Parity decision tree in classical–quantum separations for certain classes of Boolean functions

In this paper, we study the separation between the deterministic (classical) query complexity ( D ) and the exact quantum query complexity ( Q E ) of several Boolean function classes using the parity decision tree method. We first define the query friendly (QF) functions on n variables as the ones w...

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Vydané v:Quantum information processing Ročník 20; číslo 6
Hlavní autori: Mukherjee, Chandra Sekhar, Maitra, Subhamoy
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.06.2021
Springer Nature B.V
Predmet:
Boolean
Boolean algebra
Boolean functions
Codes
Complexity
Data Structures and Information Theory
Decision analysis
Decision trees
Mathematical analysis
Mathematical Physics
Parity
Physics
Physics and Astronomy
Quantum Computing
Quantum Information Technology
Quantum Physics
Queries
Separation
Spintronics
Classical–quantum separation
Boolean functions
Parity decision tree
Query complexity
Bent functions
Query friendly functions
ISSN:1570-0755, 1573-1332
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Shrnutí:In this paper, we study the separation between the deterministic (classical) query complexity ( D ) and the exact quantum query complexity ( Q E ) of several Boolean function classes using the parity decision tree method. We first define the query friendly (QF) functions on n variables as the ones with minimum deterministic query complexity D ( f ). We observe that for each n , there exists a non-separable class of QF functions such that D ( f ) = Q E ( f ) . Further, we show that for some values of n , all the QF functions are non-separable. Then, we present QF functions for certain other values of n where separation can be demonstrated, in particular, Q E ( f ) = D ( f ) - 1 . In a related effort, we also study the Maiorana–McFarland (MM)-type Bent functions. We show that while for any MM Bent function f on n variables D ( f ) = n , separation can be achieved as n 2 ≤ Q E ( f ) ≤ ⌈ 3 n 4 ⌉ . Our results highlight how different classes of Boolean functions can be analyzed for classical–quantum separation exploiting the parity decision tree method.
Bibliografia:ObjectType-Article-1
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ISSN:1570-0755
1573-1332
DOI:10.1007/s11128-021-03158-1