A. Li

Senrui Chen, Francesco Anna Mele, Marco Fanizza et al.

Continuous-variable systems enable key quantum technologies in computation, communication, and sensing. Bosonic Gaussian states emerge naturally in various such applications, including gravitational-wave and dark-matter detection. A fundamental question is how to characterize an unknown bosonic Gaussian state from as few samples as possible. Despite decades-long exploration, the ultimate efficiency limit remains unclear. In this work, we study the necessary and sufficient number of copies to learn an $n$-mode Gaussian state, with energy less than $E$, to $\varepsilon$ trace distance with high probability. We prove a lower bound of $Ω(n^3/\varepsilon^2)$ for Gaussian measurements, matching the best known upper bound up to doubly-log energy dependence, and $Ω(n^2/\varepsilon^2)$ for arbitrary measurements. We further show an upper bound of $\widetilde{O}(n^2/\varepsilon^2)$ given that the Gaussian state is promised to be either pure or passive. Interestingly, while Gaussian measurements suffice for nearly optimal learning of pure Gaussian states, non-Gaussian measurements are provably required for optimal learning of passive Gaussian states. Finally, focusing on learning single-mode Gaussian states via non-entangling Gaussian measurements, we provide a nearly tight bound of $\widetildeΘ(E/\varepsilon^2)$ for any non-adaptive schemes, showing adaptivity is indispensable for nearly energy-independent scaling. As a byproduct, we establish sharp bounds on the trace distance between Gaussian states in terms of the total variation distance between their Wigner distributions, and obtain a nearly tight sample complexity bound for learning the Wigner distribution of any Gaussian state to $\varepsilon$ total variation distance. Our results greatly advance quantum learning theory in the bosonic regimes and have practical impact in quantum sensing and benchmarking applications.

ZhengXiao He, Jinghao Wen, Huayu Li et al.

We present a novel and interpretable framework for electrocardiogram (ECG)-based disease detection that combines hyperdimensional computing (HDC) with learnable neural encoding. Unlike conventional HDC approaches that rely on static, random projections, our method introduces a rhythm-aware and trainable encoding pipeline based on RR intervals, a physiological signal segmentation strategy that aligns with cardiac cycles. The core of our design is a neural-distilled HDC architecture, featuring a learnable RR-block encoder and a BinaryLinear hyperdimensional projection layer, optimized jointly with cross-entropy and proxy-based metric loss. This hybrid framework preserves the symbolic interpretability of HDC while enabling task-adaptive representation learning. Experiments on Apnea-ECG and PTB-XL demonstrate that our model significantly outperforms traditional HDC and classical ML baselines, achieving 73.09\% precision and an F1 score of 0.626 on Apnea-ECG, with comparable robustness on PTB-XL. Our framework offers an efficient and scalable solution for edge-compatible ECG classification, with strong potential for interpretable and personalized health monitoring.