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Improved Algorithm and Lower Bound for Variable Time Quantum Search

Authors Andris Ambainis , Martins Kokainis , Jevgēnijs Vihrovs

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ACM Subject Classification
  • Theory of computation → Quantum query complexity
  • Theory of computation → Quantum complexity theory
Keywords
  • quantum search
  • amplitude amplification

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Abstract

We study variable time search, a form of quantum search where queries to different items take different time. Our first result is a new quantum algorithm that performs variable time search with complexity O(√Tlog n) where T = ∑_{i = 1}ⁿ t_i² with t_i denoting the time to check the i^th item. Our second result is a quantum lower bound of Ω(√{Tlog T}). Both the algorithm and the lower bound improve over previously known results by a factor of √{log T} but the algorithm is also substantially simpler than the previously known quantum algorithms.

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Andris Ambainis, Martins Kokainis, and Jevgēnijs Vihrovs. Improved Algorithm and Lower Bound for Variable Time Quantum Search. In 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.TQC.2023.7

Author Details

Andris Ambainis
  • Center for Quantum Computer Science, Faculty of Computing, University of Latvia, Riga, Latvia
Martins Kokainis
  • Center for Quantum Computer Science, Faculty of Computing, University of Latvia, Riga, Latvia
Jevgēnijs Vihrovs
  • Center for Quantum Computer Science, Faculty of Computing, University of Latvia, Riga, Latvia

Funding

This research was supported by the ERDF project 1.1.1.5/18/A/020.

Acknowledgements

We thank Krišjānis Prūsis for useful discussions on the lower bound proof. The authors are grateful to the anonymous referees for the helpful comments and suggestions.

References

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