Abstract
Before coming to the design of quantum machine learning algorithms, this chapter is an interlude to discuss how quantum computing can actually assist machine learning. Although quantum computing researchers often focus on asymptotic computational speedups, there is more than one measure of merit when it comes to machine learning. We will discuss three dimensions here, namely the computational complexity, the sample complexityand the model complexity. While the section on computational complexity allows us to establish the terminology already used in previous chapters with more care, the section on sample complexity ventures briefly into quantum extensions of statistical learning theory. The last section on model complexity provides arguments towards what has been called the exploratory approach to quantum machine learning, in which quantum physics is used as a resource to build new types of models altogether.
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Notes
- 1.
The three dimensions were first introduced by Peter Wittek and Vedran Dunjko.
- 2.
Applying a quantum Fourier transform effectively changes the distribution from which to sample, which leaves some question whether the comparison to a static ‘classical example generator’ is fair. However, they show that while the quantum example oracle can be simulated by a membership query oracle, this is not true vice versa. It seems therefore that the quantum example oracle ranges somewhere between a query and an example oracle.
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Schuld, M., Petruccione, F. (2018). Quantum Advantages. In: Supervised Learning with Quantum Computers. Quantum Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-96424-9_4
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