On the quantum time complexity of divide and conquer
Quantum Physics
2025-12-03 v1 Data Structures and Algorithms
Abstract
We initiate a systematic study of the time complexity of quantum divide and conquer algorithms for classical problems. We establish generic conditions under which search and minimization problems with classical divide and conquer algorithms are amenable to quantum speedup and apply these theorems to an array of problems involving strings, integers, and geometric objects. They include LONGEST DISTINCT SUBSTRING, KLEE'S COVERAGE, several optimization problems on stock transactions, and k-INCREASING SUBSEQUENCE. For most of these results, our quantum time upper bound matches the quantum query lower bound for the problem, up to polylogarithmic factors.
Cite
@article{arxiv.2311.16401,
title = {On the quantum time complexity of divide and conquer},
author = {Jonathan Allcock and Jinge Bao and Aleksandrs Belovs and Troy Lee and Miklos Santha},
journal= {arXiv preprint arXiv:2311.16401},
year = {2025}
}
Comments
48 pages, accepted to QIP 2024