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Supervised quantum machine learning models are kernel methods
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Supervised quantum machine learning models are kernel methods
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With near-term quantum devices available and the race for fault-tolerant quantum computers in full swing, researchers became interested in the question of what happens if we replace a supervised machine learning model with a quantum circuit. While such "quantum models" are sometimes called "quantum neural networks", it has been repeatedly noted that their mathematical structure is actually much more closely related to kernel methods: they analyse data in high-dimensional Hilbert spaces to which we only have access through inner products revealed by measurements. This technical manuscript summarises and extends the idea of systematically rephrasing supervised quantum models as a kernel method. With this, a lot of near-term and fault-tolerant quantum models can be replaced by a general support vector machine whose kernel computes distances between data-encoding quantum states. Kernel-based training is then guaranteed to find better or equally good quantum models than variational circuit training. Overall, the kernel perspective of quantum machine learning tells us that the way that data is encoded into quantum states is the main ingredient that can potentially set quantum models apart from classical machine learning models.
Forward citations
Cited by 35 Pith papers
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Effective Dimension Governs Generalization in Quantum Kernel Vision Models
Effective dimension d_eff of the noise-shaped quantum feature kernel governs generalization in quantum kernel vision models, with entanglement and noise acting as regularization in overfitting regimes.
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AQKA: Active Quantum Kernel Acquisition Under a Shot Budget
AQKA introduces an active shot allocator for quantum kernels using closed-form acquisition functions derived for KRR and SVM, outperforming uniform allocation in low-budget regimes on both simulation and hardware.
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Controllable Quantum Memory Capacity in Quantum Reservoir Networks with Tunable partial-SWAPs
A tunable partial-SWAP mechanism enables direct control of memory dissipation rates in quantum reservoir networks on gate-based quantum processors.
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Controllable Quantum Memory Capacity in Quantum Reservoir Networks with Tunable partial-SWAPs
A hardware-realizable tunable partial-SWAP is introduced to control the rate of memory dissipation in recurrent quantum reservoir computing architectures, validated via simulation and IBM QPUs.
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Feature-level analysis and adversarial transfer in rotationally equivariant quantum machine learning
Rotationally equivariant quantum models can rely on vulnerable invariant statistics such as ring-averaged intensities, leaving them susceptible to classical transfer attacks, but suppressing the associated symmetry se...
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Answering Counting Queries with Differential Privacy on a Quantum Computer
Counting queries on quantum data reduce to amplitude measurements, enabling differentially private algorithms via repeated measurements or amplitude estimation with proven sensitivity bounds.
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From Membership-Privacy Leakage to Quantum Machine Unlearning
Quantum neural networks exhibit membership privacy leakage that a proposed quantum machine unlearning framework with three mechanisms can mitigate in simulations and cloud device tests.
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Quantum Kernels and the Cross-Section of Stock Returns: Anatomy of a Vanishing Advantage
Quantum kernel ridge regression matches, but never beats, equal-budget classical linear models for 20-day-ahead cross-sectional return prediction in Chinese A-shares; apparent quantum advantages vanish under point-in-...
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Learning Topological Quantum Phases from Limited Subsystems
Quantum kernels built from reduced density matrices of 1–4 sites classify the full phase diagrams of the generalized cluster-Ising and anisotropic Haldane chains, including SPT phases, and generalize across system sizes.
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Quantum Kernels are Spectral Tensor Networks
Quantum kernels are spectral tensor networks because their Fourier coefficient tensors are matrix product operator factorizations, with kernel target alignment acting as Frobenius cosine similarity on frequency grids.
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Quantum Parameterized Self-Attention Network for Image Classification
QPSAN implements self-attention via PQCs with 5 parameters, establishes a theoretical framework for its scoring properties, and reports outperformance over ViT on four vision datasets that grows with data complexity.
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Controllable Quantum Memory Capacity in Quantum Reservoir Networks with Tunable partial-SWAPs
Introduces tunable partial-SWAP for controllable memory capacity in quantum reservoir networks, modeled as controlled amplitude-damping and validated via STMC and NARMA-5 benchmarks on simulators and IBM QPUs.
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Towards Automated Selection of Quantum Encoding Circuits via Meta-Learning
Meta-learning with 24 classical complexity metrics predicts the optimal quantum encoding circuit among 9 candidates with up to 85.7% top-3 accuracy.
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Double Descent in Quantum Kernel Ridge Regression
Quantum kernel ridge regression shows double descent in test risk, with the interpolation peak suppressible by regularization, via random matrix theory asymptotics in the high-dimensional limit.
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Statevector-Referenced Geometry Survival of a Four-Qubit ZZ Quantum Kernel on IBM Quantum Hardware: A Fixed-Subset Diagnostic Across Three Execution Configurations
On ibm_fez, the noiseless geometry of a fixed four-qubit ZZ kernel survives to CKA 0.933–0.989, gate twirling is the most faithful configuration, and the apparent label-alignment uplift is a normalization artifact, no...
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A Multiclass Quantum Aligned Centroid Kernel
A sample-to-centroid fidelity kernel enables linear-scaling multiclass quantum classification; in simulation it beats pure quantum baselines, and untrained 124-qubit hardware results match an RBF kernel.
