A parallel quantum eigensolver for quantum machine learning

Eigensolvers have a wide range of applications in machine learning. Quantum eigensolvers have been developed for achieving quantum speedup. Here, we propose a parallel quantum eigensolver (PQE) for solving a set of machine learning problems, which is based on quantum multi-resonant transitions that simultaneously trigger multiple energy transitions in the systems on demand. PQE has a polylogarithmic cost in problem size under certain circumstances and is hardware efficient, such that it is implementable in near-term quantum computers. As a verification, we utilize it to construct a collaborative filtering quantum recommendation system and implement an experiment of the movie recommendation tasks on a nuclear spin quantum processor. As a result, our recommendation system accurately suggests movies to the user that he/she might be interested in. We further demonstrate the applications of PQE in classification and image completion. In the future, our work will shed light on more applications in quantum machine learning.