I have recently started my journey in quantum machine learning and am having difficulty visualizing how nonlinearity is achieved in the VQC forward pass, as it does in the classical neural networks. Although I have been looking at recent papers, it is still not clear to me. To break it down further, I know this can be achieved, but what types of qubit gates (and in which part in the circuit should it) be used in order to do so?
Welcome to the forum! A demo that may be useful for understanding how non-linearity is achieved is this one. Quantum models as Fourier series — PennyLane documentation Note that quantum models are generally non-linear, and mostly sinusoidal! Therefore, with simple quantum circuit we already have access to functions expressed as finite sums of sines and cosines. This even happens with simple 1-qubit rotation gates, but we will have access to more frequencies and amplitudes if we add more complicated gates (e.g 2-qubit gates). See this paper for more details!
One thing to note here is that quantum circuits (and also classical ML models) may only model certain classes of functions. But quantum and classical models address different families of functions in general! Check Chapter 5 of Maria Schuld and Francesco Petruccione’s “Machine Learning with Quantum Computers” for an extended discussion on this.