Quantum Recommendation Systems

TL;DR

This paper introduces a quantum algorithm for recommendation systems that efficiently samples from an approximate preference matrix in polylogarithmic time, significantly outperforming classical methods in speed.

Contribution

It presents the first quantum algorithm for recommendation systems that operates in polylogarithmic time relative to matrix dimensions, enabling faster personalized recommendations.

Findings

Quantum algorithm runs in polylogarithmic time in matrix size

Efficient quantum projection onto matrix row space

First quantum machine learning application for recommendation systems

Abstract

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.