An Exponential Separation Between Quantum Query Complexity and the Polynomial Degree

While it is known that there is at most a polynomial separation between quantum query complexity and the polynomial degree for total functions, the precise relationship between the two is not clear for partial functions. In this paper, we demonstrate an exponential separation between exact polynomia...

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Bibliographic Details
Published inComputational complexity Vol. 34; no. 2; p. 14
Main Authors Ambainis, Andris, Belovs, Aleksandrs
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2025
Springer Nature B.V
Subjects
Algorithm Analysis and Problem Complexity
Boolean functions
Complexity
Computational Mathematics and Numerical Analysis
Computer Science
Polynomials
Queries
Separation
68Q12
quantum lower bounds
quantum adversary bound
68Q17
query complexity
polynomial method
Online AccessGet full text
ISSN1016-3328
1420-8954
DOI10.1007/s00037-025-00277-4

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Summary:While it is known that there is at most a polynomial separation between quantum query complexity and the polynomial degree for total functions, the precise relationship between the two is not clear for partial functions. In this paper, we demonstrate an exponential separation between exact polynomial degree and approximate quantum query complexity for a partial Boolean function. For an unbounded alphabet size, we have a constant versus polynomial separation.
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content type line 14
ISSN:1016-3328
1420-8954
DOI:10.1007/s00037-025-00277-4