Discrete optimization: Limitations of existing quantum algorithms

37 Pages Posted: 2 Aug 2023 Last revised: 11 Dec 2023

See all articles by Stefan Creemers

Stefan Creemers

Catholic University of Lille - IESEG School of Management; KU Leuven

Luis Fernando Pérez Armas

Catholic University of Lille - IÉSEG School of Management, Lille Campus

Date Written: July 31, 2023

Abstract

We investigate the limitations of existing quantum algorithms to solve discrete optimization problems. First, we discuss the quantum counting algorithm of Brassard et al. (1998), and show that it has performance that is equivalent to that of a brute-force approach when approximating the number of valid solutions. In addition, we show that a straightforward application of Grover's algorithm (referred to as GUM by Creemers and Pérez (2023b)) dominates any quantum counting algorithm when verifying whether a valid solution exists. Next, we discuss the nested quantum search algorithm of Cerf et al. (2000), and show that it is dominated by a classical nested search that uses an approach such as GUM to find (partial) solutions to (nested) problems. Last but not least, we also discuss amplitude amplification (a procedure that generalizes Grover's algorithm), and show (once more) that it may not be possible to outperform GUM.

Keywords: Quantum, computing, algorithm, counting, nested, amplification

Suggested Citation

Creemers, Stefan and Pérez Armas, Luis Fernando, Discrete optimization: Limitations of existing quantum algorithms (July 31, 2023). Available at SSRN: https://ssrn.com/abstract=4527268 or http://dx.doi.org/10.2139/ssrn.4527268

Stefan Creemers (Contact Author)

Catholic University of Lille - IESEG School of Management ( email )

3 Rue de la Digue
Lille, 59000
France

KU Leuven ( email )

Oude Markt 13
Leuven, Vlaams-Brabant 3000
Belgium

Luis Fernando Pérez Armas

Catholic University of Lille - IÉSEG School of Management, Lille Campus ( email )

3 rue de la Digue
Lille, 59000
France

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