Corpus ID: 225061978

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

@article{Gall2020QuantumMF,
  title={Quantum Meets Fine-grained Complexity: Sublinear Time Quantum Algorithms for String Problems},
  author={Franccois Le Gall and Saeed Seddighin},
  journal={ArXiv},
  year={2020},
  volume={abs/2010.12122}
}
  • Franccois Le Gall, Saeed Seddighin
  • Published 2020
  • Mathematics, Computer Science, Physics
  • ArXiv
  • 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… CONTINUE READING

    References

    SHOWING 1-10 OF 44 REFERENCES
    The Quantum Strong Exponential-Time Hypothesis
    • 6
    • PDF
    On the quantum complexity of closest pair and related problems
    • 8
    • PDF
    Quantum speed-up of Markov chain based algorithms
    • M. Szegedy
    • Mathematics, Computer Science
    • 45th Annual IEEE Symposium on Foundations of Computer Science
    • 2004
    • 455
    • PDF
    Polynomial Degree and Lower Bounds in Quantum Complexity: Collision and Element Distinctness with Small Range
    • 104
    • PDF
    Quantum Speedups for Exponential-Time Dynamic Programming Algorithms
    • 25
    • PDF
    Quantum algorithms for search with wildcards and combinatorial group testing
    • 9
    • PDF
    Quantum walk algorithm for element distinctness
    • A. Ambainis
    • Mathematics, Physics
    • 45th Annual IEEE Symposium on Foundations of Computer Science
    • 2004
    • 617
    • PDF
    Reconstructing Strings from Substrings with Quantum Queries
    • 7
    • PDF
    Quantum Lower Bound for the Collision Problem with Small Range
    • S. Kutin
    • Computer Science, Mathematics
    • Theory Comput.
    • 2005
    • 71
    • PDF