Quantum anomaly detection with density estimation and multivariate Gaussian distribution

Abstract

We study quantum anomaly detection with density estimation and multivariate Gaussian distribution. Both algorithms are constructed using the standard gate-based model of quantum computing. Compared with the corresponding classical algorithms, the resource complexities of our quantum algorithm are logarithmic in the dimensionality of quantum states and the number of training quantum states. We also present a quantum procedure for efficiently estimating the determinant of any Hermitian operators A ∈ R N ×N with time complexity O(poly log N ) which forms an important subroutine in our quantum anomaly detection with multivariate Gaussian distribution. Finally, our results also include the modified quantum kernel principal component analysis (PCA) and the quantum one-class support vector machine (SVM) for detecting classical data.

Quantum algorithms for anomaly detection using amplitude estimation

“…Liang et al's algorithm [33] is reviewed in Appendix A. And we find the mistakes of this algorithm, which mainly derived from the failure of controlled rotation operation in the algorithm to extract classical information.…”

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