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Quantum density estimation with density matrices: Application to quantum anomaly detection
Journal article   Open access   Peer reviewed

Quantum density estimation with density matrices: Application to quantum anomaly detection

Diego H. Useche, Oscar A. Bustos-Brinez, Joseph A. Gallego-Mejia and Fabio A. Gonzalez
Physical review. A, v 109(3), 032418
01 Mar 2024
DOI: https://doi.org/10.1103/PhysRevA.109.032418
url
https://arxiv.org/abs/2201.10006View
Submitted Open arXiv.org - Non-exclusive license to distribute

Abstract

Physics, Atomic, Molecular & Chemical Science & Technology Optics Physical Sciences Physics
Density estimation is a central task in statistics and machine learning. This problem aims to determine the underlying probability density function that best aligns with an observed dataset. Some of its applications include statistical inference, unsupervised learning, and anomaly detection. Despite its relevance, few works have explored the application of quantum computing to density estimation. In this article, we present a quantumclassical density-matrix density estimation model, called Q-DEMDE, based on the expected values of density matrices and a quantum embedding called quantum Fourier features. The method uses quantum hardware to build probability distributions of training data via mixed quantum states. As a core subroutine, we propose an algorithm to estimate the expected value of a mixed density matrix from its spectral decomposition on a quantum computer. In addition, we present an application of the method for quantum-classical anomaly detection. We evaluated the density estimation model with quantum random and quantum adaptive Fourier features on different datasets on a quantum simulator and a real quantum computer. An important result of this work is to show that it is possible to perform density estimation and anomaly detection with high performance on present-day quantum computers.

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5 citations in Web of Science
4 citations in Scopus

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Optics
Physics, Atomic, Molecular & Chemical
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