New theoretical results prove Trotter error depends on diagonal BCH elements in the Hamiltonian eigenbasis, paired with O(n) compact BCH representations and software that enable accurate error estimates up to 100+ qubits.
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PennyLane: Automatic differentiation of hybrid quantum-classical computations
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abstract
PennyLane is a Python 3 software framework for differentiable programming of quantum computers. The library provides a unified architecture for near-term quantum computing devices, supporting both qubit and continuous-variable paradigms. PennyLane's core feature is the ability to compute gradients of variational quantum circuits in a way that is compatible with classical techniques such as backpropagation. PennyLane thus extends the automatic differentiation algorithms common in optimization and machine learning to include quantum and hybrid computations. A plugin system makes the framework compatible with any gate-based quantum simulator or hardware. We provide plugins for hardware providers including the Xanadu Cloud, Amazon Braket, and IBM Quantum, allowing PennyLane optimizations to be run on publicly accessible quantum devices. On the classical front, PennyLane interfaces with accelerated machine learning libraries such as TensorFlow, PyTorch, JAX, and Autograd. PennyLane can be used for the optimization of variational quantum eigensolvers, quantum approximate optimization, quantum machine learning models, and many other applications.
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- abstract PennyLane is a Python 3 software framework for differentiable programming of quantum computers. The library provides a unified architecture for near-term quantum computing devices, supporting both qubit and continuous-variable paradigms. PennyLane's core feature is the ability to compute gradients of variational quantum circuits in a way that is compatible with classical techniques such as backpropagation. PennyLane thus extends the automatic differentiation algorithms common in optimization and machine learning to include quantum and hybrid computations. A plugin system makes the framework co
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co-cited works
representative citing papers
A fermionic permutation protocol on 2D nearest-neighbor grids achieves the optimal O(sqrt(N)) depth with O(N sqrt(N)) gates, no ancillas, and extends to Jordan-Wigner, Bravyi-Kitaev, and Parity encodings via Hilbert-curve layout.
Qvine uses vine copula-inspired quantum circuit structures to achieve linear or quadratic depth scaling for loading high-dimensional distributions with high approximation quality.
Symmetry reductions in QAOA for MaxCut can collapse DLA dimensions from exponential to quadratic depending on the fixed variable, with graph embeddings ensuring expressivity and improved trainability.
CLAIMSTAB-QC audits 455 comparative claims from 119 quantum-software papers and identifies a materialization gap where only 8 claims provide enough matched evidence for direct auditing, yielding 2 sustained, 4 unresolved, and 2 reversed outcomes.
A randomized algorithm recovers the exact Pauli decomposition of k-sparse n-qubit matrices in poly(n, k, log(1/δ)) time with high probability under sparse query access.
MetaMorphQ defines five physics-derived invariants for VQE circuits that enable oracle-free testing with zero false positives and Youden's J of 0.57 on 500 benchmarks versus 0.02 for convergence testing.
A neural network is trained to predict parameters of a fixed quantum circuit, enabling high-fidelity quantum state preparation from classical data in one inference step with up to 0.992 fidelity on unseen MNIST and Fashion-MNIST images.
A learning-based framework constructs logical operations for arbitrary quantum codes and co-designs non-additive encodings with noise models and desired gate sets via VarEFTQC.
New SelectCopy architecture and qubit-constrained optimizations reduce QROM Toffoli cost from ~2N/λ to ~(1 + 1/b)N/λ while preserving the ability to trade dirty qubits for lower gate count.
Introduces the CULT threat model with four circuit-level attacks on quantum federated learning and shows they degrade accuracy on MNIST and CIFAR-10 even when defenses like Krum are used.
QLAM extends state-space models with quantum superposition in the hidden state for linear-time long-sequence modeling and reports consistent gains over RNN and transformer baselines on sequential image tasks.
NVQLS introduces the first hybrid quantum-classical unsupervised operator learning method for parametric PDEs via Legendre-Galerkin weak form, sign ambiguity resolution, and neural embedding.
Gated QKAN-FWP combines fast weight programming with quantum-inspired Kolmogorov-Arnold networks via single-qubit DARUAN activations and gated updates to deliver a 12.5k-parameter model that outperforms larger classical RNNs on long-horizon solar forecasting while running on NISQ devices.
At fixed encoding budget, serial QNN architectures suffer unbounded structural gradient starvation via rank(J) ≤ 2L+1 while parallel ones keep full Jacobian rank and better parameter efficiency when adding feature-map layers.
The hardware-compatible Brick-Circuit generator produces quantum test states with higher expressibility and entanglement than existing generators at shallower circuit depths.
