Fixed upload circuits approximate tunable ones to error ε with depth O_σ[(log(1/ε))^σ] for any σ>1 (improving prior polynomial bounds) and matching Ω(log(1/ε)) lower bounds for mismatch-class targets via auxiliary extensions and Turán-Nazarov analysis.
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Effect of data encoding on the expressive power of variational quantum-machine-learning models
22 Pith papers cite this work, alongside 575 external citations. Polarity classification is still indexing.
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Trainable quantum spectral models with an intermediate parameterized mixer (ε ≈ 0.5) outperform standard variational quantum circuits for PDEs by learning in spectral representation, with HHL-inspired architectures showing fastest convergence.
Pulse-level parameterization of quantum Fourier models replaces single gate angles with multiple independent sub-angles, relaxing monomial couplings and improving gradient descent performance on Fourier series tasks.
Local tensor-train surrogates approximate quantum machine learning models via Taylor polynomials and tensor networks, delivering polynomial parameter scaling and explicit generalization bounds controlled by patch radius.
MerLin is a new open-source discovery engine for photonic and hybrid quantum machine learning that integrates circuit simulations into standard ML frameworks and reproduces 18 prior works as reusable benchmarks.
All embedding quantum kernels can be understood as entangled tensor kernels, yielding new insights into their inductive bias and potential dequantization.
A quantum machine learning surrogate based on parameterized circuits with data re-uploading approximates the full BGK collision dynamics in LBM across all admissible relaxation parameters and is validated on Taylor-Green vortex and double shear layer benchmarks.
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.
Hybrid quantum-classical FBPINN for acoustic FWI achieves lower L1 velocity error than classical baselines in ~8x fewer iterations with ~33% fewer parameters on anomaly and checkerboard benchmarks.
Hybrid agent with variational quantum circuits for feature extraction in hierarchical RL outperforms classical baselines with 66% parameter savings, but quantum value estimation degrades results.
A compact 2-qubit QNN approximates Black-Scholes-Merton option prices with usable accuracy when executed on multiple commercial NISQ quantum processors.
A quantum autoencoder for multivariate time series anomaly detection achieves competitive performance with neural-network autoencoders using fewer trainable parameters.
Proposes projected quantum kernels with misspecified GP bandit algorithms and regret bounds to trade off expressivity against learnability in quantum kernel optimization.
Investigates which quantum encodings of classical datasets preserve persistent homology so that quantum algorithms can extract topological features directly from the data.
Simulated fidelity quantum kernels achieve competitive or better accuracy than RBF kernels on Indian Pines binary and multiclass tasks and Methane Detection data without heavy dimensionality reduction.
Tensor-rank quantum and quantum-inspired PINNs solve the Merton HJB PDE with lower error and fewer parameters than classical fully connected PINNs.
Hybrid quantum-classical physics-informed neural networks reach accurate solutions to nonlinear PDEs in substantially fewer training epochs than purely classical networks, with larger gains on complex problems.
Parametrized quantum circuit anomaly detector trained on classical hardware and tested on IBM devices for handwritten digits and simulated long-lived particle signals in HEP, but does not outperform classical deep neural networks due to noise and amplitude encoding requirements.
The paper introduces Recursive QLSTM via metacore recursion, numerically tests variants on sequence lengths, and offers theoretical arguments for better temporal propagation.
For noisy near-term quantum devices, the paper recommends shallow angle encoding over amplitude encoding once two-qubit error rates exceed roughly 10^-3.
Introduces a JAX-based framework for pulse-level QML with composable ansatze, end-to-end pulse optimization, and Fourier-analytic diagnostics.
A survey of variational quantum algorithms, quantum neural networks, and tensor networks for addressing scalability challenges in computational fluid dynamics.
citing papers explorer
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The Cost of Removing Tunability in Quantum Data Re-Uploading
Fixed upload circuits approximate tunable ones to error ε with depth O_σ[(log(1/ε))^σ] for any σ>1 (improving prior polynomial bounds) and matching Ω(log(1/ε)) lower bounds for mismatch-class targets via auxiliary extensions and Turán-Nazarov analysis.
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Trainable Quantum Spectral Models for Partial Differential Equations
Trainable quantum spectral models with an intermediate parameterized mixer (ε ≈ 0.5) outperform standard variational quantum circuits for PDEs by learning in spectral representation, with HHL-inspired architectures showing fastest convergence.
