12.2 Quantum Kernel Method
Wang, Du, Luo, and Ta [323] have shown a close correspondence between classical and quantum kernels. The feature map ϕ(⋅) coincides with the preparation of a quantum state via a parameterised quantum circuit U(⋅), which maps the input data sample into a high-dimensional Hilbert space described by n qubits:
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The kernel function then coincides with applying measurements on the prepared quantum states:
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and allows for more expressive models in comparison with the alternative
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Huang et al. [152] argued that even though the kernel function (12.2) seems to be more natural, the quantum kernel (12.2) can learn arbitrarily deep quantum neural networks (deep PQC). This is a strong result, especially in combination with the hierarchy of expressive power of parameterised quantum circuits (Chapter 13, Equation (10)).
Havlíček et al. [137] described...
