Testing Boolean Functions Properties
Zhengwei Xie, Daowen Qiu, Guangya Cai, Jozef Gruska, Paulo Mateus

TL;DR
This paper explores quantum algorithms for testing properties of Boolean functions, such as identity, correlation, and balancedness, demonstrating quantum advantages over classical methods and establishing optimal query complexities.
Contribution
It introduces new quantum algorithms for property testing of Boolean functions, proving their optimality and comparing them with classical complexities.
Findings
Quantum algorithms achieve lower query complexity than classical methods.
Optimality of the proposed quantum algorithms is established.
Quantum approaches outperform classical algorithms in property testing tasks.
Abstract
The goal in the area of functions property testing is to determine whether a given black-box Boolean function has a particular given property or is -far from having that property. We investigate here several types of properties testing for Boolean functions (identity, correlations and balancedness) using the Deutsch-Jozsa algorithm (for the Deutsch-Jozsa (D-J) problem) and also the amplitude amplification technique. At first, we study here a particular testing problem: namely whether a given Boolean function , of variables, is identical with a given function or is -far from , where is the parameter. We present a one-sided error quantum algorithm to deal with this problem that has the query complexity . Moreover, we show that our quantum algorithm is optimal. Afterwards we show that the classical…
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Complexity and Algorithms in Graphs · Machine Learning and Algorithms
