Quantum tests for the linearity and permutation invariance of Boolean functions

Mark Hillery, Erika Andersson

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


The goal in function property testing is to determine whether a black-box Boolean function has a certain property or is is an element of-far from having that property. The performance of the algorithm is judged by how many calls need to be made to the black box in order to determine, with high probability, which of the two alternatives is the case. Here we present two quantum algorithms, the first to determine whether the function is linear and the second to determine whether it is symmetric (invariant under permutations of the arguments). Both require order is an element of(-2/3) calls to the oracle, which is better than known classical algorithms. In addition, in the case of linearity testing, if the function is linear, the quantum algorithm identifies which linear function it is. The linearity test combines the Bernstein-Vazirani algorithm and amplitude amplification, while the test to determine whether a function is symmetric uses projective measurements and amplitude amplification.

Original languageEnglish
Article number062329
Pages (from-to)-
Number of pages7
JournalPhysical Review A
Issue number6
Publication statusPublished - 28 Dec 2011


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