Gaussian Kernel in Quantum Paradigm

Gaussian kernel is a very popular kernel function used in many machine learning algorithms, especially in support vector machines (SVM). For nonlinear training instances in machine learning, it often outperforms polynomial kernels in model accuracy. The Gaussian kernel is heavily used in formulating nonlinear classical SVM. A very elegant quantum version of least square support vector machine which is exponentially faster than the classical counterparts was discussed in literature with quantum polynomial kernel. In this paper, we have demonstrated a quantum version of the Gaussian kernel and analyzed its complexity, which is O(\epsilon^(-1)logN) with N-dimensional instances and an accuracy \epsilon. The Gaussian kernel is not only more efficient than polynomial kernel but also has broader application range than polynomial kernel.