Quantum query complexity with matrix-vector products

TitleQuantum query complexity with matrix-vector products
Publication TypeJournal Article
Year of Publication2021
AuthorsChilds, AM, Hung, S-H, Li, T
JournalProceedings of the 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021), Leibniz International Proceedings in Informatics
Date Published3/14/2021

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.