I am mostly a quantum person, and have also worked on some biological models and stochastic differential equations. After joining Berkeley and attending the Simons Institute program on the Quantum Wave in Computing, I became intrigued by quantum algorithms. At this point, my passion mainly lies in the following three different types of quantum problems:
- classical for quantum, namely to simulate and analyze quantum systems on classical computers. My expertise is to deal with the non-adiabaticity (beyond Born-Oppenheimer approximation) and/or nonlinearity of the Schroedinger equations emerging from the ab initio molecular dynamics.
The specific topics I have worked on include semiclassical descriptions, Ehrenfest mean-field dynamics, trajectory-based surface hopping, TDDFT for metallic systems.
- quantum for classical, namely to use quantum computers to solve classical differential equations. Due to no-cloning theorem, quantum measurements and so on, the major numerical challenges here can be very different from numerical analysis of classical algorithms. This area is still in its early stage and, together with collaborators, we are exploring slowly and see what we can do. (preprint in preparation)
- *quantum for quantum* (this is my current major focus), namely to use quantum computers to solve quantum practical problems. In particular, I am interested in real space Hamiltonian simulation, and development of quantum algorithms and proof of error bounds for such problems. (preprint in preparation)
The tools and techniques that I use the most are, but not limited to, numerical analysis, semiclassical analysis, stochastic analysis and quantum computation. I am by no means an expert in all these areas, but as a problem-targeted person, I learn the techniques along the way to solve the practical problems in mind.