Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry

Abstract We derive symmetric and antisymmetric kernels by symmetrizing antisymmetrizing conventional analyze their properties. In particular, we compute the feature space dimensions of resulting polynomial kernels, prove that reproducing kernel Hilbert spaces induced Gaussian are dense in functions, propose a Slater determinant representation kernel, which allows for an efficient evaluation even if state is high-dimensional. Furthermore, show exploiting symmetries or antisymmetries size training data set can be significantly reduced. The results illustrated with guiding examples simple quantum physics chemistry applications.