Easy and hard functions for the Boolean hidden shift problem

  title={Easy and hard functions for the Boolean hidden shift problem},
  author={Andrew M. Childs and Robin Kothari and M. Ozols and M. Roetteler},
  • Andrew M. Childs, Robin Kothari, +1 author M. Roetteler
  • Published in TQC 2013
  • Mathematics, Physics, Computer Science
  • We study the quantum query complexity of the Boolean hidden shift problem. Given oracle access to f(x+s) for a known Boolean function f, the task is to determine the n-bit string s. The quantum query complexity of this problem depends strongly on f. We demonstrate that the easiest instances of this problem correspond to bent functions, in the sense that an exact one-query algorithm exists if and only if the function is bent. We partially characterize the hardest instances, which include delta… CONTINUE READING
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