Quantum algorithms achieve polylogarithmic complexity for Betti number estimation and homology testing via block-encoded Laplacians and cohomological projections, claiming exponential speedups under sparsity assumptions.
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Quantum embeddings for machine learning
16 Pith papers cite this work, alongside 71 external citations. Polarity classification is still indexing.
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Maximal quantum leakage upper-bounds quantum inference accuracy; optimal encodings are pure states, with tight frames and equiangular tight frames optimal when system dimension is small.
A variational autoencoder learns quantum embeddings compressing ImageNet into 13 qubits and achieving 98.5% accuracy on MNIST 3-vs-5 classification with a quantum circuit, close to classical baselines and far above naive amplitude embeddings.
The paper delivers the first comprehensive systematization of adversarial robustness in QML with new empirical tests showing an accuracy-robustness trade-off, amplitude encoding's vulnerability, and QML's greater susceptibility to evasion attacks than classical models.
Proves mean-field limit and propagation of chaos for gradient-flow trained mixtures of experts with explicit rate depending only on expert count, applied to quantum neural networks.
Fluctuations of the empirical measure of parameters in a quantum neural network mixture of experts solve a linear transport equation as the number of experts diverges, with the MoE converging to a limit governed by the neural tangent kernel.
Generative optimization of quantum embedding circuits improves supervised classification on some datasets, with derived bounds showing performance saturation governed by Wasserstein distance of the classical input data.
Hybrid algorithm classically diagonalizes Hamiltonian tensor factors to construct block-encodings for quantum simulation via QSVD, with extensions for commuting time-dependent cases.
An efficient classical algorithm reduces the NTK average for Clifford-Pauli quantum neural networks to four discrete Clifford gates, enabling Gaussian-process simulation of wide trained networks and ruling out quantum advantage for this class.
A dual GNN predictor evaluates hardware-aware quantum circuit graphs to select task-specific kernels that balance expressivity and NISQ constraints, outperforming baselines on classification benchmarks.
LSTM trained with a QCBM generative prior beats a classical LSTM on SSE/CSI 300 realized volatility and retains much of that edge under zero-weight inference via Drop-Prior training.
Investigates which quantum encodings of classical datasets preserve persistent homology so that quantum algorithms can extract topological features directly from the data.
A hybrid quantum-classical temporal graph network with adaptive amplitude encoding claims strong link-prediction results on five TGBL benchmarks, but the evaluation is undermined by a below-random baseline and missing code.
A hybrid qDTW architecture with a Unified Pre-Embedding Adjoint Ansatz and identified spatial-temporal tradeoff outperforms classical DTW baselines on multivariate series up to 8 dimensions.
For noisy near-term quantum devices, the paper recommends shallow angle encoding over amplitude encoding once two-qubit error rates exceed roughly 10^-3.
IA-QCNN applies quantum principles via ring-topology convolution and importance weighting to achieve claimed high-accuracy MGMT methylation prediction from MRI with fewer parameters and noise robustness than classical models.
citing papers explorer
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New aspects of quantum topological data analysis: Betti number estimation, and testing and tracking of homology and cohomology classes
Quantum algorithms achieve polylogarithmic complexity for Betti number estimation and homology testing via block-encoded Laplacians and cohomological projections, claiming exponential speedups under sparsity assumptions.
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An Information-Theoretic Principle for Optimal Quantum Encoding: Tight Frames and Equiangular Ensembles
Maximal quantum leakage upper-bounds quantum inference accuracy; optimal encodings are pure states, with tight frames and equiangular tight frames optimal when system dimension is small.
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Tailor Made Embeddings for Quantum Machine Learning
A variational autoencoder learns quantum embeddings compressing ImageNet into 13 qubits and achieving 98.5% accuracy on MNIST 3-vs-5 classification with a quantum circuit, close to classical baselines and far above naive amplitude embeddings.
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SoK: Critical Evaluation of Quantum Machine Learning for Adversarial Robustness
The paper delivers the first comprehensive systematization of adversarial robustness in QML with new empirical tests showing an accuracy-robustness trade-off, amplitude encoding's vulnerability, and QML's greater susceptibility to evasion attacks than classical models.
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Mean-field limit from general mixtures of experts to quantum neural networks
Proves mean-field limit and propagation of chaos for gradient-flow trained mixtures of experts with explicit rate depending only on expert count, applied to quantum neural networks.
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On a Central Limit Theorem and Sanov's principle for quantum neural networks
Fluctuations of the empirical measure of parameters in a quantum neural network mixture of experts solve a linear transport equation as the number of experts diverges, with the MoE converging to a limit governed by the neural tangent kernel.
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Generative Quantum Data Embeddings for Supervised Learning
Generative optimization of quantum embedding circuits improves supervised classification on some datasets, with derived bounds showing performance saturation governed by Wasserstein distance of the classical input data.
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Hybrid Quantum-Classical Algorithm for Hamiltonian Simulation
Hybrid algorithm classically diagonalizes Hamiltonian tensor factors to construct block-encodings for quantum simulation via QSVD, with extensions for commuting time-dependent cases.
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Efficient classical computation of the neural tangent kernel of quantum neural networks
An efficient classical algorithm reduces the NTK average for Clifford-Pauli quantum neural networks to four discrete Clifford gates, enabling Gaussian-process simulation of wide trained networks and ruling out quantum advantage for this class.
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Hardware-Aware Quantum Kernel Design Based on Graph Neural Networks
A dual GNN predictor evaluates hardware-aware quantum circuit graphs to select task-specific kernels that balance expressivity and NISQ constraints, outperforming baselines on classification benchmarks.
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A Hybrid Quantum Circuit Born Machine Framework for Financial Volatility Forecasting: Quantum-Assisted Training and Classical Inference
LSTM trained with a QCBM generative prior beats a classical LSTM on SSE/CSI 300 realized volatility and retains much of that edge under zero-weight inference via Drop-Prior training.
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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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A2QTGN: Adaptive Amplitude Quantum-Integrated Temporal Graph Network for Dynamic Link Prediction
A hybrid quantum-classical temporal graph network with adaptive amplitude encoding claims strong link-prediction results on five TGBL benchmarks, but the evaluation is undermined by a below-random baseline and missing code.
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Quantum Dynamic Time Warping for Multivariate Time Series Classification
A hybrid qDTW architecture with a Unified Pre-Embedding Adjoint Ansatz and identified spatial-temporal tradeoff outperforms classical DTW baselines on multivariate series up to 8 dimensions.
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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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A Specialized Importance-Aware Quantum Convolutional Neural Network with Ring-Topology (IA-QCNN) for MGMT Promoter Methylation Prediction in Glioblastoma
IA-QCNN applies quantum principles via ring-topology convolution and importance weighting to achieve claimed high-accuracy MGMT methylation prediction from MRI with fewer parameters and noise robustness than classical models.