The paper proposes new first- and second-order hybrid quantum neural network-based operator splitting methods for solving high-dimensional nonlinear parabolic PDEs arising in finance. With n time steps, these methods achieve time-discretization errors of order O(n^-1) and O(n^-2) , respectively, improving on the available theoretical O(n^-1/2) time-discretization error bound for the deep BSDE solver and potentially reducing computational cost for a given accuracy. From a theoretical perspective, we provide a time-discretization error analysis for the proposed methods that also quantifies the propagation of approximation errors, assuming that the error of each hybrid quantum neural network approximation is uniformly bounded by ε >0 . Numerical experiments demonstrate the effectiveness of the proposed methods for PDEs with dimensions up to 100 that typically appear in credit valuation adjustment (CVA) computation in finance. In most tested cases, the second-order method achieves smaller errors with a shorter computational time than the hybrid quantum neural network-based BSDE baseline. In particular, for a 100-dimensional nonlinear Black–Scholes model with correlated asset prices, the second-order method achieves high accuracy with only n=4 time steps and hence with only three trained hybrid quantum neural networks. This result motivates further research toward implementations on noisy intermediate-scale quantum (NISQ) devices, where training hybrid quantum neural networks is computationally demanding.
Understanding trainability in variational quantum models requires separating the task-relevant signal available to a model from the geometry through which a concrete parametrization converts that signal into gradients. We develop a task-resolved Lie-algebraic framework that separates these effects. The dynamical Lie algebra is distinguished from the instantaneous tangent space realized at a given parameter configuration, and the accessible first-order signal is decomposed into its total amount and its density across independent directions. We derive an exact geometric characterization of these quantities, establish restriction and invariance properties, and show that compatibility acquires a direct gradient-variance interpretation only under isotropic directional sampling. For actual circuits, an additional tangent-frame geometry is required to relate accessible signal to parameter gradients. Numerical experiments validate this decomposition: task-relevant directions may be present in the dynamical algebra but absent from the instantaneous tangent space, ansätze with identical algebraic dimension can exhibit markedly different task alignment, and real tangent frames are strongly anisotropic. In scaling experiments, pooled gradient decay is explained by causal-cone dilution rather than systematic suppression of comparable active directions, while idle extensions leave active compatibility and gradient statistics unchanged. The framework therefore isolates a structural component of first-order trainability without identifying compatibility itself with a barren-plateau criterion.
We present a quantum-native approach to feature selection (QFS) based on analog quantum simulation with neutral-atom arrays. Feature relevance, measured through mutual information with the target variable, is encoded in site-dependent local detunings, while pairwise feature redundancy is mapped to distance-dependent van der Waals interactions through a two-dimensional atomic layout. The analog dynamics bias the system toward low-energy configurations that balance relevance and redundancy, and the resulting measurement bitstrings are post-processed to extract feature subsets of prescribed cardinality. The protocol is evaluated in simulation on three binary classification datasets: Adult Income, Bank Marketing, and Telco Churn. We quantify the main approximation and robustness properties of the pipeline, including multidimensional-scaling reconstruction error, subset stability across embedding seeds, sensitivity to post-processing parameters, and predictive performance across repeated train/test splits. QFS achieves competitive, dataset-dependent performance relative to mutual-information ranking, tree-based feature importance, L1-logistic selection, and classical optimizers of the same relevance-redundancy objective. The results establish a physically interpretable neutral-atom implementation of a feature-selection objective and identify the embedding, noise-modelling, and scalability requirements that must be addressed in larger experimental realizations.
Quantum Natural Language Processing (QNLP) applies quantum computational models to the representation and processing of language, yet its literature remains fragmented, and no prior study treats it as an autonomous object of analysis. This study maps the field by combining scientometric analysis with a qualitative, category-based assessment. The corpus was drawn from Scopus and Web of Science using search strings that combine quantum-computing and natural-language-processing descriptors; after cleaning, deduplication, and eligibility screening, 128 articles were retained. Scientometric methods examined publication trends, influential authors, collaboration networks, sources, and keyword co-occurrence, while each article was manually classified by application area and language-processing technique. Research concentrates on text representation and classification, with a predominance of foundational methods and tools. Health and biosciences, accounting and finance, environment and energy, and text generation appear markedly underrepresented, but comparison with domain-specific reviews indicates that these scarcities are not all of one kind: the apparent scarcity of health-related work substantially reflects the database and descriptor scope of general-purpose searches rather than inactivity, whereas the scarcity of text generation is at least partly consistent with the documented limits of current quantum hardware. Distinguishing artifactual from substantive gaps requires combining quantitative mapping with qualitative categorization and has direct implications for innovation policy and research management: it supports targeted funding for quantum-native generative architectures, collaboration with domain specialists where gaps survive scrutiny, and broader cross-database indexing to avoid systematically underestimating activity in fast-moving interdisciplinary fields.
Quantum-inspired (QI) optimizers are increasingly proposed as alternatives to classical gradient-based training, yet are frequently benchmarked through classical stand-ins rather than themselves. Across tabular, vision, and language tasks we evaluate three classes: direct implementations of published update rules (Spall’s SPSA; quantum-behaved particle swarm optimization, QPSO, adapted to stochastic minibatches), a documented classical analog of quantum natural gradient (an NGD-style diagonal second-moment preconditioner), and the hyperparameter-control configurations under which such methods are often reported. The gap between these classes is our central result: on the tabular benchmark the hyperparameter control trains with the classical baselines while the direct algorithms fall ≈ 10–24 points below it, and on CIFAR-10/ResNet18, where v1’s “SPSA” arm was a learning-rate-scaled Adam, Adam itself stands ≈ 59 points above genuine SPSA. The QPSO adaptation stays at chance on LSTM tasks a legacy “QPSO” proxy solves at 79–81 × Adam’s cost there and up to 74 × on the small CV model. A seed-paired 2× 2 factorial on RoBERTa identifies the smaller learning rate as the dominant observed component of the earlier “QNG advantage” ( +0.50 points at the dataset level); with only three datasets, modified Hartung–Knapp uncertainty spans zero. The configured NGD arm shows no detectable advantage over a learning-rate-matched AdamW (descriptive pooled p=0.23 ) at 6– 7% extra cost, and on ResNet18 its trained endpoints have larger dominant-curvature estimates than the Adam family’s. Headline comparisons use five seeds, paired tests, Holm correction, and stated detection limits. We conclude with an auditing taxonomy (direct algorithm / analog / hyperparameter control): within the arms, protocols, and scales evaluated, no advantage attributable to a QI mechanism is detected after these controls.