-
Beyond Gates: Pulse Level Quantum Fourier Models
Pulse-level parameterization of quantum Fourier models replaces single gate angles with multiple independent sub-angles, relaxing monomial couplings and improving gradient descent performance on Fourier series tasks.
-
Local tensor-train surrogates for quantum learning models
Local tensor-train surrogates approximate quantum machine learning models via Taylor polynomials and tensor networks, delivering polynomial parameter scaling and explicit generalization bounds controlled by patch radius.
-
MerLin: A Discovery Engine for Photonic and Hybrid Quantum Machine Learning
MerLin is a new open-source discovery engine for photonic and hybrid quantum machine learning that integrates circuit simulations into standard ML frameworks and reproduces 18 prior works as reusable benchmarks.
-
New perspectives on quantum kernels through the lens of entangled tensor kernels
All embedding quantum kernels can be understood as entangled tensor kernels, yielding new insights into their inductive bias and potential dequantization.
-
A Quantum-Classical Surrogate Model for the Collision Operator of the Lattice Boltzmann Method
A quantum machine learning surrogate based on parameterized circuits with data re-uploading approximates the full BGK collision dynamics in LBM across all admissible relaxation parameters and is validated on Taylor-Green vortex and double shear layer benchmarks.
-
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.
-
Accelerating physics-informed neural networks for full waveform inversion using a hybrid quantum-classical finite-basis architecture
Hybrid quantum-classical FBPINN for acoustic FWI achieves lower L1 velocity error than classical baselines in ~8x fewer iterations with ~33% fewer parameters on anomaly and checkerboard benchmarks.
-
Quantum Hierarchical Reinforcement Learning via Variational Quantum Circuits
Hybrid agent with variational quantum circuits for feature extraction in hierarchical RL outperforms classical baselines with 66% parameter savings, but quantum value estimation degrades results.
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Option Pricing on Noisy Intermediate-Scale Quantum Computers: A Quantum Neural Network Approach
A compact 2-qubit QNN approximates Black-Scholes-Merton option prices with usable accuracy when executed on multiple commercial NISQ quantum processors.
-
Quantum Autoencoder for Multivariate Time Series Anomaly Detection
A quantum autoencoder for multivariate time series anomaly detection achieves competitive performance with neural-network autoencoders using fewer trainable parameters.
-
Balancing Expressivity and Learnability in Quantum Kernel Bandit Optimization
Proposes projected quantum kernels with misspecified GP bandit algorithms and regret bounds to trade off expressivity against learnability in quantum kernel optimization.
-
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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Large-Scale Quantum Kernels for Hyperspectral Data Classification
Simulated fidelity quantum kernels achieve competitive or better accuracy than RBF kernels on Indian Pines binary and multiclass tasks and Methane Detection data without heavy dimensionality reduction.
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Learning PDEs for Portfolio Optimization with Quantum Physics-Informed Neural Networks
Tensor-rank quantum and quantum-inspired PINNs solve the Merton HJB PDE with lower error and fewer parameters than classical fully connected PINNs.
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Quantum-Enhanced Convergence of Physics-Informed Neural Networks
Hybrid quantum-classical physics-informed neural networks reach accurate solutions to nonlinear PDEs in substantially fewer training epochs than purely classical networks, with larger gains on complex problems.
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Long-lived Particles Anomaly Detection with Parametrized Quantum Circuits
Parametrized quantum circuit anomaly detector trained on classical hardware and tested on IBM devices for handwritten digits and simulated long-lived particle signals in HEP, but does not outperform classical deep neural networks due to noise and amplitude encoding requirements.
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Recursive QLSTM with Dynamic Variational Quantum Circuit Adaptation
The paper introduces Recursive QLSTM via metacore recursion, numerically tests variants on sequence lengths, and offers theoretical arguments for better temporal propagation.
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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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Software Between Quantum and Machine Learning -- And Down to Pulses
Introduces a JAX-based framework for pulse-level QML with composable ansatze, end-to-end pulse optimization, and Fourier-analytic diagnostics.
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A review of quantum machine learning and quantum-inspired applied methods to computational fluid dynamics
A survey of variational quantum algorithms, quantum neural networks, and tensor networks for addressing scalability challenges in computational fluid dynamics.