Intro

I am currently a Postdoctoral Scholar at Berkeley Lab in the Applied Mathematics and Computational Research Division. Computational mathematics and theoretical applied mathematics are the areas I would mainly work on. I would also be interested in understanding properties(electronic, mechanical, or optical) of quantum materials through a fundamental and first-principles way. 

Before joining the lab, I received my Ph.D. in Applied Mathematics from the University of Minnesota, where I was advised by Mitch Luskin. During my time there, I also worked closely with Alex Watson and Stephen Carr. I earned my B.S. in Mathematics and Applied Mathematics from Shanghai Jiao Tong University, where I was advised by Lei Zhang and completed my undergraduate thesis under the supervision of Houman Owhadi.

My research focuses on developing numerical methods and mathematical tools motivated by applications in condensed matter physics, mechanics, and medical science. More specifically, I have worked on numerical analysis, applied analysis, and mathematical physics with an emphasis on quantum materials and quantum technologies. In addition, I am interested in applying machine learning and quantum computing to scientific computing. 

Although I am currently less active in areas such as ab initio calculations + classical method for electronic structure, domain decomposition methods, and applied probability due to time constraints, I remain engaged with these topics and hope to return to them in the future.

Recent focus:

(1) Moire Material:  TMD with multi-scale analysis

(2) Quantum Simulation: 

I-Block Encoding and state preparation

II-Magnus Expansion

III-Open Quantum System

Q&A:

1. People asked me why an applied math guy cares about QEC and hardware. What is wrong with me?

For a long time, I was thinking about what numerical analysis would be like in the Quantum Era, where an early fault-tolerant quantum computer exists even with a small code distance (leading to large machine error). About 60-70 years ago,  many great numerical analysts developed algorithms for solving linear algebra problems, differential equations, tensor calculations and etl. You may have heard a lot of names of people(Saad, Trefethen, Osher, Greengard.......). Today, can we do the same thing with a quantum computer? What is different?

Error correction can be a major difference. Achieving error correction is much harder for quantum devices. When the machine error (determined by error correction and hardware) is comparable to or exceeds the algorithm error, it may be necessary for a quantum numerical analyst to analyze both the algorithm, error correction, and hardware influence to understand what on earth does the output data means. It may take a very, very long time to have a quantum computer with machine error 10^{-20}. This will likely be a smooth phase transition from a noisy quantum device to a high-performance quantum computer. This could be needed for people doing analog computing as well.

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