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

Obtaining a linear combination of the principal components of a matrix on quantum computers 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 $$\left[ a, b\right]$$ a , b , where a and b are real and $$0 \le a \le b \le 1$$ 0 ≤ a ≤ b ≤ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

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

Quantum Information Processing, Volume 15 (10) – Jul 19, 2016
15 pages

/lp/springer_journal/obtaining-a-linear-combination-of-the-principal-components-of-a-matrix-U9h61M2rQj
Publisher
Springer Journals
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-016-1388-7
Publisher site
See Article on Publisher Site

### 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 $$\left[ a, b\right]$$ a , b , where a and b are real and $$0 \le a \le b \le 1$$ 0 ≤ a ≤ b ≤ 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.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Jul 19, 2016

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