Recent years have seen an incredible interest in the use of parameterized quantum circuits (PQCs) for machine learning tasks. As of yet however, it remains unclear to what extent one can use PQC based algorithms to obtain a meaningful advantage over state-of-the-art classical methods. In this talk I will discuss evidence for and against the use of some specific PQC based algorithms. Specifically, I will first show that the output distributions of local quantum circuits are hard to learn on average, and discuss the implications this has for quantum circuit born machines. Next, I will shift the focus to supervised learning, and discuss the extent to which a widely-used class of PQC based algorithms can be dequantized via classical kernel regression with random Fourier features.
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