Learning quantum models for physical and non-physical data

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In this talk I address the problem of simultaneously inferring unknown quantum states and unknown quantum measurements from empirical data. This task goes beyond state tomography because we are not assuming anything about the measurement devices. I am going to talk about the time and sample complexity of the inference of states and measurements, and I am going to talk about the robustness of the minimal Hilbert space dimension. Moreover, I will describe a simple heuristic algorithm (alternating optimization) to fit states and measurements to empirical data. For this algorithm the dataset does not need to be quantum. Hence, the proposed algorithm enables us to interpret general datasets from a quantum perspective. By analyzing movie ratings, we demonstrate the power of quantum models in the context of item recommendation which is a key discipline in machine learning. We observe that quantum models can compete with state-of-the-art algorithms for item recommendation. Based on joint work with Aram Harrow. Relevant preprints: arXiv:1412.7437 and arXiv:1510.02800.