Quantum Kernels Unlock Complex Data Processing for Near-Term Quantum Computers

Researchers are tackling a central challenge in Quantum Machine Learning: effectively translating real-world data into a format usable by current quantum computers. Philipp Altmann, Maximilian Mansky, and Maximilian Zorn, all from LMU Munich, alongside Jonas Stein and Claudia Linnhoff-Popien, introduce Quantum Generator Kernels (QGKs) , a novel generator-based approach designed to compress and embed large datasets into the limited capacity of existing quantum devices. This work is significant because QGKs move beyond fixed embedding processes common in hybrid architectures, potentially unlocking the full power of quantum computation by dynamically adapting to the data and demonstrating superior performance in projection and classification tasks compared with existing quantum and classical methods.

This work addresses a critical challenge in the field, namely the difficulty of utilising the full potential of quantum computing due to the constraints of Noisy Intermediate-Scale Quantum (NISQ) devices.

The QGK framework employs Variational Generator Groups (VGGs), which merge universal generators into a parameterizable operator, enabling scalable coverage of the quantum space and offering a flexible alternative to fixed embedding processes. By optimising kernel alignment to the target domain through a trainable weight vector, the QGK effectively projects data into a quantum representation suitable for machine learning tasks.
Central to this breakthrough is the innovative use of Lie algebraic generators aggregated into VGGs, creating a novel embedding framework for data-dependent state preparation. Unlike previous hybrid architectures reliant on static, gate-based embeddings, the QGK utilises Hamiltonian-driven unitaries with learnable generator weights, allowing for expressive and scalable data encoding.

This approach achieves high parameter efficiency per qubit and flexible embedding capacity, effectively leveraging the expressive power of the Hilbert space. Theoretical analyses confirm the expressivity and scalability of the VGGs, while experimental results demonstrate superior classification accuracy and robustness to noise across both synthetic and real-world benchmarks.

Empirical evaluations on datasets including MNIST and CIFAR10 demonstrate consistent improvements over state-of-the-art classical and quantum kernels, highlighting the QGK’s potential as a versatile framework for various QML applications. The research details three key contributions: the introduction of VGGs, the proposal of the QGK itself, and a comprehensive analysis of its theoretical kernel properties, including entanglement capability and parameter scalability. This work presents a classically efficient strategy for high-dimensional inputs, remaining fully compatible with future fault-tolerant quantum execution and paving the way for more powerful and practical quantum machine learning algorithms.

Constructing and implementing the Quantum Generator Kernel for data encoding requires significant computational resources

Variational Generator Groups (VGGs) form the core of this research, merging universal Lie algebraic generators into parameterizable Hermitian operators to facilitate expressive, data-dependent quantum state preparation. The study constructs a set of these generators and aggregates them into VGGs, collectively defining the Quantum Generator Kernel (QGK), which is then executed using its associated operators.

To optimise kernel alignment with the target domain, a linear feature extractor was pre-trained to project high-dimensional input data into a compressed generator space before quantum encoding. This methodology diverges from static, gate-based embeddings by employing Hamiltonian-driven unitaries with learnable generator weights, enabling both expressive and scalable data encoding.

High-dimensional data is projected into this compact, generator-weighted space, achieving high parameter efficiency per qubit and flexible embedding capacity, while leveraging the full Hilbert space. Theoretical analyses were conducted to confirm the expressivity and scalability of the VGGs, specifically characterising entanglement capability, parameter scalability, and computational complexity.

Empirical validation involved classification tasks using both synthetic and real-world benchmark datasets, assessing the QGK’s performance against state-of-the-art quantum and classical kernel approaches. The research demonstrates superior classification accuracy and robustness to noise, highlighting the potential of QGKs as a versatile framework for various Quantum Machine Learning applications. The research introduces the Quantum Generator Kernel, or QGK, a generator-driven kernel building on these groups to utilise Hamiltonian evolution with data-conditioned weights, yielding compact, highly expressive feature maps.

Theoretical analyses confirm the kernel’s expressivity and scalability, while experimental results demonstrate superior classification accuracy and robustness to noise across benchmarks. Specifically, the study details a novel embedding framework that characterises entanglement capability, expressivity, parameter scalability, and computational complexity.

This framework presents a classically efficient strategy for high-dimensional inputs, remaining compatible with future fault-tolerant quantum execution. The work summarises contributions including the introduction of Variational Generator Groups and the proposal of the Quantum Generator Kernel itself.

Kernel target alignment, or KTA, was used to quantify the similarity between a computed kernel matrix and an ideal target kernel derived from class labels. The feature map quality can be measured and adjusted to provide a better data embedding structure using this method. Quantum systems are described by quantum states, represented as complex vectors encoding observables, with a single qubit written as |q⟩= α |0⟩+β |1⟩, where α, β are complex numbers. These kernels utilise Variational Generator Groups (VGGs) which merge universal generators into parameterizable groups, effectively addressing limitations found in hybrid architectures with fixed embedding processes.

Empirical studies across five benchmark datasets demonstrate that QGKs achieve superior trainability and classification accuracy, consistently exceeding the performance of both quantum and classical kernel baselines, even when subjected to hardware noise. Specifically, QGKs outperformed classical and quantum embedding methods on synthetic binary tasks, achieved 85% accuracy on a real-world bank dataset, and reached 94% accuracy on the MNIST benchmark, matching the best classical linear kernel.

Notably, on the more complex CIFAR10 dataset, QGKs attained 41% accuracy, significantly surpassing other quantum kernels and even outperforming small multilayer perceptrons and linear kernels. This demonstrates the effective embedding of high-dimensional data into systems with limited qubits, facilitated by expressive generator-grouped unitaries.

The authors acknowledge that while theoretically well-defined for arbitrary system sizes, the native execution of generator-based quantum kernels is currently limited by existing hardware capabilities. Compiled QGK circuits for larger-scale datasets exceed the gate depth capabilities of present-day noisy devices, however, efficient tensor-based classical implementations combined with input compression offer a practical pathway for execution until fault-tolerant hardware becomes available. Future research directions include hardware, algorithm co-design to natively support generator-based quantum models, and hybrid execution strategies utilising classical preprocessing to reduce dimensionality before quantum embedding.