



01245nas a2200157   4500008004100000245005700041210005600098260001400154300001500168490000800183520080000191100002300991700001901014700001701033856003701050       2021                        eng d00aQuantum query complexity with matrix-vector products0 aQuantum query complexity with matrixvector products  c3/14/2021  a55:1-55:190 v1983 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://arxiv.org/abs/2102.11349