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}
}
  • S. Aaronson, N. Chia, +2 authors Ruizhe Zhang
  • Published 2020
  • Mathematics, Computer Science, Physics
  • 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
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