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Encoding classical data into quantum states is considered a quantum feature map to map classical data into a quantum Hilbert space.
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See Supplemental Materials for proofs of Results 1–4, which include Refs. Heitzinger 2002 ; Wouodjié 2014 ; Foupouagnigni and Wouodjié 2020 ; Davis 1975
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This scheme is analogous with the classical extreme learning machine (ELM) framework Huang et al. 2000 ; Huang et al. 2006b . In the ELM, the input data 𝒙 \bm{x} is fed into a single- or multi-layer perceptron where all weights between layers are fixed. The states of hidden nodes at some layers are regarded as basis functions that play a similar role as ψ i ( 𝒙 ) \psi_{i}(\bm{x})
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