Quantum Anomaly Detection with Density Estimation and Multivariate Gaussian Distribution

Understand

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 $\mathcal{A}\in\mathcal{R}^{N\times N}$ with time complexity $O(poly\log N)$ which forms an important subroutine in our quantum anomaly detection with multivariate Gaussian distribution.