arXiv:2607. 09906v1 Announce Type: cross Abstract: We present, to our knowledge, the first adaptation of Pauli Correlation Encoding (PCE) to quantum topological data analysis, reformulating Betti number estimation as a depth-efficient variational optimization over a compressed qubit register.
arXiv:2604. 23743v2 Announce Type: replace-cross Abstract: Variational quantum circuits train poorly on chaotic forecasting, usually blamed on barren plateaus (exponentially vanishing gradients).
arXiv:2605. 30952v2 Announce Type: replace Abstract: Two recent results have reshaped quantum Gaussian processes (QGPs).
arXiv:2608. 04252v1 Announce Type: cross Abstract: The dynamical Lie algebraic (DLA) theory of variational quantum algorithms (VQAs) predicts commonplace exponentially vanishing loss and gradient variances for sufficiently deep parametrized circuits.
arXiv:2609.14424v1 Announce Type: cross Abstract: Reporting the Fisher geometry of a trained variational quantum model is routine; quoting the shot budget that would establish it is not. Certifying a...
arXiv:2606. 13422v2 Announce Type: replace-cross Abstract: We develop theoretical foundations for a practical quantum-advantage mechanism in quantum-informed machine learning for chaotic dynamical systems.
arXiv:2607. 01329v1 Announce Type: cross Abstract: The geometric and topological structure of quantum cost landscapes (QCLs) governs the optimization and thus the predictive power of variational quantum algorithms (VQAs).
arXiv:2606. 20183v1 Announce Type: new Abstract: Recent quantum vision models-quantum vision transformers and quantum convolutional networks-report two striking but unexplained empirical phenomena: (i) ansatze with more, or more uniformly distributed, entanglement generalize better, and (ii) injecting quantum noise can improve test accuracy rather than degrade it.
arXiv:2607. 11013v1 Announce Type: cross Abstract: Data re-uploading parameterized quantum circuits (DRU-PQCs) are universal function approximators, yet their expressivity produces oscillatory, non-convex loss landscapes that resist gradient-based optimization.
arXiv:2608.24527v1 Announce Type: cross Abstract: We prove the first quantum--classical separation for a sampling problem over a continuous domain. For a class of Gibbs states $p\propto e^{-\beta E}$...
arXiv:2608. 14941v1 Announce Type: new Abstract: Counting the global optima of a classical optimization problem is a #P-hard task.
arXiv:2607. 03278v1 Announce Type: cross Abstract: Topological data analysis (TDA) is a machine learning technique that uses topology to extract patterns from data and has shown the potential to exhibit quantum advantage.
arXiv:2605. 03573v4 Announce Type: replace-cross Abstract: Score-based diffusion can be defined intrinsically on the manifold of quantum pure states, $\mathbb{CP}^{d-1}$ with the Fubini--Study metric, but no closed-form transition density is available, so the score must be supervised by a local-time teacher taken from the Euclidean limit of the diffusion in normal coordinates.