Abstract
After the discussion of classical-quantum interfaces, we are now ready to dive into techniques that can bee used to construct quantum machine learning algorithms. As laid out in the introduction, there are two strategies to solve learning task with quantum computers. First, one can try to translate a classical machine learning method into the language of quantum computing. The challenge here is to combine quantum routines in a clever way so that the overall quantum algorithm reproduces the results of the classical model. The second strategy is more exploratory and creates new models that are tailor-made for the working principles of a quantum device. Here, the numerical analysis of the model performance can be much more important than theoretical promises of asymptotic speedups. In the remaining chapters we will look at methods that are useful for both approaches.
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Notes
- 1.
Such an angle encoded qubit has been called a quron [10] in the context of quantum neural networks.
- 2.
Thanks to Gian Giacomo Guerreschi for this simplified presentation.
- 3.
The form of Eq. (6.10) is a so called non-parametric model: The number of (potentially zero) parameters \(\nu _m \) grows with the size M of the training set.
- 4.
In fact, the Hilbert space of some quantum systems can easily be constructed as a reproducing kernel Hilbert space [14].
- 5.
Strictly speaking, according to the definition in Eq. (6.8) a feature map maps an input to a function, and not to a vector. However, a quantum state is also called a wave function, and a more general definition of a feature map is a map from \(\mathcal {X}\) to a general Hilbert space. We can therefore overlook this subtlety here and refer to [14] for more details.
- 6.
In statistical physics, a Gibbs distribution is a state of a system that does not change under the evolution of the system.
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Schuld, M., Petruccione, F. (2018). Quantum Computing for Inference. In: Supervised Learning with Quantum Computers. Quantum Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-96424-9_6
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