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Quantum Approximate k-Minimum Finding

Authors Minbo Gao , Zhengfeng Ji , Qisheng Wang

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ACM Subject Classification
  • Theory of computation → Quantum query complexity
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Quantum Computing
  • Quantum Algorithms
  • Quantum Minimum Finding

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Abstract

Quantum k-minimum finding is a fundamental subroutine with numerous applications in combinatorial problems and machine learning. Previous approaches typically assume oracle access to exact function values, making it challenging to integrate this subroutine with other quantum algorithms. In this paper, we propose an (almost) optimal quantum k-minimum finding algorithm that works with approximate values for all k ≥ 1, extending a result  of van Apeldoorn, Gilyén, Gribling, and de Wolf (FOCS 2017) for k = 1. As practical applications, we present efficient quantum algorithms for identifying the k smallest expectation values among multiple observables and for determining the k lowest ground state energies of a Hamiltonian with a known eigenbasis.

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Minbo Gao, Zhengfeng Ji, and Qisheng Wang. Quantum Approximate k-Minimum Finding. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 51:1-51:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ESA.2025.51

Author Details

Minbo Gao
  • Key Laboratory of System Software (Chinese Academy of Sciences) and State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China
  • University of Chinese Academy of Sciences, Beijing, China
Zhengfeng Ji
  • Department of Computer Science and Technology, Tsinghua University, Beijing, China
Qisheng Wang
  • School of Informatics, University of Edinburgh, UK

Funding

MG and ZJ were supported by National Key Research and Development Program of China (Grant No. 2023YFA1009403).
  • Ji, Zhengfeng: ZJ was supported by National Natural Science Foundation of China (Grant No. 12347104 and No. 61832015), Beijing Natural Science Foundation (Grant No. Z220002), and a startup funding from Tsinghua University.
  • Wang, Qisheng: QW was supported by the Engineering and Physical Sciences Research Council under Grant EP/X026167/1.

Acknowledgements

The authors thank Mingsheng Ying and François Le Gall for helpful suggestions and discussions. Minbo Gao would like to thank François Le Gall for supporting his visit to Nagoya University where part of the work was completed.

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