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

Creemers, Stefan;Pérez Armas, Luis Fernando
(2025) Philosophical transactions. Series A, Mathematical, physical, and engineering sciences — (2025)

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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.
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Creemers, S., & Pérez Armas, L. F. (2025). Limitations of Quantum Counting, Nested Quantum Search, and Amplitude Amplification and Their Potential to Solve Discrete Optimization Problems. Philosophical transactions. Series A, Mathematical, physical, and engineering sciences. Accepted/in-press. (Original work published 2025)