Nonlinear regression based on a hybrid quantum computer

Understand

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.