# QUACK: Quantum Aligned Centroid Kernel

arXiv: https://arxiv.org/abs/2405.00304 · HTML: https://mlsanity.com/paper/2405.00304/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 23 references that are in the map.
- First posted on arXiv 1 May 2024.

## Builds on (most cited first, 11 of 11)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [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)
- [Better than classical? The subtle art of benchmarking quantum machine learning models](https://mlsanity.com/paper/2403.07059/) (2024)
- [Training Quantum Embedding Kernels on Near-Term Quantum Computers](https://mlsanity.com/paper/2105.02276/) (2021)
- [Let Quantum Neural Networks Choose Their Own Frequencies](https://mlsanity.com/paper/2309.03279/) (2023)
- [Training robust and generalizable quantum models](https://mlsanity.com/paper/2311.11871/) (2023)
- [Quantum Kernel Alignment with Stochastic Gradient Descent](https://mlsanity.com/paper/2304.09899/) (2023)
- [Double-Adversarial Activation Anomaly Detection: Adversarial Autoencoders are Anomaly Generators](https://mlsanity.com/paper/2101.04645/) (2021)
- [R2-AD2: Detecting Anomalies by Analysing the Raw Gradient](https://mlsanity.com/paper/2206.10259/) (2022)
- [Towards Efficient Quantum Anomaly Detection: One-Class SVMs using Variable Subsampling and Randomized Measurements](https://mlsanity.com/paper/2312.09174/) (2023)

## Built on by (most cited first, 4 of 4)

- [Quantum Kernel Learning for Small Dataset Modeling in Semiconductor Fabrication: Application to Ohmic Contact](https://mlsanity.com/paper/2409.10803/) (2024)
- [Quantum Autoencoder for Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2504.17548/) (2025)
- [Q2SAR: A Quantum Multiple Kernel Learning Approach for Drug Discovery](https://mlsanity.com/paper/2506.14920/) (2025)
- [A Multiclass Quantum Aligned Centroid Kernel](https://mlsanity.com/paper/2607.19782/) (2026)

## Abstract (arXiv)

Quantum computing (QC) seems to show potential for application in machine learning (ML). In particular quantum kernel methods (QKM) exhibit promising properties for use in supervised ML tasks. However, a major disadvantage of kernel methods is their unfavorable quadratic scaling with the number of training samples. Together with the limits imposed by currently available quantum hardware (NISQ devices) with their low qubit coherence times, small number of qubits, and high error rates, the use of QC in ML at an industrially relevant scale is currently impossible. As a small step in improving the potential applications of QKMs, we introduce QUACK, a quantum kernel algorithm whose time complexity scales linear with the number of samples during training, and independent of the number of training samples in the inference stage. In the training process, only the kernel entries for the samples and the centers of the classes are calculated, i.e. the maximum shape of the kernel for n samples and c classes is (n, c). During training, the parameters of the quantum kernel and the positions of the centroids are optimized iteratively. In the inference stage, for every new sample the circuit is only evaluated for every centroid, i.e. c times. We show that the QUACK algorithm nevertheless provides satisfactory results and can perform at a similar level as classical kernel methods with quadratic scaling during training. In addition, our (simulated) algorithm is able to handle high-dimensional datasets such as MNIST with 784 features without any dimensionality reduction.