Entropy

We present hybrid quantum–classical algorithms to compute time-dependent Møller wavepacket correlation functions via digital quantum simulation. Reactant and product channel wavepackets are encoded as qubit states, evolved under a discretized molecular Hamiltonian, and their correlation is reconstructed using both a modified Hadamard test and a multi-fidelity estimation (MFE) protocol. The method is applied to the collinear H + H₂ exchange reaction on a London–Eyring–Polanyi–Sato potential energy surface. Quantum-estimated correlation functions show quantitative agreement with high-resolution classical wavepacket simulations across the full time domain, reproducing both short-time scattering peaks and long-time oscillatory dynamics. The ancilla-free MFE protocol achieves matching results with reduced circuit depth. These results provide a proof of principle that digital quantum circuits can be used to accurately calculate the wavepacket correlation functions for a benchmark chemical reaction system.

This work implements deep learning models to capture non-linear and complex data behavior in aluminum price data. Deep learning models include the long short-term memory (LSTM) and deep feedforward neural networks (FFNN). The support vector regression (SVR) is employed as a base model for comparison. Each predictive model is tuned by using two different optimization methods: Bayesian optimization (BO) and random search (RS). All models are tested on daily, weekly, and monthly data. Three performance metrics are used to evaluate each forecasting model: the root mean squared error (RMSE), mean absolute error (MAE), and the coefficient of determination (R²). The experimental results show that the LSTM-BO is the best-performing model across the time horizons (daily, weekly, and monthly). By consistently achieving the lowest RMSE, MAE, and highest R², the LSTM-BO outperformed all the other models, including SVR-BO, FFNN-BO, LSTM-RS, SVR-RS, and FFNN-RS. In addition, predictive models utilizing BO regularly outperformed those using RS. In summary, LSTM-BO is highly beneficial for aluminum spot price forecasting.

Learning from heterogeneous graphs under the constraints of both data scarcity and data privacy presents a significant challenge. While graph prompt learning offers a pathway for efficient few-shot adaptation, and federated learning provides a paradigm for decentralized training, their direct integration for heterogeneous graphs is non-trivial due to structural complexity and the need for rigorous privacy guarantees. This paper proposes FedHGPrompt, a novel federated framework that bridges this gap through a cohesive architectural design. Our approach introduces a three-layer model: a unification layer employing dual templates to standardize heterogeneous graphs and tasks, an adaptation layer utilizing trainable dual prompts to steer a frozen pre-trained model for few-shot learning, and a privacy layer integrating a cryptographic secure aggregation protocol. This design ensures that the central server only accesses aggregated updates, thereby cryptographically safeguarding individual client data. Extensive evaluations on three real-world heterogeneous graph datasets (ACM, DBLP, and Freebase) demonstrate that FedHGPrompt achieves superior few-shot learning performance compared to existing federated graph learning baselines (including FedGCN, FedGAT, FedHAN, and FedGPL) while maintaining strong privacy assurances and practical communication efficiency. The framework establishes an effective approach for collaborative learning on distributed, heterogeneous graph data where privacy is paramount.