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Obtaining a linear combination of the principal components of a matrix on quantum computers

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Abstract

Principal component analysis is a multivariate statistical method frequently used in science and engineering to reduce the dimension of a problem or extract the most significant features from a dataset. In this paper, using a similar notion to the quantum counting, we show how to apply the amplitude amplification together with the phase estimation algorithm to an operator in order to procure the eigenvectors of the operator associated to the eigenvalues defined in the range \(\left[ a, b\right] \), where a and b are real and \(0 \le a \le b \le 1\). This makes possible to obtain a combination of the eigenvectors associated with the largest eigenvalues and so can be used to do principal component analysis on quantum computers.

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Acknowledgments

This work is supported by TUBITAK under the project number 115E747.

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  1. Department of Computer Engineering, Istanbul Medeniyet University, Kadikoy, Istanbul, Turkey

    Ammar Daskin

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  1. Ammar Daskin
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Correspondence to Ammar Daskin.

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Daskin, A. Obtaining a linear combination of the principal components of a matrix on quantum computers. Quantum Inf Process 15, 4013–4027 (2016). https://doi.org/10.1007/s11128-016-1388-7

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  • DOI: https://doi.org/10.1007/s11128-016-1388-7

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