English

An Exponential Separation Between Quantum Query Complexity and the Polynomial Degree

Quantum Physics 2023-05-12 v2

Abstract

While it is known that there is at most a polynomial separation between quantum query complexity and the polynomial degree for total functions, the precise relationship between the two is not clear for partial functions. In this paper, we demonstrate an exponential separation between exact polynomial degree and approximate quantum query complexity for a partial Boolean function. For an unbounded alphabet size, we have a constant versus polynomial separation.

Cite

@article{arxiv.2301.09218,
  title  = {An Exponential Separation Between Quantum Query Complexity and the Polynomial Degree},
  author = {Andris Ambainis and Aleksandrs Belovs},
  journal= {arXiv preprint arXiv:2301.09218},
  year   = {2023}
}

Comments

13 pages, minimal changes with v1

R2 v1 2026-06-28T08:17:27.479Z