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Limitations of Quantum Counting, Nested Quantum Search, and Amplitude Amplification and Their Potential to Solve Discrete Optimization Problems

Author

Listed:
  • Creemers, Stefan

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

  • Pérez Armas, Luis Fernando

Abstract

Severalquantumalgorithmshavebeenproposedforsolving discrete optimization problems. In this paper, we focus on the quantum counting algorithm of Brassard et al. (1998), the nested quantum search algorithm of Cerf et al. (2000), and amplitude amplification. We discuss potential limitationsofthesequantumalgorithmsandinvestigatehow they can be used to solve discrete optimization problems. Our goal is to provide a set of practical guidelines that can help researchers to effectively implement Grover-based quantum algorithms.

Suggested Citation

  • Creemers, Stefan & Pérez Armas, Luis Fernando, 2025. "Limitations of Quantum Counting, Nested Quantum Search, and Amplitude Amplification and Their Potential to Solve Discrete Optimization Problems," LIDAM Reprints CORE 3338, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:3338
    Note: In: Philosophical Transactions A, 2025
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