Variational quantum recommendation system with embedded latent vectors

As digital content expands, the need to deliver recommendations quickly becomes increasingly important. In traditional recommendation methods the online recommendation time scales linearly with the number of items, making such approaches less effective as datasets grow. Quantum computing offers novel techniques for parallel computation and sampling, yet current hardware remains constrained by noise and limited scalability. Variational quantum algorithms (VQAs), which rely on shallow circuits, are better suited for noisy quantum machines. In this work, we explore a scheme for variational quantum recommendation system (VQRS), which combines classical matrix factorization (MF) and data re-uploading in the offline phase with quantum sampling in the online phase, aiming to accelerate inference. Using noiseless simulations on small-size standard datasets, we assess the method's performance and analyze its computational resource requirements. Our findings indicate that the scheme is capable of learning accurate recommendations on small datasets, but faces scalability challenges and may requires long offline training. Nonetheless, the results show that the proposed quantum circuit design supports the inference of user preferences, and that a relatively small number of online circuit executions suffices to yield moderately accurate predictions. This highlights a trade-off between inference time and accuracy, which may be of interest in applications where online speed is prioritized over precision.