文章基本信息

标题：Quantum Recommendation Systems
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作者：Iordanis Kerenidis ; Anupam Prakash
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2017
卷号：67
页码：49:1-49:21
DOI：10.4230/LIPIcs.ITCS.2017.49
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：Recommendation systems; quantum machine learning; singular value estimation; matrix sampling; quantum algorithms.