# Obtaining A Linear Combination of the Principal Components of a Matrix on Quantum Computers

arXiv: https://arxiv.org/abs/1512.02109 · HTML: https://mlsanity.com/paper/1512.02109/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Nov 2015.

## Built on by (most cited first, 1 of 1)

- [Dimension reduction with structure-aware quantum circuits for hybrid machine learning](https://mlsanity.com/paper/2508.00048/) (2025)

## Abstract (arXiv)

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, bright], where a and b are real and 0 ≤ a ≤ b ≤ 1. This makes possible to obtain a combination of the eigenvectors associated to the largest eigenvalues and so can be used to do principal component analysis on quantum computers.