IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v116y2003i3d10.1023_a1023061218864.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1023061218864
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1023061218864?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Samuel H. Brooks, 1958. "A Discussion of Random Methods for Seeking Maxima," Operations Research, INFORMS, vol. 6(2), pages 244-251, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alok Shukla & Prakash Vedula, 2019. "Trajectory optimization using quantum computing," Journal of Global Optimization, Springer, vol. 75(1), pages 199-225, September.
    2. Benjamin Lev, 2005. "Book Reviews," Interfaces, INFORMS, vol. 35(4), pages 339-345, August.
    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. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Yipeng Liu & Gary Koehler, 2012. "A hybrid method for quantum global optimization," Journal of Global Optimization, Springer, vol. 52(3), pages 607-626, March.
    9. Coelho, Leandro dos Santos, 2008. "A quantum particle swarm optimizer with chaotic mutation operator," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1409-1418.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kyung-Yong Lee & Jung-Sung Park & Yun-Su Kim, 2021. "Optimal Placement of PMU to Enhance Supervised Learning-Based Pseudo-Measurement Modelling Accuracy in Distribution Network," Energies, MDPI, vol. 14(22), pages 1-18, November.
    2. David E. Kaufman & Robert L. Smith, 1998. "Direction Choice for Accelerated Convergence in Hit-and-Run Sampling," Operations Research, INFORMS, vol. 46(1), pages 84-95, February.
    3. Barkema, Alan Dean, 1985. "Farm survival under uncertainty," ISU General Staff Papers 1985010108000017535, Iowa State University, Department of Economics.
    4. E. A. Tsvetkov & R. A. Krymov, 2022. "Pure Random Search with Virtual Extension of Feasible Region," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 575-595, November.
    5. Boehlje, M. D. & Eisgruber, L. M., 1975. "A Decision Model For The Estate Management Problem," ISU General Staff Papers 197508010700001017, Iowa State University, Department of Economics.
    6. Rinnooy Kan, A. H. G. & Timmer, G. T., 1985. "Stochastic Global Optimization Methods Part I: Clustering Methods," Econometric Institute Archives 272329, Erasmus University Rotterdam.
    7. 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.
    8. Taymaz, Erol, 1993. "A Calibration Algorithm for Micro-Simulation Models," Working Paper Series 374, Research Institute of Industrial Economics.
    9. Alok Shukla & Prakash Vedula, 2019. "Trajectory optimization using quantum computing," Journal of Global Optimization, Springer, vol. 75(1), pages 199-225, September.
    10. Giulia Pedrielli & K. Selcuk Candan & Xilun Chen & Logan Mathesen & Alireza Inanalouganji & Jie Xu & Chun-Hung Chen & Loo Hay Lee, 2019. "Generalized Ordinal Learning Framework (GOLF) for Decision Making with Future Simulated Data," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(06), pages 1-35, December.
    11. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:116:y:2003:i:3:d:10.1023_a:1023061218864. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.