On the quantum complexity of closest pair and related problems

@article{Aaronson2020OnTQ,
title={On the quantum complexity of closest pair and related problems},
author={S. Aaronson and N. Chia and H. Lin and C. Wang and Ruizhe Zhang},
journal={Proceedings of the 35th Computational Complexity Conference},
year={2020}
}

Proceedings of the 35th Computational Complexity Conference

The closest pair problem is a fundamental problem of computational geometry: given a set of n points in a d-dimensional space, find a pair with the smallest distance. A classical algorithm taught in introductory courses solves this problem in O(n log n) time in constant dimensions (i.e., when d = O(1)). This paper asks and answers the question of the problem's quantum time complexity. Specifically, we give an Õ(n2/3) algorithm in constant dimensions, which is optimal up to a polylogarithmic… CONTINUE READING