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Quantum Simulation

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

arXiv

Authors: François Le Gall, Saeed Seddighin

Year

2020

Paper ID

19710

Status

Preprint

Abstract Read

~2 min

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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 O\(sqrt{n}\) time algorithm for LPS, we prove that LCS needs at least time Ω\(n^2/3\) even for 0/1 strings.

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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.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2010.12122 [2] arXiv https://arxiv.org/abs/2010.12122 [3] Publisher https://arxiv.org/abs/2010.12122

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