Yes it can -- quantum ML is an active area of research for the MS QuArC group and others. (Well, I'm not sure it's an exponential speed up, but it's an area of research.)

eg, https://www.microsoft.com/en-us/research/publication/quantum...

There's a lot of work on this, although no breakthrough applications yet.

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"Quantum Machine Learning"

Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, Seth Lloyd

Recent progress implies that a crossover between machine learning and quantum information processing benefits both fields. Traditional machine learning has dramatically improved the benchmarking and control of experimental quantum computing systems, including adaptive quantum phase estimation and designing quantum computing gates. On the other hand, quantum mechanics offers tantalizing prospects to enhance machine learning, ranging from reduced computational complexity to improved generalization performance. The most notable examples include quantum enhanced algorithms for principal component analysis, quantum support vector machines, and quantum Boltzmann machines. Progress has been rapid, fostered by demonstrations of midsized quantum optimizers which are predicted to soon outperform their classical counterparts. Further, we are witnessing the emergence of a physical theory pinpointing the fundamental and natural limitations of learning. Here we survey the cutting edge of this merger and list several open problems.

https://arxiv.org/abs/1611.09347

Quantum mechanics and machine learning seem to be closely related, such that they can emulate each other efficiently.¹

Both can be represented with very high dimensional vectors, non-commuting observables and linear algebra. I personally suspect there are a lot more similarities but the area of research is still quite young.

[1] one recent example, https://arxiv.org/pdf/1709.06475.pdf