June 2008

Ralf Stadelhofer ,
Wolfgang Banzhaf  and
Dieter Suter
Ralf Stadelhofer
Affiliation:
Department of Computer Science, University of Dortmund, Dortmund, Germany
Wolfgang Banzhaf
Affiliation:
Department of Computer Science, Memorial University of Newfoundland, St. John's, Canada
Dieter Suter
Affiliation:
Department of Physics, University of Dortmund, Dortmund, Germany
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Abstract

Although it is known that quantum computers can solve certain computational problems exponentially faster than classical computers, only a small number of quantum algorithms have been developed so far. Designing such algorithms is complicated by the rather nonintuitive character of quantum physics. In this paper we present a genetic programming system that uses some new techniques to develop and improve quantum algorithms. We have used this system to develop two formerly unknown quantum algorithms. We also address a potential deficiency of the quantum decision tree model used to prove lower bounds on the query complexity of the parity problem.

Keywords

Genetic ProgrammingQuantum ComputationQuantum Information Processing

Information

Type
Research Article
Information
AI EDAM , Volume 22 , Issue 3 , August 2008 , pp. 285 - 297
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Beals, R., Buhrman, H., Cleve, R., Mosca, M., & de Wolf, R. (2001). Quantum lower bounds by polynomials. Journal of the Association for Computing Machinery 48, 778.CrossRefGoogle Scholar
Bennett, C.H., Bernstein, E., Brassard, G., & Vazirani, U. (1997). Strengths and weaknesses of quantum computing. SIAM Journal on Computing 26(5), 1510–1523.CrossRefGoogle Scholar
Bernstein, E., & Vazirani, U. (1997). Quantum complexity theory. SIAM Journal on Computing 26, 1411.CrossRefGoogle Scholar
Brassard, G., & Høyer, P. (1997). An exact quantum polynomial-time algorithm for Simon's problem. Proc. Fifth Israeli Symp. Theory of Computing and Systems (ISTCS), pp. 12–23.CrossRefGoogle Scholar
Burhman, H., & de Wolf, R. (2002). Complexity measures and decision tree complexity: a survey. Theoretical Computer Science 288, 21.CrossRefGoogle Scholar
Collins, D., Kim, K.W., & Holton, W.C. (1998). Deutsch–Jozsa algorithm as a test of quantum computation. Physical Review A 58, R1633.CrossRefGoogle Scholar
Deutsch, D., & Jozsa, R. (1992). Rapid solution of problems by quantum computation. Proceedings of the Royal Society of London A 439, 553–558.Google Scholar
Farhi, E., Goldstone, J., Gutmann, S., & Sipser, M. (1998). Limit on the speed of quantum computation in determining parity. Physical Review Letters 81, 5442.CrossRefGoogle Scholar
Leier, A., & Banzhaf, W. (2003a). Exploring the search space of quantum programs. Proc. 2003 Congr. Evolutionary Computation, Vol. I, pp. 170–177.CrossRefGoogle Scholar
Leier, A., & Banzhaf, W. (2003b). Evolving Hogg's quantum algorithm using linear-tree GP. Proc. Genetic and Evolutionary Computation Conf. GECCO-03, pp. 390–400.Google Scholar
Lloyd, S. (2000). Quantum search without entanglement. Physical Review A, 61, 010301.CrossRefGoogle Scholar
Massey, P., Clark, J., & Stepney, S. (2004). Evolving quantum circuits and programs through genetic programming. Proc. Genetic and Evolutionary Computation Conf. GECCO-2004.Google Scholar
Nielsen, M., & Chuang, I. (2000). Quantum Computation and Quantum Information. New York: Cambridge University Press.Google Scholar
Rieffel, E., & Polak, W. (2000). An introduction to quantum computing for non-physicists. ACM Computing Surveys 32, 300.CrossRefGoogle Scholar
Shor, P.W. (1994). Algorithms for quantum computation: discrete logarithm and factoring. IEEE Symp. Foundations of Computer Science, pp. 124–134.Google Scholar
Simon, D.R. (1994). On the power of quantum computation. Proc. 35th Annual Symp. Foundations of Computer Science, pp. 116–123.CrossRefGoogle Scholar
Spector, L. (2004). Automatic Quantum Computer Programming: A Genetic Programming Approach. New York: Kluwer Academic.Google Scholar
Spector, L., Barnum, H., Bernstein, H.J., & Swamy, N. (1999). Quantum computing applications of genetic programming. In Advances in Genetic Programming (Spector, L., Langdon, W.B., O'Reilly, U., & Angeline, P.J., Eds.), Vol. 3, p. 135. Cambridge, MA: MIT Press.CrossRefGoogle Scholar
Stadelhofer, R., Suter, D., & Banzhaf, W. (2005). Quantum and classical parallelism in parity algorithms for ensemble quantum computers. Physical Review A 71, 032345.CrossRefGoogle Scholar
Williams, C.P., & Gray, A.G. (1998). Automated design of quantum circuits. Proc. First NASA Int. Conf. Quantum Computing and Quantum Communications (QCQC), pp. 113–125.Google Scholar