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Trajectory optimization using quantum computing

Author

Listed:
  • Alok Shukla

    (The University of Oklahoma)

  • Prakash Vedula

    (The University of Oklahoma)

Abstract

We present a framework wherein the trajectory optimization problem (or a problem involving calculus of variations) is formulated as a search problem in a discrete space. A distinctive feature of our work is the treatment of discretization of the optimization problem wherein we discretize not only independent variables (such as time) but also dependent variables. Our discretization scheme enables a reduction in computational cost through selection of coarse-grained states. It further facilitates the solution of the trajectory optimization problem via classical discrete search algorithms including deterministic and stochastic methods for obtaining a global optimum. This framework also allows us to efficiently use quantum computational algorithms for global trajectory optimization. We demonstrate that the discrete search problem can be solved by a variety of techniques including a deterministic exhaustive search in the physical space or the coefficient space, a randomized search algorithm, a quantum search algorithm or by employing a combination of randomized and quantum search algorithms depending on the nature of the problem. We illustrate our methods by solving some canonical problems in trajectory optimization. We also present a comparative study of the performances of different methods in solving our example problems. Finally, we make a case for using quantum search algorithms as they offer a quadratic speed-up in comparison to the traditional non-quantum algorithms.

Suggested Citation

  • Alok Shukla & Prakash Vedula, 2019. "Trajectory optimization using quantum computing," Journal of Global Optimization, Springer, vol. 75(1), pages 199-225, September.
    • Handle: RePEc:spr:jglopt:v:75:y:2019:i:1:d:10.1007_s10898-019-00754-5
    DOI: 10.1007/s10898-019-00754-5
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    References listed on IDEAS

    as
    1. Pedro Lara & Renato Portugal & Carlile Lavor, 2014. "A new hybrid classical-quantum algorithm for continuous global optimization problems," Journal of Global Optimization, Springer, vol. 60(2), pages 317-331, October.
    2. Samuel H. Brooks, 1958. "A Discussion of Random Methods for Seeking Maxima," Operations Research, INFORMS, vol. 6(2), pages 244-251, April.
    3. 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.
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