Nonlinear regression based on a hybrid quantum computer
This work addresses the challenge of learning complex input-output mappings in quantum machine learning, offering a novel hybrid quantum computing approach that could enhance efficiency in this domain.
The authors tackled the problem of incorporating nonlinearity into quantum machine learning by proposing quantum algorithms for nonlinear regression using feature maps to load classical data into quantum states, achieving exponentially faster processing relative to the number of samples.
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.