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.

在本文中，我们提出了一种用于推荐系统的量子算法，该算法将用户的上下文信息整合到个性化推荐中。用户的偏好信息被编码为维度N的三阶张量，该张量可以通过子样本张量的截短张量奇异值分解（t-svd）近似。与经典的算法使用截断的t-svd重建近似的偏好张量不同，我们的量子算法通过测量与用户动态偏好近似相对应的输出量子状态，在特定上下文中获得推荐乘积。与具有复杂度的经典对应物相比，该算法实现了时间复杂度\（\ mathcal {O}（\ sqrt {k} N \ mathrm {polylog}（N））\）\（\ mathcal {O}（kN ^ 3）\），其中k是截短的输卵管等级。