Quantum Generator Kernels
Philipp Altmann, Maximilian Mansky, Maximilian Zorn, Jonas Stein, Claudia Linnhoff-Popien
TL;DR
Quantum Generator Kernels (QGKs) introduce a scalable, generator-based quantum kernel approach that enhances data embedding and classification in quantum machine learning, outperforming existing methods on real-world data.
Contribution
The paper presents QGKs, a novel generator-based quantum kernel framework that improves data embedding and classification in quantum machine learning applications.
Findings
QGKs outperform state-of-the-art quantum and classical kernels in classification tasks.
QGKs effectively embed large-scale real-world data into quantum space.
Empirical results demonstrate superior projection and classification capabilities.
Abstract
Quantum kernel methods offer significant theoretical benefits by rendering classically inseparable features separable in quantum space. Yet, the practical application of Quantum Machine Learning (QML), currently constrained by the limitations of Noisy Intermediate-Scale Quantum (NISQ) hardware, necessitates effective strategies to compress and embed large-scale real-world data like images into the constrained capacities of existing quantum devices or simulators. To this end, we propose Quantum Generator Kernels (QGKs), a generator-based approach to quantum kernels, comprising a set of Variational Generator Groups (VGGs) that merge universal generators into a parameterizable operator, ensuring scalable coverage of the available quantum space. Thereby, we address shortcomings of current leading strategies employing hybrid architectures, which might prevent exploiting quantum computing's…
Peer Reviews
Decision·Submitted to ICLR 2026
QGK directly tackles the practical and important issue of embedding high-dimensional data into quantum states, which is a major bottleneck for QML. The use of Variational Generator Groups (VGGs) is a fresh and powerful idea, allowing for a learnable feature map rather than a fixed one. This is a commendable cross-disciplinary innovation. The fact that QGK’s advantage persists under noise simulations is a major strength. This demonstrates robustness and suggests viability for NISQ devices, which
The method relies on a classical linear compression stage before the quantum kernel. This blurs the line of quantum advantage. It's unclear how much of the performance gain comes from the trained classical pre-processing versus the quantum kernel itself. The paper needs a stronger ablation study to disentangle these two contributions. Experiments on MNIST/CIFAR-10 use small subsets (n=1000). This is insufficient to demonstrate scalability. Kernel methods are notoriously difficult to scale with t
1. The writing of this paper is good and easy to follow. 2. This paper has a certain degree of innovation, introducing a novel method for constructing quantum kernels. 3. The authors provide theoretical analysis and experimental verification of their own algorithm.
1. The authors are advised to conduct experiments in larger quantum systems (e.g. 20 qubits). 2. The results in Table 1 do not reflect the superiority of the quantum generator kernels (QGK). Because the dimension of moons, circles and bank are too small, it does not conform to the actual application scenario as we are in big data era. While for cifar10, the accuracy achieved by the QGK is clearly unacceptable. The reviewer suggested that the authors include additional experiments to illustrate
1. This work introduces a novel data encoding paradigm that moves beyond state-based methods by constructing parameterized unitary operators derived from the Lie algebra su(2^n), offering exponential increase in representational capacity; variational generator group (VGG) is proposed by structuring these unitaries through systematic combinations of algebraic generators, 2. Quantum generator kernel is defined on top of VGG with groups parametrized by a trainable linear projection; it supports s
1. While the paper presents the Quantum Generator Kernel (QGK) as its central contribution, the more fundamental innovation appears to be the Variational Generator Group (VGG) framework for data embedding. The kernel method itself builds upon well-established concepts in quantum machine learning. 2. The VGG approach is positioned as a departure from traditional angle encoding, but it can be more precisely characterized as a generalized, structured multi-qubit angle encoding that systematically
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum many-body systems · Quantum Information and Cryptography