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Quantum Query Complexity of Multilinear Identity Testing Arvind, Vikraman Mukhopadhyay, Partha Quantum algorithm Identity testing Query complexity Multilinear polynomials Motivated by the quantum algorithm for testing commutativity of black-box groups (Magniez and Nayak, 2007), we study the following problem: Given a black-box finite ring by an additive generating set and a multilinear polynomial over that ring, also accessed as a black-box function (we allow the indeterminates of the polynomial to be commuting or noncommuting), we study the problem of testing if the polynomial is an \emph{identity} for the given ring. We give a quantum algorithm with query complexity sub-linear in the number of generators for the ring, when the number of indeterminates of the input polynomial is small (ideally a constant). Towards a lower bound, we also show a reduction from a version of the collision problem (which is well studied in quantum computation) to a variant of this problem. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Vikraman Arvind and Partha Mukhopadhyay 2009 Is Part Of LIPIcs, Volume 3, 26th International Symposium on Theoretical Aspects of Computer Science (2009) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2009.1801 urn:nbn:de:0030-drops-18014 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1801 eng https://creativecommons.org/licenses/by-nd/3.0/legalcode