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Mitigating Measurement-Induced Training Instability in Hybrid Quantum Neural Networks for Protein Classification
The paper identifies measurement-induced logit contraction in hybrid QNNs and proposes Quantum Measurement Temperature, a learnable rescaling of bounded quantum outputs, to stabilize training and boost accuracy on flu...
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Feature Encoding in Quantum Machine Learning: A Survey and Practical Guidelines
Survey of quantum feature encoding families with a cost-expressivity-robustness taxonomy, closed-form NISQ bounds, and a five-regime decision framework that recommends shallow angle encodings when gate error rate p is...
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Quantum encodings that preserve persistent homology
Investigates which quantum encodings of classical datasets preserve persistent homology so that quantum algorithms can extract topological features directly from the data.
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AQKA: Active Quantum Kernel Acquisition Under a Shot Budget
For shot-budgeted quantum kernel learning, AQKA allocates shots as s_ij ∝ |g_ij| sqrt(K_ij(1−K_ij)) and reports up to +32 accuracy points over uniform, mainly under planted-sparse sensitivity.
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A Quantum Inspired Variational Kernel and Explainable AI Framework for Cross Region Solar and Wind Energy Forecasting
A hybrid classical-plus-quantum-inspired framework for cross-region renewable energy forecasting matches top baselines within 1% accuracy and separates calm versus stormy conditions with a 15-fold higher Fisher discri...
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Quantum Kernels for Parity-Structured Classification: A Hybrid Pipeline
ZZ quantum kernel with binary encoding reaches 66.3% accuracy on 11-feature parity tasks where binary RBF gets 54.3% and other classical methods ~50%, showing a complexity threshold for quantum advantage.
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Scalable Quantum Reservoir Computing over Distributed Quantum Architectures
Quantum reservoir computing with distributed architectures reduces time-series forecasting errors by up to 78.8% MAE and 72.3% RMSE in NISQ simulations compared to classical methods.
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Measuring Accuracy and Energy-to-Solution of Quantum Fine-Tuning of Foundational AI Models
Trapped-ion quantum fine-tuning of AI models shows linear energy scaling and 24% better classification error than classical logistic regression or SVM baselines, with a projected energy break-even at 34 qubits.
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Parameterized Quantum Circuits as Feature Maps: Representation Quality and Readout Effects in Multispectral Land-Cover Classification
Quantum feature maps from trained VQCs boost land-cover classification performance when reused in classical kernel-based frameworks, though linear-readout VQCs fail to surpass RBF-SVM baselines on EuroSAT-MS.
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Quantum Spectral Clustering: Comparing Parameterized and Neuromorphic Quantum Kernels
Quantum neuromorphic kernels outperform parameterized quantum kernels on low-dimensional datasets like Iris but underperform on high-dimensional SDSS data in spectral clustering tasks.
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Invariance Audits for Quantum Kernels and Variational Rewinding: A Real-to-Hermitian Taxonomy of Projector, Flag, Anchor, and Density Geometry
Noiseless quantum fidelity kernels and QVR return scores are exactly Hermitian projector/anchor overlaps, so representation choice is an invariance audit, not a quantum-vs-classical contest.
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Quantum Topological Data Encoding
QTDE encodes higher-order topological structure into quantum states via evolution under the combinatorial Laplacian; on clique-complex benchmarks it edges out a Laplacian-comparison baseline only in easy, high-dimensi...
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QBioFusion-QSAR: Morgan-Anchored Quantum Multiple Kernel Learning for Small-Data Ligand Classification
QMKL on the PsychLight-A benchmark yields a modest accuracy lift in stratified 5-fold CV but fails to beat the Morgan/Tanimoto baseline on mean MCC across ten random partitions.
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Feature Encoding in Quantum Machine Learning: A Survey and Practical Guidelines
For noisy near-term quantum devices, the paper recommends shallow angle encoding over amplitude encoding once two-qubit error rates exceed roughly 10^-3.
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Benchmarking a machine-learning differential equations solver on a neutral-atom logical processor
Logical quantum kernels outperform physical ones when solving differential equations on a neutral-atom processor, with gains traced to noise error detection in the logical encoding.
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Off-line quantum-advantage feature extraction for industrial production
Quantum feature surrogates let a quantum processor act as a teacher on a small data subsample while a classical surrogate applies the learned representations to the entire industrial dataset.
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Parameterized Quantum Circuits as Feature Maps: Representation Quality and Readout Effects in Multispectral Land-Cover Classification
A trained 4-qubit variational circuit used as a quantum kernel slightly outperforms its own linear readout on EuroSAT-MS land-cover pairs, but remains below an RBF-SVM.
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Toward selective quantum advantage in hadronic tomography:explicit cases from Compton form factors, GPDs, TMDs, and GTMDs
Quantum advantage in hadronic tomography should be evaluated selectively for CFFs, GPDs, TMDs, and GTMDs because their light-front and real-time correlation functions create ill-posed inverse problems that quantum alg...
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Meta-Quantum Ensemble Framework for Robust Network Intrusion Detection
A meta-ensemble fusing QSVM and QNN outputs with a Random Forest improves selected IDS metrics over standalone quantum models on TON IoT and CICIDS2017 datasets.
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