



01323nas a2200145   4500008004100000020002200041245005700063210005600120260008600176520080000262100002301062700001901085700001701104856005601121       2021                        eng d  a978-3-95977-195-500aQuantum Query Complexity with Matrix-Vector Products0 aQuantum Query Complexity with MatrixVector Products  aDagstuhl, GermanybSchloss Dagstuhl – Leibniz-Zentrum für Informatikc2/7/20213 a<p>We study quantum algorithms that learn properties of a matrix using queries that return its action on an input vector. We show that for various problems, including computing the trace, determinant, or rank of a matrix or solving a linear system that it specifies, quantum computers do not provide an asymptotic speedup over classical computation. On the other hand, we show that for some problems, such as computing the parities of rows or columns or deciding if there are two identical rows or columns, quantum computers provide exponential speedup. We demonstrate this by showing equivalence between models that provide matrix-vector products, vector-matrix products, and vector-matrix-vector products, whereas the power of these models can vary significantly for classical computation.</p>1 aChilds, Andrew, M.1 aHung, Shih-Han1 aLi, Tongyang  uhttps://drops.dagstuhl.de/opus/volltexte/2021/14124