About
I am a PhD student in computer science at Caltech, advised by Thomas Vidick, Urmila Mahadev, and John Preskill . I am broadly interested in quantum algorithm and quantum complexity, especially in understanding potential quantum advantage for solving quantum many-body systems, like estimating ground energy and preparing ground states / Gibbs states. Understanding quantum many-body systems are fundamanetal questions in quanutum chemistry and condense matter physics, examples are the electronic structure problem, the 2D Hubbard model, and the SYK model.
My dream result would be finding rigorous and explicit evidence that quantum computer can provide advantage for the ground energy estimation problems, that is a many-body system which can be solved by efficient quantum algorithm, but not by any known efficient classical algorithm. Here explicit means the many-body system is of physics or chemistry interest. Examples of such results would be proving fast thermalization for SYK model and other natural Hamiltonians.
Recently I was working on understanding the boundary of quantum advantage, for ground energy estimation with guided states (See as Arxiv:2309.10155), and the role of non-commutativity in the hardness of estimating ground energy (See as Arxiv:2309.04910). I am also interested in classical algorithms for ground energy estimation like quantum monte-caro method and tensor-network based method. I am getting more and more interested in fermionic Hamiltonian due to its close relationship with nature.
Feel free to contact me if you happen to be interested in similar questions, or just want to say hello :)