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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| Published in | Computational complexity Vol. 34; no. 2; p. 14 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
01.12.2025
Springer Nature B.V |
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| Online Access | Get full text |
| ISSN | 1016-3328 1420-8954 |
| DOI | 10.1007/s00037-025-00277-4 |
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| Abstract | 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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| AbstractList | 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. |
| ArticleNumber | 14 |
| Author | Belovs, Aleksandrs Ambainis, Andris |
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| SubjectTerms | Algorithm Analysis and Problem Complexity Boolean functions Complexity Computational Mathematics and Numerical Analysis Computer Science Polynomials Queries Separation |
| Title | An Exponential Separation Between Quantum Query Complexity and the Polynomial Degree |
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