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Evolving blackbox quantum algorithms using genetic programming

  • Ralf Stadelhofer (a1), Wolfgang Banzhaf (a2) and Dieter Suter (a3)

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.

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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.
Bennett, C.H., Bernstein, E., Brassard, G., & Vazirani, U. (1997). Strengths and weaknesses of quantum computing. SIAM Journal on Computing 26(5), 15101523.
Bernstein, E., & Vazirani, U. (1997). Quantum complexity theory. SIAM Journal on Computing 26, 1411.
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. 1223.
Burhman, H., & de Wolf, R. (2002). Complexity measures and decision tree complexity: a survey. Theoretical Computer Science 288, 21.
Collins, D., Kim, K.W., & Holton, W.C. (1998). Deutsch–Jozsa algorithm as a test of quantum computation. Physical Review A 58, R1633.
Deutsch, D., & Jozsa, R. (1992). Rapid solution of problems by quantum computation. Proceedings of the Royal Society of London A 439, 553558.
Farhi, E., Goldstone, J., Gutmann, S., & Sipser, M. (1998). Limit on the speed of quantum computation in determining parity. Physical Review Letters 81, 5442.
Leier, A., & Banzhaf, W. (2003a). Exploring the search space of quantum programs. Proc. 2003 Congr. Evolutionary Computation, Vol. I, pp. 170177.
Leier, A., & Banzhaf, W. (2003b). Evolving Hogg's quantum algorithm using linear-tree GP. Proc. Genetic and Evolutionary Computation Conf. GECCO-03, pp. 390400.
Lloyd, S. (2000). Quantum search without entanglement. Physical Review A, 61, 010301.
Massey, P., Clark, J., & Stepney, S. (2004). Evolving quantum circuits and programs through genetic programming. Proc. Genetic and Evolutionary Computation Conf. GECCO-2004.
Nielsen, M., & Chuang, I. (2000). Quantum Computation and Quantum Information. New York: Cambridge University Press.
Rieffel, E., & Polak, W. (2000). An introduction to quantum computing for non-physicists. ACM Computing Surveys 32, 300.
Shor, P.W. (1994). Algorithms for quantum computation: discrete logarithm and factoring. IEEE Symp. Foundations of Computer Science, pp. 124134.
Simon, D.R. (1994). On the power of quantum computation. Proc. 35th Annual Symp. Foundations of Computer Science, pp. 116123.
Spector, L. (2004). Automatic Quantum Computer Programming: A Genetic Programming Approach. New York: Kluwer Academic.
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.
Stadelhofer, R., Suter, D., & Banzhaf, W. (2005). Quantum and classical parallelism in parity algorithms for ensemble quantum computers. Physical Review A 71, 032345.
Williams, C.P., & Gray, A.G. (1998). Automated design of quantum circuits. Proc. First NASA Int. Conf. Quantum Computing and Quantum Communications (QCQC), pp. 113125.
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  • ISSN: 0890-0604
  • EISSN: 1469-1760
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