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Implementing Pure Adaptive Search with Grover's Quantum Algorithm

Author

Listed:
  • D. Bulger

    (Massey University)

  • W. P. Baritompa

    (University of Canterbury)

  • G. R. Wood

    (Massey University)

Abstract

Pure adaptive search (PAS) is an idealized stochastic algorithm for unconstrained global optimization. The number of PAS iterations required to solve a problem increases only linearly in the domain dimension. However, each iteration requires the generation of a random domain point uniformly distributed in the current improving region. If no regularity conditions are known to hold for the objective function, then this task requires a number of classical function evaluations varying inversely with the proportion of the domain constituted by the improving region, entirely counteracting the PAS apparent speedup. The Grover quantum computational search algorithm provides a way to generate the PAS iterates. We show that the resulting implementation, which we call the Grover adaptive search (GAS), realizes PAS for functions satisfying certain conditions, and we believe that, when quantum computers will be available, GAS will be a practical algorithm.

Suggested Citation

  • D. Bulger & W. P. Baritompa & G. R. Wood, 2003. "Implementing Pure Adaptive Search with Grover's Quantum Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 116(3), pages 517-529, March.
    • Handle: RePEc:spr:joptap:v:116:y:2003:i:3:d:10.1023_a:1023061218864
    DOI: 10.1023/A:1023061218864
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    References listed on IDEAS

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    1. Samuel H. Brooks, 1958. "A Discussion of Random Methods for Seeking Maxima," Operations Research, INFORMS, vol. 6(2), pages 244-251, April.
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    Cited by:

    1. G. R. Wood & D. W. Bulger & W. P. Baritompa & D. L. J. Alexander, 2006. "Backtracking Adaptive Search: Distribution of Number of Iterations to Convergence," Journal of Optimization Theory and Applications, Springer, vol. 128(3), pages 547-562, March.
    2. Alok Shukla & Prakash Vedula, 2019. "Trajectory optimization using quantum computing," Journal of Global Optimization, Springer, vol. 75(1), pages 199-225, September.
    3. D. W. Bulger, 2007. "Combining a Local Search and Grover’s Algorithm in Black-Box Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 289-301, June.
    4. Benjamin Lev, 2005. "Book Reviews," Interfaces, INFORMS, vol. 35(4), pages 339-345, August.
    5. Dylan Herman & Cody Googin & Xiaoyuan Liu & Alexey Galda & Ilya Safro & Yue Sun & Marco Pistoia & Yuri Alexeev, 2022. "A Survey of Quantum Computing for Finance," Papers 2201.02773, arXiv.org, revised Jun 2022.
    6. Coelho, Leandro dos Santos, 2008. "A quantum particle swarm optimizer with chaotic mutation operator," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1409-1418.
    7. Yipeng Liu & Gary Koehler, 2012. "A hybrid method for quantum global optimization," Journal of Global Optimization, Springer, vol. 52(3), pages 607-626, March.
    8. Liu, Yipeng & Koehler, Gary J., 2010. "Using modifications to Grover's Search algorithm for quantum global optimization," European Journal of Operational Research, Elsevier, vol. 207(2), pages 620-632, December.
    9. Zheng Peng & Donghua Wu & Wenxing Zhu, 2016. "The robust constant and its applications in random global search for unconstrained global optimization," Journal of Global Optimization, Springer, vol. 64(3), pages 469-482, March.

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