# A kernel-based quantum random forest for improved classification

arXiv: https://arxiv.org/abs/2210.02355 · HTML: https://mlsanity.com/paper/2210.02355/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 69 references that are in the map.
- First posted on arXiv 5 Oct 2022.

## Builds on (most cited first, 16 of 16)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [The Inductive Bias of Quantum Kernels](https://mlsanity.com/paper/2106.03747/) (2021)
- [Towards understanding the power of quantum kernels in the NISQ era](https://mlsanity.com/paper/2103.16774/) (2021)
- [Quantum support vector machine for big data classification](https://mlsanity.com/paper/1307.0471/) (2013)
- [Importance of Kernel Bandwidth in Quantum Machine Learning](https://mlsanity.com/paper/2111.05451/) (2021)
- [Pseudo-dimension of quantum circuits](https://mlsanity.com/paper/2002.01490/) (2020)
- [Universal expressiveness of variational quantum classifiers and quantum kernels for support vector machines](https://mlsanity.com/paper/2207.05865/) (2022)
- [Quantum ensembles of quantum classifiers](https://mlsanity.com/paper/1704.02146/) (2017)
- [The Quantum Version of Prediction for Binary Classification Problem by Ensemble Methods](https://mlsanity.com/paper/2112.13346/) (2021)

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

- [Benchmarking Adversarially Robust Quantum Machine Learning at Scale](https://mlsanity.com/paper/2211.12681/) (2022)
- [Generalization Error Bound for Quantum Machine Learning in NISQ Era -- A Survey](https://mlsanity.com/paper/2409.07626/) (2024)
- [AQKA: Active Quantum Kernel Acquisition Under a Shot Budget](https://mlsanity.com/paper/2605.14672/) (2026)
- [Adapting Quantum Machine Learning for Energy Dissociation of Bonds](https://mlsanity.com/paper/2510.06563/) (2025)
- [Comparative Analysis of Quantum and Classical Support Vector Classifiers for Software Bug Prediction: An Exploratory Study](https://mlsanity.com/paper/2501.04690/) (2025)
- [A Quantum Bagging Algorithm with Unsupervised Base Learners for Label Corrupted Datasets](https://mlsanity.com/paper/2509.07040/) (2025)
- [Quantum Random Forest for the Regression Problem](https://mlsanity.com/paper/2603.22790/) (2026)

## Abstract (arXiv)

The emergence of Quantum Machine Learning (QML) to enhance traditional classical learning methods has seen various limitations to its realisation. There is therefore an imperative to develop quantum models with unique model hypotheses to attain expressional and computational advantage. In this work we extend the linear quantum support vector machine (QSVM) with kernel function computed through quantum kernel estimation (QKE), to form a decision tree classifier constructed from a decision directed acyclic graph of QSVM nodes - the ensemble of which we term the quantum random forest (QRF). To limit overfitting, we further extend the model to employ a low-rank Nystr"om approximation to the kernel matrix. We provide generalisation error bounds on the model and theoretical guarantees to limit errors due to finite sampling on the Nystr"om-QKE strategy. In doing so, we show that we can achieve lower sampling complexity when compared to QKE. We numerically illustrate the effect of varying model hyperparameters and finally demonstrate that the QRF is able obtain superior performance over QSVMs, while also requiring fewer kernel estimations.