Yixuan Liang

Yixuan Liang, Jin-Peng Liu

We give detailed analysis and circuit design of structure-preserving quantum algorithms for second-order linear evolutionary PDEs, including parabolic equations and hyperbolic equations with mixed Dirichlet, Neumann, and periodic boundary conditions and source terms. While prior quantum algorithms usually neglect the stability problem from the PDE-to-ODE reduction, our method-of-lines approach investigates the boundary lifting via Coons interpolation and boundary-aware discretization, so that the resulting semi-discrete systems are stable and compatible with efficient quantum ODE primitives. For the parabolic problem, we use a diagonal similarity transform to ensure the semi-discrete generator must have a positive semi-definite Hermitian part, and then solve the resulting ODE system by the optimal linear combination of Hamiltonian simulation (LCHS). For the hyperbolic problem, we rewrite the semi-discrete equation as an equivalent first-order system and solve it by Hamiltonian simulation. We implement our quantum algorithms with explicit block-encoding constructions and circuit implementations, as well as demonstrating the end-to-end complexity bounds together with spatial and quadrature error estimates. We conduct classical numerical experiments on the convection-diffusion equation, inhomogeneous heat equation, and Klein-Gordon equation to validate our structure-preserving analysis and algorithmic constructions.

Yixuan Liang, Yuncong Liu, Neng Wang et al.

Financial sentiment analysis is crucial for understanding the influence of news on stock prices. Recently, large language models (LLMs) have been widely adopted for this purpose due to their advanced text analysis capabilities. However, these models often only consider the news content itself, ignoring its dissemination, which hampers accurate prediction of short-term stock movements. Additionally, current methods often lack sufficient contextual data and explicit instructions in their prompts, limiting LLMs' ability to interpret news. In this paper, we propose a data-driven approach that enhances LLM-powered sentiment-based stock movement predictions by incorporating news dissemination breadth, contextual data, and explicit instructions. We cluster recent company-related news to assess its reach and influence, enriching prompts with more specific data and precise instructions. This data is used to construct an instruction tuning dataset to fine-tune an LLM for predicting short-term stock price movements. Our experimental results show that our approach improves prediction accuracy by 8\% compared to existing methods.