# Quantum algorithms for SVD-based data representation and analysis

arXiv: https://arxiv.org/abs/2104.08987 · HTML: https://mlsanity.com/paper/2104.08987/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 64 references that are in the map.
- First posted on arXiv 19 Apr 2021.

## Builds on (most cited first, 21 of 21)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Entanglement Induced Barren Plateaus](https://mlsanity.com/paper/2010.15968/) (2020)
- [Quantum Recommendation Systems](https://mlsanity.com/paper/1603.08675/) (2016)
- [q-means: A quantum algorithm for unsupervised machine learning](https://mlsanity.com/paper/1812.03584/) (2018)
- [Sampling-based sublinear low-rank matrix arithmetic framework for dequantizing quantum machine learning](https://mlsanity.com/paper/1910.06151/) (2019)
- [The power of block-encoded matrix powers: improved regression techniques via faster Hamiltonian simulation](https://mlsanity.com/paper/1804.01973/) (2018)
- [Quantum-inspired algorithms in practice](https://mlsanity.com/paper/1905.10415/) (2019)
- [A Quantum Interior Point Method for LPs and SDPs](https://mlsanity.com/paper/1808.09266/) (2018)
- [Quantum algorithms for feedforward neural networks](https://mlsanity.com/paper/1812.03089/) (2018)
- [Variational Quantum Singular Value Decomposition](https://mlsanity.com/paper/2006.02336/) (2020)
- [Quantum Expectation-Maximization for Gaussian Mixture Models](https://mlsanity.com/paper/1908.06657/) (2019)
- [Quantum Algorithms for Portfolio Optimization](https://mlsanity.com/paper/1908.08040/) (2019)
- [Towards quantum advantage via topological data analysis](https://mlsanity.com/paper/2005.02607/) (2020)
- [Quantum-Inspired Algorithms from Randomized Numerical Linear Algebra](https://mlsanity.com/paper/2011.04125/) (2020)
- [Correspondence Analysis Using Neural Networks](https://mlsanity.com/paper/1902.07828/) (2019)
- [Privacy with Estimation Guarantees](https://mlsanity.com/paper/1710.00447/) (2017)
- [Quantum Algorithm for Linear Regression](https://mlsanity.com/paper/1402.0660/) (2014)
- [Quantum Latent Semantic Analysis](https://mlsanity.com/paper/1903.03082/) (2019)
- [Quantum-inspired canonical correlation analysis for exponentially large dimensional data](https://mlsanity.com/paper/1907.03236/) (2019)

## Built on by (most cited first, 3 of 3)

- [Evaluating the Potential of Quantum Machine Learning in Cybersecurity: A Case-Study on PCA-based Intrusion Detection Systems](https://mlsanity.com/paper/2502.11173/) (2025)
- [Quantum Algorithms for Projection-Free Sparse Convex Optimization](https://mlsanity.com/paper/2507.08543/) (2025)
- [Quantum Sparse Recovery and Quantum Orthogonal Matching Pursuit](https://mlsanity.com/paper/2510.06925/) (2025)

## Abstract (arXiv)

This paper narrows the gap between previous literature on quantum linear algebra and practical data analysis on a quantum computer, formalizing quantum procedures that speed-up the solution of eigenproblems for data representations in machine learning. The power and practical use of these subroutines is shown through new quantum algorithms, sublinear in the input matrix's size, for principal component analysis, correspondence analysis, and latent semantic analysis. We provide a theoretical analysis of the run-time and prove tight bounds on the randomized algorithms' error. We run experiments on multiple datasets, simulating PCA's dimensionality reduction for image classification with the novel routines. The results show that the run-time parameters that do not depend on the input's size are reasonable and that the error on the computed model is small, allowing for competitive classification performances.