QIBP adapts interval bound propagation to quantum neural networks for certified adversarial robustness via interval and affine arithmetic implementations.
A graph-conditioned meta-optimizer learns QAOA parameter trajectories from one problem class and transfers them to others, yielding better initializations than standard methods in an empirical study of 64 settings.
Q-SINDy adds quantum kernels to SINDy and proves that orthogonalization eliminates coefficient cannibalization bias exactly, recovering equations as accurately as classical SINDy on six tested systems.
LP2B encoding converts Lund plane jet representations into Bloch sphere qubit states, enabling a QTTN that matches classical LundNet performance on polarization tagging and W/top tagging with three orders of magnitude fewer parameters and improved low-data regime results.
Hybrid quantum PINN for hydrology reports 3x faster convergence and 44% fewer parameters than classical PINN on Sri Lankan flood data while using physics constraints for uncertainty quantification.
A quantum residual neural network using deterministic mixtures of identity and variational unitaries to enable post-selection-free residual learning with 10x fewer gates and reported accuracies of 99% binary and 80% multi-class on image datasets.
A formal audit of 45 quantum simulators identifies 547 vulnerabilities across memory corruption, resource exhaustion, code injection, and a new QASM injection class, with all patterns verified by Z3 SAT proofs.
HQ-LP-FNO replaces part of the spectral channel mixing in a 3D FNO with a mode-shared VQC, reducing parameters by 15.6% and phase-fraction MAE by 26% on laser-processing surrogates while remaining stable under calibrated noise.
citing papers explorer
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Practical Estimation of Trotter Error for Hamiltonian Simulation
New theoretical results prove Trotter error depends on diagonal BCH elements in the Hamiltonian eigenbasis, paired with O(n) compact BCH representations and software that enable accurate error estimates up to 100+ qubits.
-
Asymptotically Optimal Depth Fermionic Permutation on 2D Grid Quantum Architecture without Ancillas
A fermionic permutation protocol on 2D nearest-neighbor grids achieves the optimal O(sqrt(N)) depth with O(N sqrt(N)) gates, no ancillas, and extends to Jordan-Wigner, Bravyi-Kitaev, and Parity encodings via Hilbert-curve layout.
-
Qvine: Vine Structured Quantum Circuits for Loading High Dimensional Distributions
Qvine uses vine copula-inspired quantum circuit structures to achieve linear or quadratic depth scaling for loading high-dimensional distributions with high approximation quality.
-
Reductions of QAOA Induced by Classical Symmetries: Theoretical Insights and Practical Implications
Symmetry reductions in QAOA for MaxCut can collapse DLA dimensions from exponential to quadratic depending on the fixed variable, with graph embeddings ensuring expressivity and improved trainability.
-
Auditing Empirical Comparisons in Quantum Software
CLAIMSTAB-QC audits 455 comparative claims from 119 quantum-software papers and identifies a materialization gap where only 8 claims provide enough matched evidence for direct auditing, yielding 2 sustained, 4 unresolved, and 2 reversed outcomes.
-
An efficient Pauli decomposition algorithm for structured matrices
A randomized algorithm recovers the exact Pauli decomposition of k-sparse n-qubit matrices in poly(n, k, log(1/δ)) time with high probability under sparse query access.
-
MetaMorphQ: Physics-Based Metamorphic Testing of Variational Quantum Circuits
MetaMorphQ defines five physics-derived invariants for VQE circuits that enable oracle-free testing with zero false positives and Youden's J of 0.57 on 500 benchmarks versus 0.02 for convergence testing.
-
Quantum State Preparation via Neural Network Encoding in Quantum Machine Learning
A neural network is trained to predict parameters of a fixed quantum circuit, enabling high-fidelity quantum state preparation from classical data in one inference step with up to 0.992 fidelity on unseen MNIST and Fashion-MNIST images.
-
Learning Logical Operations for Arbitrary Quantum Error Correction Codes
A learning-based framework constructs logical operations for arbitrary quantum codes and co-designs non-additive encodings with noise models and desired gate sets via VarEFTQC.
-
Halving the cost of QROM
New SelectCopy architecture and qubit-constrained optimizations reduce QROM Toffoli cost from ~2N/λ to ~(1 + 1/b)N/λ while preserving the ability to trade dirty qubits for lower gate count.
-
Can Quantum Federated Learning Withstand Circuit-Level Backdoors?
Introduces the CULT threat model with four circuit-level attacks on quantum federated learning and shows they degrade accuracy on MNIST and CIFAR-10 even when defenses like Krum are used.
