# Study of Feature Importance for Quantum Machine Learning Models

arXiv: https://arxiv.org/abs/2202.11204 · HTML: https://mlsanity.com/paper/2202.11204/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 21 references that are in the map.
- First posted on arXiv 18 Feb 2022.

## Builds on (most cited first, 6 of 6)

- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [All Models are Wrong, but Many are Useful: Learning a Variable's Importance by Studying an Entire Class of Prediction Models Simultaneously](https://mlsanity.com/paper/1801.01489/) (2018)
- [Visualizing the Effects of Predictor Variables in Black Box Supervised Learning Models](https://mlsanity.com/paper/1612.08468/) (2016)
- [q-means: A quantum algorithm for unsupervised machine learning](https://mlsanity.com/paper/1812.03584/) (2018)
- [TED: Teaching AI to Explain its Decisions](https://mlsanity.com/paper/1811.04896/) (2018)
- [Large Scale Diverse Combinatorial Optimization: ESPN Fantasy Football Player Trades](https://mlsanity.com/paper/2111.02859/) (2021)

## Built on by (most cited first, 7 of 7)

- [Quantum Neural Network Classifiers: A Tutorial](https://mlsanity.com/paper/2206.02806/) (2022)
- [Feature Importance and Explainability in Quantum Machine Learning](https://mlsanity.com/paper/2405.08917/) (2024)
- [Quantum Machine Learning Applied to the Classification of Diabetes](https://mlsanity.com/paper/2301.00109/) (2022)
- [Several fitness functions and entanglement gates in quantum kernel generation](https://mlsanity.com/paper/2309.03307/) (2023)
- [A novel feature selection method based on quantum support vector machine](https://mlsanity.com/paper/2311.17646/) (2023)
- [Detecting underdetermination in parameterized quantum circuits](https://mlsanity.com/paper/2504.03315/) (2025)
- [Component Based Quantum Machine Learning Explainability](https://mlsanity.com/paper/2506.12378/) (2025)

## Abstract (arXiv)

Predictor importance is a crucial part of data preprocessing pipelines in classical and quantum machine learning (QML). This work presents the first study of its kind in which feature importance for QML models has been explored and contrasted against their classical machine learning (CML) equivalents. We developed a hybrid quantum-classical architecture where QML models are trained and feature importance values are calculated from classical algorithms on a real-world dataset. This architecture has been implemented on ESPN Fantasy Football data using Qiskit statevector simulators and IBM quantum hardware such as the IBMQ Mumbai and IBMQ Montreal systems. Even though we are in the Noisy Intermediate-Scale Quantum (NISQ) era, the physical quantum computing results are promising. To facilitate current quantum scale, we created a data tiering, model aggregation, and novel validation methods. Notably, the feature importance magnitudes from the quantum models had a much higher variation when contrasted to classical models. We can show that equivalent QML and CML models are complementary through diversity measurements. The diversity between QML and CML demonstrates that both approaches can contribute to a solution in different ways. Within this paper we focus on Quantum Support Vector Classifiers (QSVC), Variational Quantum Circuit (VQC), and their classical counterparts. The ESPN and IBM fantasy football Trade Assistant combines advanced statistical analysis with the natural language processing of Watson Discovery to serve up personalized trade recommendations that are fair. Here, player valuation data of each player has been considered and this work can be extended to calculate the feature importance of other QML models such as Quantum Boltzmann machines.