2026-07-22T01:29:22Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:8154 2024-03-06T10:39:22Z ddc:004 open_access

Quantum Recommendation Systems Kerenidis, Iordanis Prakash, Anupam Recommendation systems quantum machine learning singular value estimation matrix sampling quantum algorithms. A recommendation system uses the past purchases or ratings of n products by a group of m users, in order to provide personalized recommendations to individual users. The information is modeled as an m \times n preference matrix which is assumed to have a good rank-k approximation, for a small constant k. In this work, we present a quantum algorithm for recommendation systems that has running time O(\text{poly}(k)\text{polylog}(mn)). All known classical algorithms for recommendation systems that work through reconstructing an approximation of the preference matrix run in time polynomial in the matrix dimension. Our algorithm provides good recommendations by sampling efficiently from an approximation of the preference matrix, without reconstructing the entire matrix. For this, we design an efficient quantum procedure to project a given vector onto the row space of a given matrix. This is the first algorithm for recommendation systems that runs in time polylogarithmic in the dimensions of the matrix and provides an example of a quantum machine learning algorithm for a real world application. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Iordanis Kerenidis and Anupam Prakash 2017 Is Part Of LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ITCS.2017.49 urn:nbn:de:0030-drops-81541 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.49 eng https://creativecommons.org/licenses/by/3.0/legalcode