English

Speed from Repetition

Quantum Physics 2015-03-17 v2

Abstract

We present an oracle problem, which we call the Repeated Randomness problem, that a quantum algorithm can solve in one query, while any classical algorithm requires Ω(logn)\Omega(\log n) queries, where the oracle function has 2n2^n inputs. This problem has connections to the parity problem introduced by Bernstein and Vazirani \cite{Bernstein1993} and to a variation of the NAND tree described by Zhan et al \cite{Zhan}.

Keywords

Cite

@article{arxiv.1101.0798,
  title  = {Speed from Repetition},
  author = {Shelby Kimmel},
  journal= {arXiv preprint arXiv:1101.0798},
  year   = {2015}
}

Comments

This paper has been withdrawn because it has been subsumed by arXiv:1101.0797 (Quantum Adversary (Upper) Bound)

R2 v1 2026-06-21T17:07:28.526Z