Robust polynomials and quantum algorithms

Authors:
Harry Buhrman;Ilan Newman;Hein Röhrig;Ronald de Wolf
Affiliations:
,CWI, Amsterdam, the Netherlands;Dept. of Computer Science, Haifa University, Israel;Dept. of Computer Science, University of Calgary, Canada;CWI, Amsterdam, the Netherlands
Venue:
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Year:
2005

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Abstract

We define and study the complexity of robust polynomials for Boolean functions and the related fault-tolerant quantum decision trees, where input bits are perturbed by noise. We show that, in contrast to the classical model of Feige et al., every Boolean function can be computed by O(n) quantum queries even in the model with noise. This implies, for instance, the somewhat surprising result that every Boolean function has robust degree bounded by O(n).