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The Power of Parameterised Quantum Circuits
As we have seen in the previous chapters, there is a wide range of QML models based on parameterised quantum circuits. One reason for this is their tolerance to noise  [222], which is important when we work with the NISQ hardware. However, this does not fully explain the popularity of PQCs or why they are considered strong competitors to classical ML models. There must be some fundamental properties of PQCs that make them superior to their classical counterparts. In this chapter, we discuss two such properties: resistance to overfitting and larger expressive power.
Resistance to overfitting is a direct consequence of the fact that a typical PQC – one without mid-circuit measurement – can be represented by a linear unitary operator. Linear models impose strong regularisation, thus preventing overfitting. At the same time, the model remains powerful due to the mapping of the input into the higher-dimensional Hilbert...
