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Despite years of effort, the quantum machine learning community has only beenable to show quantum learning advantages for certain contrivedcryptography-inspired datasets in the case of classical data. In this note, wediscuss the challenges of finding learning problems that quantum learningalgorithms can learn much faster than any classical learning algorithm, and westudy how to identify such learning problems. Specifically, we reflect on themain concepts in computational learning theory pertaining to this question, andwe discuss how subtle changes in definitions can mean conceptuallysignificantly different tasks, which can either lead to a separation or noseparation at all. Moreover, we study existing learning problems with aprovable quantum speedup to distill sets of more general and sufficientconditions (i.e., ``checklists'') for a learning problem to exhibit aseparation between classical and quantum learners. These checklists areintended to streamline one's approach to proving quantum speedups for learningproblems, or to elucidate bottlenecks. Finally, to illustrate its application,we analyze examples of potential separations (i.e., when the learning problemis build from computational separations, or when the data comes from a quantumexperiment) through the lens of our approach.

On establishing learning separations between classical and quantum machine learning with classical data