# On the explainability of quantum neural networks based on variational quantum circuits

arXiv: https://arxiv.org/abs/2301.05549 · HTML: https://mlsanity.com/paper/2301.05549/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 38 references that are in the map.
- First posted on arXiv 12 Jan 2023.

## Builds on (most cited first, 10 of 10)

- [Explaining Explanations: An Overview of Interpretability of Machine Learning](https://mlsanity.com/paper/1806.00069/) (2018)
- [A Survey on Explainable Artificial Intelligence (XAI): Towards Medical XAI](https://mlsanity.com/paper/1907.07374/) (2019)
- [The Kolmogorov-Arnold representation theorem revisited](https://mlsanity.com/paper/2007.15884/) (2020)
- [Universal Approximation Property of Quantum Machine Learning Models in Quantum-Enhanced Feature Spaces](https://mlsanity.com/paper/2009.00298/) (2020)
- [Explainable Neural Networks based on Additive Index Models](https://mlsanity.com/paper/1806.01933/) (2018)
- [Quantum Neural Networks: Concepts, Applications, and Challenges](https://mlsanity.com/paper/2108.01468/) (2021)
- [Fock State-enhanced Expressivity of Quantum Machine Learning Models](https://mlsanity.com/paper/2107.05224/) (2021)
- [A Leap among Quantum Computing and Quantum Neural Networks: A Survey](https://mlsanity.com/paper/2107.03313/) (2021)
- [A Simple Quantum Neural Net with a Periodic Activation Function](https://mlsanity.com/paper/1804.07633/) (2018)
- [Minimax Lower Bounds for Ridge Combinations Including Neural Nets](https://mlsanity.com/paper/1702.02828/) (2017)

## Abstract (arXiv)

Ridge functions are used to describe and study the lower bound of the approximation done by the neural networks which can be written as a linear combination of activation functions. If the activation functions are also ridge functions, these networks are called explainable neural networks. In this brief paper, we first show that quantum neural networks which are based on variational quantum circuits can be written as a linear combination of ridge functions by following matrix notations. Consequently, we show that the interpretability and explainability of such quantum neural networks can be directly considered and studied as an approximation with the linear combination of ridge functions.