Robust polynomials and quantum algorithms

Harry Buhrman; Ilan Newman; Hein Röhrig; Ronald De Wolf

doi:10.1007/978-3-540-31856-9_49

Robust polynomials and quantum algorithms

Harry Buhrman, Ilan Newman, Hein Röhrig, Ronald De Wolf

Department of Computer Science

Research output: Contribution to journal › Conference article › peer-review

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).

Original language	English
Pages (from-to)	593-604
Number of pages	12
Journal	Lecture Notes in Computer Science
Volume	3404
DOIs	https://doi.org/10.1007/978-3-540-31856-9_49
State	Published - 2005
Event	22nd Annual Symposium on Theoretical Aspects of Computer Science, STACS 2005 - Stuttgart, Germany Duration: 24 Feb 2005 → 26 Feb 2005

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1007/978-3-540-31856-9_49

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title = "Robust polynomials and quantum algorithms",

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).",

author = "Harry Buhrman and Ilan Newman and Hein R{\"o}hrig and {De Wolf}, Ronald",

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AU - Röhrig, Hein

AU - De Wolf, Ronald

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AB - 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).

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SN - 0302-9743

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ER -

Robust polynomials and quantum algorithms

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