The Polynomial Degree of Recursive Fourier Sampling

  • Benjamin Johnson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6519)

Abstract

We present matching upper and lower bounds for the “weak” polynomial degree of the recursive Fourier sampling problem from quantum complexity theory. The degree bound is h + 1, where h is the order of recursion in the problem’s definition, and this bound is exponentially lower than the bound implied by the existence of a BQP algorithm for the problem. For the upper bound we exhibit a degree-h + 1 real polynomial that represents the problem on its entire domain. For the lower bound, we show that any non-zero polynomial agreeing with the problem, even on just its zero-inputs, must have degree at least h + 1. The lower bound applies to representing polynomials over any Field.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Benjamin Johnson
    • 1
  1. 1.School of InformationUniversity of CaliforniaBerkeleyUSA

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