Abstract
Finding the maximum value of a function in a dynamic model plays an important role in many application settings, including discrete optimization in the presence of hard constraints. We present an iterative quantum algorithm for finding the maximum value of a function in which prior search results update the acceptable response. Our approach is based on quantum search and utilizes a dynamic oracle function to mark items in a specified input set. As a realization of function optimization, we verify the correctness of the algorithm using numerical simulations of quantum circuits for the Knapsack problem. Our simulations make use of an explicit oracle function based on arithmetic operations and a comparator subroutine, and we verify these implementations using numerical simulations up to 30 qubits.
T. S. Humble—This manuscript has been authored by UT-Battelle, LLC, under Contract No. DE-AC0500OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for the United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan.
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Acknowledgments
CM and HC acknowledge support from Total and TSH acknowledges support from the U.S. Department of Energy, Office of Science, Early Career Research Program. Access to the Atos Quantum Learning Machine was provided by the Quantum Computing Institute at Oak Ridge National Laboratory.
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A Pseudo-code for the Knapsack Example
A Pseudo-code for the Knapsack Example
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Moussa, C., Calandra, H., Humble, T.S. (2019). Function Maximization with Dynamic Quantum Search. In: Feld, S., Linnhoff-Popien, C. (eds) Quantum Technology and Optimization Problems. QTOP 2019. Lecture Notes in Computer Science(), vol 11413. Springer, Cham. https://doi.org/10.1007/978-3-030-14082-3_8
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DOI: https://doi.org/10.1007/978-3-030-14082-3_8
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