Quantum Information

Quantum Computation: Pioneering Scientific Innovation

Research Focus: Quantum Computation & Information Theory

My research explores the intersection of quantum computation and information theory, emphasizing data complexity and entropy. This approach enables novel insights into handling and understanding massive, complex datasets.

Optimization of NP-Hard Problems

I am currently developing methods to approximate NP-hard quantities, essential for assessing data diversity. These methods improve how we interpret and manage complex information.

Advancements in Quantum Algorithms

I focus on quantum algorithms for solving linear systems and differential equations, crucial for advancing fields like physics and engineering.

Innovation in Stiefel Manifolds

Together with my advisors, I've developed a descent flow on Stiefel manifolds, defining critical orthogonality requirements for quantum algorithms and mathematical modeling.

--Joint work with Matthew. M. Lin and Yu-Chen Shu

Subdiffusion Equations

Research Insight: Numerical Solutions for Subdiffusion

My research employs Caputo-type fractional order diffusion equations to model subdiffusion—a phenomenon characterized by anomalous diffusion. By providing reliable numerical solutions, we gain a deeper understanding of the evolutionary processes of such systems.

Error Estimation and Application

I have estimated the error between semi-discrete and fully discrete solutions within the complex space, assessing the temporary errors that emerge during computation. This analysis is vital for refining our numerical approaches and ensuring accuracy in simulations.

Case Study: Time-Fractional Allen Cahn Equation

Applying these methods, I tackled the nonhomogeneous linear subdiffusion equation, also known as the time-fractional Allen Cahn Equation. I meticulously documented the evolution process across each iteration, enhancing our understanding of dynamic changes over time.

Visualizing Changes Across Iterations

The accompanying figures illustrate the solution at various iteration steps and fractional orders, providing a visual representation of the theory in practice and showcasing the impacts of different fractional orders on the solution behavior.

--Joint work with Yu-Chen Shu

Euler System with Relativistic Effects

The Euler system or the p-System describes the relationship between the velocity and the pressure in a fluid. In addition, as the velocity is sufficiently fast, relativistic effects occur. We discussed the spherical-symmetric solution to the Riemann problem.

--Joint work Chou Kou, Wen-Ching Lian

Image Segmentation

Segmentation in a medical image is a primary task before scientific research or diagnosis. PDE-based algorithms characterize contours by either level sets or parametrized curves. We accomplished the problem by minimizing an energy functional that consists of a data description term and a regularization term. The minimizer of the energy functional leads to the results of our inquiries. We establish a descent flow through the variation method and resolve it by existing numerical methods.

Medical Applications

In 2020, we released a patent to predict types of pathogens in patients with septicemia.

-- Joint work with Chen, Po Lin, Tsai, Cheng Yu, Shu, Yu Chen, Ko, Nai Ying, Yeh, Chun Yin, Ko, Wen Chien, Chuang, Kun Ta, Kao, Hung Yu

In 2021, we proposed a paper to examine the spatiotemporal dynamics of cerebral vascular permeability (Ktrans) in the progression of type 2 diabetes mellitus (T2DM).

-- Joint work with Ying-Chen Chen, Yu-Chen Shu, and Yuan-Ting Sun

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