# Quantum-inspired algorithms in practice

arXiv: https://arxiv.org/abs/1905.10415 · HTML: https://mlsanity.com/paper/1905.10415/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2019.

## Built on by (most cited first, 18 of 18)

- [Information-theoretic bounds on quantum advantage in machine learning](https://mlsanity.com/paper/2101.02464/) (2021)
- [projUNN: efficient method for training deep networks with unitary matrices](https://mlsanity.com/paper/2203.05483/) (2022)
- [An Invitation to Distributed Quantum Neural Networks](https://mlsanity.com/paper/2211.07056/) (2022)
- [Quantum-Inspired Machine Learning: a Survey](https://mlsanity.com/paper/2308.11269/) (2023)
- [Are Quantum Computers Practical Yet? A Case for Feature Selection in Recommender Systems using Tensor Networks](https://mlsanity.com/paper/2205.04490/) (2022)
- [Quantum algorithms for SVD-based data representation and analysis](https://mlsanity.com/paper/2104.08987/) (2021)
- [Quantum Machine Learning For Classical Data](https://mlsanity.com/paper/2105.03684/) (2021)
- [Covariance matrix preparation for quantum principal component analysis](https://mlsanity.com/paper/2204.03495/) (2022)
- [Photonic Quantum Computers](https://mlsanity.com/paper/2409.08229/) (2024)
- [Scalable Community Detection Using Quantum Hamiltonian Descent and QUBO Formulation](https://mlsanity.com/paper/2411.14696/) (2024)
- [Advances in Machine Learning: Where Can Quantum Techniques Help?](https://mlsanity.com/paper/2507.08379/) (2025)
- [Spectral Geometry and Bosonic-Bloch Probes: Explorations in Quantum Learning](https://mlsanity.com/paper/2607.00063/) (2026)
- [Fast Extraction of Word Embedding from Q-contexts](https://mlsanity.com/paper/2109.07084/) (2021)
- [Quantum Semi-Supervised Kernel Learning](https://mlsanity.com/paper/2204.10700/) (2022)
- [Quantum-Inspired Machine Learning for Molecular Docking](https://mlsanity.com/paper/2401.12999/) (2024)
- [A Framework for Quantum Finite-State Languages with Density Mapping](https://mlsanity.com/paper/2407.02776/) (2024)
- [Boosting Classification with Quantum-Inspired Augmentations](https://mlsanity.com/paper/2506.22241/) (2025)
- [Mutable Low-Rank Sketches for Retrain-Free Recommendation](https://mlsanity.com/paper/2607.15242/) (2026)

## Abstract (arXiv)

We study the practical performance of quantum-inspired algorithms for recommendation systems and linear systems of equations. These algorithms were shown to have an exponential asymptotic speedup compared to previously known classical methods for problems involving low-rank matrices, but with complexity bounds that exhibit a hefty polynomial overhead compared to quantum algorithms. This raised the question of whether these methods were actually useful in practice. We conduct a theoretical analysis aimed at identifying their computational bottlenecks, then implement and benchmark the algorithms on a variety of problems, including applications to portfolio optimization and movie recommendations. On the one hand, our analysis reveals that the performance of these algorithms is better than the theoretical complexity bounds would suggest. On the other hand, their performance as seen in our implementation degrades noticeably as the rank and condition number of the input matrix are increased. Overall, our results indicate that quantum-inspired algorithms can perform well in practice provided that stringent conditions are met: low rank, low condition number, and very large dimension of the input matrix. By contrast, practical datasets are often sparse and high-rank, precisely the type that can be handled by quantum algorithms.