# Quantum Kernel Alignment with Stochastic Gradient Descent

arXiv: https://arxiv.org/abs/2304.09899 · HTML: https://mlsanity.com/paper/2304.09899/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 28 references that are in the map.
- First posted on arXiv 19 Apr 2023.

## Builds on (most cited first, 12 of 12)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (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)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Entanglement Induced Barren Plateaus](https://mlsanity.com/paper/2010.15968/) (2020)
- [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)
- [Exploiting symmetry in variational quantum machine learning](https://mlsanity.com/paper/2205.06217/) (2022)
- [The complexity of quantum support vector machines](https://mlsanity.com/paper/2203.00031/) (2022)

## Built on by (most cited first, 14 of 14)

- [Let Quantum Neural Networks Choose Their Own Frequencies](https://mlsanity.com/paper/2309.03279/) (2023)
- [Quantum Machine Learning on Near-Term Quantum Devices: Current State of Supervised and Unsupervised Techniques for Real-World Applications](https://mlsanity.com/paper/2307.00908/) (2023)
- [Neural auto-designer for enhanced quantum kernels](https://mlsanity.com/paper/2401.11098/) (2024)
- [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)
- [Efficient Parameter Optimisation for Quantum Kernel Alignment: A Sub-sampling Approach in Variational Training](https://mlsanity.com/paper/2401.02879/) (2024)
- [QUACK: Quantum Aligned Centroid Kernel](https://mlsanity.com/paper/2405.00304/) (2024)
- [Learning to Classify Quantum Phases of Matter with a Few Measurements](https://mlsanity.com/paper/2409.05188/) (2024)
- [Algorithms for the Training of Neural Support Vector Machines](https://mlsanity.com/paper/2308.07204/) (2023)
- [Position: Quantum Kernel Machines Should Move Beyond Scalar-Valued Kernels to Realize Their Potential](https://mlsanity.com/paper/2506.03779/) (2025)
- [On Neural Quantum Support Vector Machines](https://mlsanity.com/paper/2308.08467/) (2023)
- [Predicting Open-Hole Laminates Failure Using Support Vector Machines With Classical and Quantum Kernels](https://mlsanity.com/paper/2405.02903/) (2024)
- [Quantum feature encoding optimization](https://mlsanity.com/paper/2512.02422/) (2025)
- [Generative Quantum Data Embeddings for Supervised Learning](https://mlsanity.com/paper/2605.30866/) (2026)
- [A Multiclass Quantum Aligned Centroid Kernel](https://mlsanity.com/paper/2607.19782/) (2026)

## Abstract (arXiv)

Quantum support vector machines have the potential to achieve a quantum speedup for solving certain machine learning problems. The key challenge for doing so is finding good quantum kernels for a given data set -- a task called kernel alignment. In this paper we study this problem using the Pegasos algorithm, which is an algorithm that uses stochastic gradient descent to solve the support vector machine optimization problem. We extend Pegasos to the quantum case and and demonstrate its effectiveness for kernel alignment. Unlike previous work which performs kernel alignment by training a QSVM within an outer optimization loop, we show that using Pegasos it is possible to simultaneously train the support vector machine and align the kernel. Our experiments show that this approach is capable of aligning quantum feature maps with high accuracy, and outperforms existing quantum kernel alignment techniques. Specifically, we demonstrate that Pegasos is particularly effective for non-stationary data, which is an important challenge in real-world applications.