# Efficient Parameter Optimisation for Quantum Kernel Alignment: A Sub-sampling Approach in Variational Training

arXiv: https://arxiv.org/abs/2401.02879 · HTML: https://mlsanity.com/paper/2401.02879/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 39 references that are in the map.
- First posted on arXiv 5 Jan 2024.

## Builds on (most cited first, 17 of 17)

- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [The Inductive Bias of Quantum Kernels](https://mlsanity.com/paper/2106.03747/) (2021)
- [Exponential concentration in quantum kernel methods](https://mlsanity.com/paper/2208.11060/) (2022)
- [Training Quantum Embedding Kernels on Near-Term Quantum Computers](https://mlsanity.com/paper/2105.02276/) (2021)
- [Hierarchical Graph Representations in Digital Pathology](https://mlsanity.com/paper/2102.11057/) (2021)
- [A Survey on Graph-Based Deep Learning for Computational Histopathology](https://mlsanity.com/paper/2107.00272/) (2021)
- [Scalable Kernel Methods via Doubly Stochastic Gradients](https://mlsanity.com/paper/1407.5599/) (2014)
- [Bandwidth Enables Generalization in Quantum Kernel Models](https://mlsanity.com/paper/2206.06686/) (2022)
- [Importance of Kernel Bandwidth in Quantum Machine Learning](https://mlsanity.com/paper/2111.05451/) (2021)
- [The complexity of quantum support vector machines](https://mlsanity.com/paper/2203.00031/) (2022)
- [Quantum Machine Learning Framework for Virtual Screening in Drug Discovery: a Prospective Quantum Advantage](https://mlsanity.com/paper/2204.04017/) (2022)
- [Quantum tangent kernel](https://mlsanity.com/paper/2111.02951/) (2021)
- [Quantum Kernel Alignment with Stochastic Gradient Descent](https://mlsanity.com/paper/2304.09899/) (2023)

## Built on by (most cited first, 6 of 6)

- [Qiskit Machine Learning: an open-source library for quantum machine learning tasks at scale on quantum hardware and classical simulators](https://mlsanity.com/paper/2505.17756/) (2025)
- [AQKA: Active Quantum Kernel Acquisition Under a Shot Budget](https://mlsanity.com/paper/2605.14672/) (2026)
- [Quantum Kernel Methods: Convergence Theory, Separation Bounds and Applications to Marketing Analytics](https://mlsanity.com/paper/2510.11744/) (2025)
- [Domain-Aware Quantum Circuit for QML](https://mlsanity.com/paper/2512.17800/) (2025)
- [Spectral Phase Encoding for Quantum Kernel Methods](https://mlsanity.com/paper/2602.19644/) (2026)
- [A Multiclass Quantum Aligned Centroid Kernel](https://mlsanity.com/paper/2607.19782/) (2026)

## Abstract (arXiv)

Quantum machine learning with quantum kernels for classification problems is a growing area of research. Recently, quantum kernel alignment techniques that parameterise the kernel have been developed, allowing the kernel to be trained and therefore aligned with a specific dataset. While quantum kernel alignment is a promising technique, it has been hampered by considerable training costs because the full kernel matrix must be constructed at every training iteration. Addressing this challenge, we introduce a novel method that seeks to balance efficiency and performance. We present a sub-sampling training approach that uses a subset of the kernel matrix at each training step, thereby reducing the overall computational cost of the training. In this work, we apply the sub-sampling method to synthetic datasets and a real-world breast cancer dataset and demonstrate considerable reductions in the number of circuits required to train the quantum kernel while maintaining classification accuracy.