This paper presents a novel anomaly detection method, called AD-DMKDE, based on the use of Kernel Density Estimation (KDE) along with density matrices (a powerful mathematical formalism from quantum mechanics) and Fourier features. The proposed method was systematically compared with eleven state-of-the-art anomaly detection methods on various data sets is presented, and AD-DMKDE shows competitive performance. The method uses neural-network optimization to find the parameters of data embedding, and the prediction phase complexity of the proposed algorithm is constant relative to the training data size.