Quantum algorithms for learning the algebraic normal form of quadratic Boolean functions

Quantum algorithms for the analysis of Boolean functions have received a lot of attention over the last few years. The algebraic normal form (ANF) of a linear Boolean function can be recovered by using the Bernstein–Vazirani (BV) algorithm. No research has been carried out on quantum algorithms for...

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Vydáno v:Quantum information processing Ročník 19; číslo 8
Hlavní autoři: Hao, Xuexuan, Zhang, Fengrong, Xia, Shixiong, Zhou, Yong
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.08.2020
Springer Nature B.V
Témata:
Algorithms
Boolean
Boolean algebra
Boolean functions
Canonical forms
Codes
Data Structures and Information Theory
Independent variables
Machine learning
Mathematical analysis
Mathematical Physics
Physics
Physics and Astronomy
Quadratic equations
Quantum Computing
Quantum Information Technology
Quantum Physics
Spintronics
Boolean function
Quantum computation
Bernstein–Vazirani algorithm
Quantum cryptanalysis
ISSN:1570-0755, 1573-1332
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Shrnutí:Quantum algorithms for the analysis of Boolean functions have received a lot of attention over the last few years. The algebraic normal form (ANF) of a linear Boolean function can be recovered by using the Bernstein–Vazirani (BV) algorithm. No research has been carried out on quantum algorithms for learning the ANF of general Boolean functions. In this paper, quantum algorithms for learning the ANF of quadratic Boolean functions are studied. We draw a conclusion about the influences of variables on quadratic functions, so that the BV algorithm can be run on them. We study the functions obtained by inversion and zero-setting of some variables in the quadratic function and show the construction of their quantum oracle. We introduce the concept of “club” to group variables that appear in quadratic terms and study the properties of clubs. Furthermore, we propose a bunch of algorithms for learning the full ANF of quadratic Boolean functions. The most efficient algorithm, among those we propose, provides an O ( n ) speedup over the classical one, and the number of queries is independent of the degenerate variables.
Bibliografie:ObjectType-Article-1
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content type line 14
ISSN:1570-0755
1573-1332
DOI:10.1007/s11128-020-02778-3