# Quantum Splines for Non-Linear Approximations

arXiv: https://arxiv.org/abs/2303.05428 · HTML: https://mlsanity.com/paper/2303.05428/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 17 references that are in the map.
- First posted on arXiv 9 Mar 2023.

## Builds on (most cited first, 2 of 2)

- [Quantum machine learning: a classical perspective](https://mlsanity.com/paper/1707.08561/) (2017)
- [Quantum Neuron: an elementary building block for machine learning on quantum computers](https://mlsanity.com/paper/1711.11240/) (2017)

## Built on by (most cited first, 4 of 4)

- [Quantum computing and artificial intelligence: status and perspectives](https://mlsanity.com/paper/2505.23860/) (2025)
- [MAQA: A Quantum Framework for Supervised Learning](https://mlsanity.com/paper/2303.11028/) (2023)
- [Quantum Supervised Learning](https://mlsanity.com/paper/2407.17161/) (2024)
- [Quantum Artificial Intelligence: A Brief Survey](https://mlsanity.com/paper/2408.10726/) (2024)

## Abstract (arXiv)

Quantum Computing offers a new paradigm for efficient computing and many AI applications could benefit from its potential boost in performance. However, the main limitation is the constraint to linear operations that hampers the representation of complex relationships in data. In this work, we propose an efficient implementation of quantum splines for non-linear approximation. In particular, we first discuss possible parametrisations, and select the most convenient for exploiting the HHL algorithm to obtain the estimates of spline coefficients. Then, we investigate QSpline performance as an evaluation routine for some of the most popular activation functions adopted in ML. Finally, a detailed comparison with classical alternatives to the HHL is also presented.