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

arXiv: https://arxiv.org/abs/2010.12122 · HTML: https://mlsanity.com/paper/2010.12122/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2020.

## Built on by (most cited first, 1 of 1)

- [Quantum Algorithm for the Shortest Superstring Problem](https://mlsanity.com/paper/2112.13319/) (2021)

## Abstract (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 an exact tilde O(√n) time algorithm for LPS, we prove that LCS needs at least time tilde Omega(n2/3) even for 0/1 strings.