-
QLAM: A Quantum Long-Attention Memory Approach to Long-Sequence Token Modeling
QLAM extends state-space models with quantum superposition in the hidden state for linear-time long-sequence modeling and reports consistent gains over RNN and transformer baselines on sequential image tasks.
-
Neural Quantum Spectral Operator Learning for Solving Partial Differential Equations
NVQLS introduces the first hybrid quantum-classical unsupervised operator learning method for parametric PDEs via Legendre-Galerkin weak form, sign ambiguity resolution, and neural embedding.
-
Gated QKAN-FWP: Scalable Quantum-inspired Sequence Learning
Gated QKAN-FWP combines fast weight programming with quantum-inspired Kolmogorov-Arnold networks via single-qubit DARUAN activations and gated updates to deliver a 12.5k-parameter model that outperforms larger classical RNNs on long-horizon solar forecasting while running on NISQ devices.
-
Architecture Shape Governs QNN Trainability: Jacobian Null Space Growth and Parameter Efficiency
At fixed encoding budget, serial QNN architectures suffer unbounded structural gradient starvation via rank(J) ≤ 2L+1 while parallel ones keep full Jacobian rank and better parameter efficiency when adding feature-map layers.
-
Randomized and Diverse Input State Generation for Quantum Program Testing
The hardware-compatible Brick-Circuit generator produces quantum test states with higher expressibility and entanglement than existing generators at shallower circuit depths.
-
Quantum Interval Bound Propagation for Certified Training of Quantum Neural Networks
QIBP adapts interval bound propagation to quantum neural networks for certified adversarial robustness via interval and affine arithmetic implementations.
-
Graph-Conditioned Meta-Optimizer for QAOA Parameter Generation on Multiple Problem Classes
A graph-conditioned meta-optimizer learns QAOA parameter trajectories from one problem class and transfers them to others, yielding better initializations than standard methods in an empirical study of 64 settings.
-
Q-SINDy: Quantum-Kernel Sparse Identification of Nonlinear Dynamics with Provable Coefficient Debiasing
Q-SINDy adds quantum kernels to SINDy and proves that orthogonalization eliminates coefficient cannibalization bias exactly, recovering equations as accurately as classical SINDy on six tested systems.
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Lund Plane to Bloch (LP2B) Encoding for Object and Polarization Tagging with Quantum Jet Substructure
LP2B encoding converts Lund plane jet representations into Bloch sphere qubit states, enabling a QTTN that matches classical LundNet performance on polarization tagging and W/top tagging with three orders of magnitude fewer parameters and improved low-data regime results.
-
Variational Quantum Physics-Informed Neural Networks for Hydrological PDE-Constrained Learning with Inherent Uncertainty Quantification
Hybrid quantum PINN for hydrology reports 3x faster convergence and 44% fewer parameters than classical PINN on Sri Lankan flood data while using physics constraints for uncertainty quantification.
-
A hardware efficient quantum residual neural network without post-selection
A quantum residual neural network using deterministic mixtures of identity and variational unitaries to enable post-selection-free residual learning with 10x fewer gates and reported accuracies of 99% binary and 80% multi-class on image datasets.
-
Broken Quantum: A Systematic Formal Verification Study of Security Vulnerabilities Across the Open-Source Quantum Computing Simulator Ecosystem
A formal audit of 45 quantum simulators identifies 547 vulnerabilities across memory corruption, resource exhaustion, code injection, and a new QASM injection class, with all patterns verified by Z3 SAT proofs.
-
Hybrid Fourier Neural Operator for Surrogate Modeling of Laser Processing with a Quantum-Circuit Mixer
HQ-LP-FNO replaces part of the spectral channel mixing in a 3D FNO with a mode-shared VQC, reducing parameters by 15.6% and phase-fraction MAE by 26% on laser-processing surrogates while remaining stable under calibrated noise.
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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.
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A Methodological Analysis of Empirical Studies in Quantum Software Testing
A systematic analysis of 59 quantum software testing empirical studies reveals highly diverse designs, inconsistent reporting, and open methodological challenges, leading to recommendations for future work.
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Quantum Masked Autoencoders for Vision Learning
Quantum masked autoencoders reconstruct masked MNIST-family images in quantum states and achieve 12.86% higher average classification accuracy than prior quantum autoencoders under masking.
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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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Cobble: Compiling Block Encodings for Quantum Computational Linear Algebra
Cobble is a domain-specific language for quantum block encodings that compiles high-level matrix expressions to optimized circuits using analyses and quantum singular value transformation, achieving 2.6x-25.4x speedups over unoptimized baselines on benchmarks.
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Inference of maximum parsimony phylogenetic trees with model-based classical and quantum methods
Introduces branch-based and other optimization models for maximum parsimony trees, with classical validation outperforming heuristics on GAPDH data and quantum simulations solving small instances exactly.
