Quantum convolution offers a natural inductive bias for extracting local structure from high-dimensional data, yet its practical reach is constrained by direct feature-wise encoding, which ties broader receptive fields to wider quantum registers. This raises a central question: can local quantum representations retain their predictive content when receptive-field growth is redirected from circuit width to sequential processing on a compact register? Generalized Quantum Neural Modules address this question through incremental data upload, partitioning each receptive field into ordered batches, preserving a single evolving quantum state across successive encode–entangle stages, and reusing shared trainable transformations as the local window moves across the input. State-vector experiments on controlled three- and four-dimensional motif tensors, MNIST images, and selected UCF101 action videos show that moderate serialization substantially narrows the active register while preserving the predictive behaviour of direct encoding; more aggressive partitioning, by contrast, reveals a progressive trade-off between sequential depth and within-batch feature interaction, with mixed CRZ–CRX entanglement providing the most effective fixed-width configuration. Together, these results delineate a practical operating regime for high-dimensional local quantum learning and show that receptive-field scaling can be managed through a coordinated choice of upload granularity, entangling structure, information retention, and execution depth.
Wen-Bin Yu, Yan-Feng Fan, You-Le Wang et al.· Machine Learning: Science an...· 0 citations
Learning continuous quantum dynamical trajectories—essential for understanding non-equilibrium phenomena in quantum chemistry and condensed matter physics—remains prohibitively expensive on quantum computers. Conventional data-driven surrogates treat observables as generic time series, ignoring the governing Schrödinger evolution, and consequently require an infeasible density of samples to resolve highly oscillatory dynamics. We first establish a fundamental information-theoretic lower bound: any incoherent learning protocol that measures independently prepared copies without quantum memory needs Ω(T/ϵ2) oracle queries, revealing a quadratic penalty in 1/ϵ that renders naive dense sampling impossible. To circumvent this barrier, we introduce physics-informed kernel ridge regression (PI-KRR), which encodes the Heisenberg equation as a differentiable constraint. By extracting time derivatives from Hamiltonian commutators at zero additional quantum cost, PI-KRR doubles the information density per simulation shot without violating quantum estimation limits. Furthermore, integrated with classical shadow tomography, our framework reconstructs trajectories for M local observables simultaneously with measurement overhead scaling only as O(logM). We establish robustness guarantees for NISQ devices: isolated measurement outliers are suppressed as 1/m with training size m, and systematic Hamiltonian miscalibrations yield only linearly bounded prediction errors. Numerical experiments on transverse-field Ising models demonstrate that PI-KRR resolves sharp features such as light-cone fronts with drastically fewer simulations than standard kernel methods, achieving up to two orders of magnitude lower mean absolute error. This establishes a practical protocol for compressing complex quantum dynamics into classical predictive models, bridging quantum simulation and machine learning for experimental quantum science.
You-Le Wang, Lei Zhang· Quantum Science and Technolo...· 0 citations
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