  There are schemes for realizing different types of kernels by quantum states
of light. It is particularly interesting to realize the Gaussian kernel due to
its wider applicability. A multimode coherent state can generate the Gaussian
kernel with a constant value of hyperparameter. This constant hyperparameter
has limited the application of the Gaussian kernel when it is applied to
complex learning problems. We realize the variable hyperparameterized Gaussian
kernel with a multimode-displaced squeezed vacuum state. The learning capacity
of this kernel is tested with the support vector machines over some synthesized
data sets as well as public benchmark data sets. We establish that the proposed
variable hyperparameterized Gaussian kernel offers better accuracy over the
constant Gaussian kernel.
