# Quantum Annealing for Robust Principal Component Analysis

arXiv: https://arxiv.org/abs/2501.10431 · HTML: https://mlsanity.com/paper/2501.10431/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 37 references that are in the map.
- First posted on arXiv 11 Jan 2025.

## Builds on (most cited first, 6 of 6)

- [Support vector machines on the D-Wave quantum annealer](https://mlsanity.com/paper/1906.06283/) (2019)
- [Feature Selection on Quantum Computers](https://mlsanity.com/paper/2203.13261/) (2022)
- [Training and Classification using a Restricted Boltzmann Machine on the D-Wave 2000Q](https://mlsanity.com/paper/2005.03247/) (2020)
- [Optimal Algorithms for L1-subspace Signal Processing](https://mlsanity.com/paper/1405.6785/) (2014)
- [Efficient L1-Norm Principal-Component Analysis via Bit Flipping](https://mlsanity.com/paper/1610.01959/) (2016)
- [Lossy compression of statistical data using quantum annealer](https://mlsanity.com/paper/2110.02142/) (2021)

## Abstract (arXiv)

Principal component analysis is commonly used for dimensionality reduction, feature extraction, denoising, and visualization. The most commonly used principal component analysis method is based upon optimization of the L2-norm, however, the L2-norm is known to exaggerate the contribution of errors and outliers. When optimizing over the L1-norm, the components generated are known to exhibit robustness or resistance to outliers in the data. The L1-norm components can be solved for with a binary optimization problem. Previously, L1-BF has been used to solve the binary optimization for multiple components simultaneously. In this paper we propose QAPCA, a new method for finding principal components using quantum annealing hardware which will optimize over the robust L1-norm. The conditions required for convergence of the annealing problem are discussed. The potential speedup when using quantum annealing is demonstrated through complexity analysis and experimental results. To showcase performance against classical principal component analysis techniques experiments upon synthetic Gaussian data, a fault detection scenario and breast cancer diagnostic data are studied. We find that the reconstruction error when using QAPCA is comparable to that when using L1-BF.