2026-07-28T07:32:46Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:14124 2024-03-06T10:53:32Z ddc:004 open_access

Quantum Query Complexity with Matrix-Vector Products Childs, Andrew M. Hung, Shih-Han Li, Tongyang Quantum algorithms quantum query complexity matrix-vector products 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Andrew M. Childs and Shih-Han Hung and Tongyang Li 2021 Is Part Of LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2021.55 urn:nbn:de:0030-drops-141242 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.55 eng https://creativecommons.org/licenses/by/4.0/legalcode