Quantum context-aware recommendation systems based on tensor singular value decomposition

Abstract

In this paper, we propose a quantum algorithm for recommendation systems which incorporates the contextual information of users to the personalized recommendation. The preference information of users is encoded in a third-order tensor of dimension N which can be approximated by the truncated tensor singular value decomposition (t-svd) of the subsample tensor. Unlike the classical algorithm that reconstructs the approximated preference tensor using truncated t-svd, our quantum algorithm obtains the recommended product under certain context by measuring the output quantum state corresponding to an approximation of a user’s dynamic preferences. The algorithm achieves the time complexity \(\mathcal {O}(\sqrt{k}N\mathrm{polylog}(N))\), compared to the classical counterpart with complexity \(\mathcal {O}(kN^3)\), where k is the truncated tubal rank.