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Quantum Meets Fine-Grained Complexity: Sublinear Time Quantum Algorithms for String Problems

Authors François Le Gall, Saeed Seddighin

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Author Details

François Le Gall
  • Nagoya University, Japan
Saeed Seddighin
  • Toyota Technological Institute at Chicago, IL, USA

Funding

  • Le Gall, François: FLG was supported by the JSPS KAKENHI grants Nos. JP16H01705, JP19H04066, JP20H00579 and JP20H04139, and by the MEXT Quantum Leap Flagship Program (MEXT Q-LEAP) grant No. PMXS0120319794.
  • Seddighin, Saeed: SS was supported by a Google Research Gift.

Acknowledgements

The authors are grateful to Michael Saks and C. Seshadhri for helpful correspondence.

Cite As Get BibTex

François Le Gall and Saeed Seddighin. Quantum Meets Fine-Grained Complexity: Sublinear Time Quantum Algorithms for String Problems. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 97:1-97:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.ITCS.2022.97

Abstract

Longest common substring (LCS), longest palindrome substring (LPS), and Ulam distance (UL) are three fundamental string problems that can be classically solved in near linear time. In this work, we present sublinear time quantum algorithms for these problems along with quantum lower bounds. Our results shed light on a very surprising fact: Although the classic solutions for LCS and LPS are almost identical (via suffix trees), their quantum computational complexities are different. While we give an exact Õ(√n) time algorithm for LPS, we prove that LCS needs at least time ̃ Ω(n^{2/3}) even for 0/1 strings.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Longest common substring
  • Longest palindrome substring
  • Quantum algorithms
  • Sublinear algorithms

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