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

References in corpus (11)

• Quantum Mechanics helps in searching for a needle in a haystack
• Quantum algorithm for solving linear systems of equations
• Quantum support vector machine for big data classification
• Quantum principal component analysis
• Quantum generative adversarial learning
• Prediction by linear regression on a quantum computer
• Quantum machine learning for quantum anomaly detection
• Quantum Discriminant Analysis for Dimensionality Reduction and Classification
• Quantum algorithm and quantum circuit for A-Optimal Projection: dimensionality reduction
• Exact Identification of a Quantum Change Point
• Online optimal exact identification of a quantum change point

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