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The Lie Algebra of XY-mixer Topologies and Warm Starting QAOA for Constrained Optimization
The paper decomposes dynamical Lie algebras of XY-mixer topologies and demonstrates warm-starting QAOA via pre-training on restricted generators to improve convergence on constrained optimization problems.
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Exploring nontrivial topology at quantum criticality in a superconducting processor
Experimental preparation of topologically nontrivial critical states of the cluster Ising model on a 100-qubit superconducting processor, verified by boundary g-function and two-fold entanglement spectrum degeneracy under periodic boundaries.
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An Operational Framework for Nonclassicality in Quantum Communication Networks
A variational optimization framework computes linear classical bounds on network input/output probabilities whose violation certifies nonclassicality, finding entanglement necessary for nonclassicality in single-sender broadcast networks but not in multi-sender networks.
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Works on My QPU: Reproducibility in Quantum Computing Research
A large-scale audit finds that only ~25% of quantum-computing papers provide code artifacts and ~65% of those artifacts fail to execute in a clean environment.
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Spectral Born machines: classically trainable quantum generative models for discrete data
Spectral Born machines are Fourier-phase quantum generative models over Z_d^n that train classically via graph-spectral MMD and show reduced parameters plus apparent overfitting resistance on integer data.
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Perturbatively Corrected Linear Response Selected Configuration Interaction
LR-SCI-PT with second-order Epstein-Nesbet corrections improves static polarizabilities toward FCI limits for small molecules but preserves the parent pole structure, limiting it to static properties.
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Split-Head Quantum Generative Adversarial Network for Crystalline Material Discovery
Split-head QGAN generates more structurally diverse and novel metastable Mg-Mn-O crystals than its classical ablation counterpart but shows lower thermodynamic precision.
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Locally Acting Grover Mixers for Constraint-Preserving QAOA
Locally acting Grover mixers for constraint-preserving QAOA achieve comparable convergence to global versions using shallower circuits with fewer gates on exact-cover and TSP instances.
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QnRL: Quantum-Native Reinforcement Learning
QnRL is a distributional quantum RL framework that distills conditional action policies from moments of quantum generative models in Hilbert space via the QuAK algorithm, reporting higher scores and fewer parameters than baselines.
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Efficient and Expressive Boundary Conditions in Quantum Lattice Boltzmann Methods
New boundary condition approach for QLBM using one coherent operation on the full boundary, claimed to use fewer resources asymptotically and practically for bounce-back and specular reflection.
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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.
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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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Q-ANCHOR: Federated Quantum Learning with ZNE-guided Correction
Q-ANCHOR combines ZNE-guided server anchoring with stateful client correction to reduce both non-IID client drift and quantum hardware bias in federated quantum learning.
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Q-LEAK: Quantum-Based LEAKage Verification for Side-Channel Countermeasures
Q-LEAK uses Grover's algorithm on oracles encoding two-trace leakage CNFs to recover satisfying assignments for side-channel verification faster than classical SAT on small benchmarks.
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Bipartite Cholesky Graph Networks for Many-Body Quantum Chemistry
Bipartite Cholesky Graph Networks from density-fitted ERI decomposition achieve 0.0296 Ha in-distribution MAE on six diatomic molecules under FCI reference, outperforming compressed-integral baselines, with generalization tied to orbital environment similarity.
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Local-Observable-Guided Generative Quantum Circuits for Degenerate Ground Spaces
Hybrid generative quantum circuits guided by local observable correlators sample diverse ensembles whose span reproduces degenerate ground spaces in Majumdar-Ghosh, AKLT, and XXZ models.
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QUTest: A Native Testing Framework for Quantum Programs
QUTest is a native OpenQASM testing framework that encodes Arrange/Act/Assert tests and 12 assertion types via pragma comments while remaining compatible with existing tools.
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Quantum Feature Pyramid Gating for Seismic Image Segmentation
A 4-qubit quantum feature pyramid gating architecture raises mean IoU from 0.8404 to 0.9389 over classical addition in controlled ablations on the TGS salt segmentation dataset.
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Quantum End-to-End Learning for Contextual Combinatorial Optimization
QEL is the first quantum end-to-end learning framework for contextual combinatorial optimization using QAOA with a context re-uploading phase-separator, achieving competitive performance with fewer parameters.
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A QPINN Framework with Quantum Trainable Embeddings for the Lid-Driven Cavity Problem
QPINN framework with QNN-based trainable embeddings solves the lid-driven cavity problem with stable training, competitive accuracy, and fewer parameters than classical PINNs.