  The support vector machine (SVM) is a popular machine learning classification
method which produces a nonlinear decision boundary in a feature space by
constructing linear boundaries in a transformed Hilbert space. It is well known
that these algorithms when executed on a classical computer do not scale well
with the size of the feature space both in terms of data points and
dimensionality. One of the most significant limitations of classical algorithms
using non-linear kernels is that the kernel function has to be evaluated for
all pairs of input feature vectors which themselves may be of substantially
high dimension. This can lead to computationally excessive times during
training and during the prediction process for a new data point. Here, we
propose using both canonical and generalized coherent states to rapidly
calculate specific nonlinear kernel functions. The key link will be the
reproducing kernel Hilbert space (RKHS) property for SVMs that naturally arise
from canonical and generalized coherent states. Specifically, we discuss the
fast evaluation of radial kernels through a positive operator valued measure
(POVM) on a quantum optical system based on canonical coherent states. A
similar procedure may also lead to fast calculations of kernels not usually
used in classical algorithms such as those arising from generalized coherent
states.
