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A Note About Claw Function with a Small Range

Authors Andris Ambainis, Kaspars Balodis, Jānis Iraids

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Author Details

Andris Ambainis
  • Center for Quantum Computer Science, Faculty of Computing, University of Latvia, Riga, Latvia
Kaspars Balodis
  • Center for Quantum Computer Science, Faculty of Computing, University of Latvia, Riga, Latvia
Jānis Iraids
  • Center for Quantum Computer Science, Faculty of Computing, University of Latvia, Riga, Latvia

Funding

Supported by the project "Quantum algorithms: from complexity theory to experiment" funded under ERDF programme 1.1.1.5.

Cite AsGet BibTex

Andris Ambainis, Kaspars Balodis, and Jānis Iraids. A Note About Claw Function with a Small Range. In 16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 197, pp. 6:1-6:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.TQC.2021.6

Abstract

In the claw detection problem we are given two functions f:D → R and g:D → R (|D| = n, |R| = k), and we have to determine if there is exist x,y ∈ D such that f(x) = g(y). We show that the quantum query complexity of this problem is between Ω(n^{1/2}k^{1/6}) and O(n^{1/2+ε}k^{1/4}) when 2 ≤ k < n.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum query complexity
Keywords
  • collision
  • claw
  • quantum query complexity

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References

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