# Quantum-Inspired Classical Algorithms for Singular Value Transformation

arXiv: https://arxiv.org/abs/1910.05699 · HTML: https://mlsanity.com/paper/1910.05699/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Oct 2019.

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

- [Quantum-Inspired Machine Learning: a Survey](https://mlsanity.com/paper/2308.11269/) (2023)
- [Robust Dequantization of the Quantum Singular value Transformation and Quantum Machine Learning Algorithms](https://mlsanity.com/paper/2304.04932/) (2023)
- [A Quantum-Inspired Dequantization Method for Diagonally Weighted Matrix Functions: Application to Learning with Optimized Random Features](https://mlsanity.com/paper/2609.10729/) (2026)

## Abstract (arXiv)

A recent breakthrough by Tang (STOC 2019) showed how to "dequantize" the quantum algorithm for recommendation systems by Kerenidis and Prakash (ITCS 2017). The resulting algorithm, classical but "quantum-inspired", efficiently computes a low-rank approximation of the users' preference matrix. Subsequent works have shown how to construct efficient quantum-inspired algorithms for approximating the pseudo-inverse of a low-rank matrix as well, which can be used to (approximately) solve low-rank linear systems of equations. In the present paper, we pursue this line of research and develop quantum-inspired algorithms for a large class of matrix transformations that are defined via the singular value decomposition of the matrix. In particular, we obtain classical algorithms with complexity polynomially related (in most parameters) to the complexity of the best quantum algorithms for singular value transformation recently developed by Chakraborty, Gily'en and Jeffery (ICALP 2019) and Gily'en, Su, Low and Wiebe (STOC19).