  Incorporating nonlinearity into quantum machine learning is essential for
learning a complicated input-output mapping. We here propose quantum algorithms
for nonlinear regression, where nonlinearity is introduced with feature maps
when loading classical data into quantum states. Our implementation is based on
a hybrid quantum computer, exploiting both discrete and continuous variables,
for their capacity to encode novel features and efficiency of processing
information. We propose encoding schemes that can realize well-known polynomial
and Gaussian kernel ridge regressions, with exponentially speed-up regarding to
the number of samples.
