AD-DMKDE is a novel anomaly detection method that combines density matrices (a mathematical formalism from quantum mechanics) and Fourier features. The method can be seen as an efficient approximation of Kernel Density Estimation (KDE) . AD-DMKDE was systematically compared against eleven state-of-the-art anomaly detection methods on a variety of benchmark data sets, showing competitive performance . The method uses optimization in order to find the parameters of data embedding. Its architecture can be easily implemented on GPU/TPU hardware. % . The prediction stage complexity of AD-DMKDE is constant relative to the training data size, in contrast with KDE, and it performs well in data sets with different anomaly rates