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A Note About Claw Function with a Small Range

Authors Andris Ambainis, Kaspars Balodis, Jānis Iraids



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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

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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

  1. Scott Aaronson, Nai-Hui Chia, Han-Hsuan Lin, Chunhao Wang, and Ruizhe Zhang. On the Quantum Complexity of Closest Pair and Related Problems. In Shubhangi Saraf, editor, 35th Computational Complexity Conference (CCC 2020), volume 169 of Leibniz International Proceedings in Informatics (LIPIcs), pages 16:1-16:43, Dagstuhl, Germany, 2020. Schloss Dagstuhl-Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.CCC.2020.16.
  2. Scott Aaronson and Yaoyun Shi. Quantum lower bounds for the collision and the element distinctness problems. Journal of the ACM (JACM), 51(4):595-605, 2004. Google Scholar
  3. Andris Ambainis. Polynomial degree and lower bounds in quantum complexity: Collision and element distinctness with small range. Theory of Computing, 1(1):37-46, 2005. Google Scholar
  4. Andris Ambainis. Quantum walk algorithm for element distinctness. SIAM Journal on Computing, 37(1):210-239, 2007. Google Scholar
  5. Daniel J. Bernstein, Stacey Jeffery, Tanja Lange, and Alexander Meurer. Quantum algorithms for the subset-sum problem. In Philippe Gaborit, editor, Post-Quantum Cryptography, pages 16-33, Berlin, Heidelberg, 2013. Springer Berlin Heidelberg. Google Scholar
  6. Gilles Brassard, Peter Høyer, Kassem Kalach, Marc Kaplan, Sophie Laplante, and Louis Salvail. Key establishment à la merkle in a quantum world. Journal of Cryptology, 32(3):601-634, 2019. URL: https://doi.org/10.1007/s00145-019-09317-z.
  7. Harry Buhrman and Ronald de Wolf. Complexity measures and decision tree complexity: a survey. Theoretical Computer Science, 288(1):21-43, 2002. Complexity and Logic. URL: https://doi.org/10.1016/S0304-3975(01)00144-X.
  8. Harry Buhrman, Christoph Dürr, Mark Heiligman, Peter Høyer, Frédéric Magniez, Miklos Santha, and Ronald de Wolf. Quantum algorithms for element distinctness. SIAM Journal on Computing, 34(6):1324-1330, 2005. URL: https://doi.org/10.1137/S0097539702402780.
  9. Andrew M. Childs and Jason M. Eisenberg. Quantum algorithms for subset finding. Quantum Info. Comput., 5(7):593-604, 2005. Google Scholar
  10. Andrew M. Childs, Shelby Kimmel, and Robin Kothari. The quantum query complexity of read-many formulas. In Proceedings of the 20th Annual European Conference on Algorithms, ESA'12, pages 337-348, Berlin, Heidelberg, 2012. Springer-Verlag. URL: https://doi.org/10.1007/978-3-642-33090-2_30.
  11. Fan Chung and Linyuan Lu. Concentration inequalities and martingale inequalities: a survey. Internet Mathematics, 3(1):79-127, 2006. Google Scholar
  12. François Le Gall and Saeed Seddighin. Quantum meets fine-grained complexity: Sublinear time quantum algorithms for string problems, 2020. URL: http://arxiv.org/abs/2010.12122.
  13. Frédéric Magniez, Miklos Santha, and Mario Szegedy. Quantum algorithms for the triangle problem. SIAM Journal on Computing, 37(2):413-424, 2007. URL: https://doi.org/10.1137/050643684.
  14. Ansis Rosmanis. Adversary lower bound for element distinctness with small range, 2014. URL: http://arxiv.org/abs/1401.3826.
  15. Seiichiro Tani. Claw finding algorithms using quantum walk. Theoretical Computer Science, 410(50):5285-5297, 2009. Mathematical Foundations of Computer Science (MFCS 2007). URL: https://doi.org/10.1016/j.tcs.2009.08.030.
  16. Shengyu Zhang. Promised and distributed quantum search. In Lusheng Wang, editor, Computing and Combinatorics, pages 430-439, Berlin, Heidelberg, 2005. Springer Berlin Heidelberg. Google Scholar
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