Browsing by Author "Stocklin, Annina"
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- Quantum Principal Component Analysis
Perustieteiden korkeakoulu | Bachelor's thesis(2024-04-26) Stocklin, AnninaPrincipal component analysis (PCA) is a dimension reduction technique that is applied in, for example, signal processing and machine learning. Principal components refer to a small set of linear combinations derived from the original variables, and they capture the maximum variance of all the variables. This method involves approximating the original data table by relying solely on these key components, offering a more concise representation of the dataset. This has important applications in the analysis of large datasets where the parameters have complex relationships to each other. However, PCA becomes non-tractable when the dimension of the data becomes considerably large. Quantum PCA (qPCA) is an approach to tackling this problem. In addition, qPCA should be able to offer a speed up to machine learning problems. qPCA involves creating many copies of a density matrix to apply quantum phase estimation in order to find the eigenvalues and eigenvectors of the matrix. In this thesis, the aim is to determine the extent of current research on qPCA by conducting a state-of-the-art literature review. For this purpose, this thesis first examines the mathematical background of PCA and demonstrates the application of it in data visualization and pattern recognition. Subsequently, it introduces the quantum formulation of PCA and different variations to it. Finally, this thesis examines the current applications and challenges of qPCA and demonstrates how it can be utilized to find eigenvalues and eigenvectors from a covariance matrix.