Research

Quantum mechanics is over one hundred years old and remains one of the most successful and tested scientific theories ever developed. It explains particle behavior with extraordinary precision, using classical mathematics to describe phenomena—phase, interference, and entanglement—which are inherently global rather than local. In parallel, modern mathematics and computer science have evolved dramatically during the twentieth century and beyond, introducing new ways to describe structure, dynamics, information, and computation.

My research investigates how modern mathematical ideas—particularly topology, category theory, type theory, and homotopy—can clarify the structure of quantum dynamics governed by Hamiltonians. In quantum physics, Hamiltonians describe how systems evolve in time, and they play a central role in quantum simulation, quantum algorithms, and emerging quantum technologies. A key observation is that many important quantum effects, such as phase accumulation and interference, depend not on local details but on global structure, often best described using geometric or topological concepts.

I study how quantum system simulation and Hamiltonian dynamics can be understood in terms of loops, connectivity, and equivalence between different descriptions of the same physical process. This approach reveals that seemingly different quantum models or simulations may represent the same underlying dynamics when viewed at the right level of abstraction. These ideas also connect naturally to research on quantum programming languages and formal models of computation, which aim to describe quantum processes in a precise, compositional way.

Alongside theory, I have worked in a trapped-ion quantum computing laboratory, where Hamiltonian control and geometric phase play a direct experimental role. My long-term goal is to develop unifying frameworks that connect Hamiltonian physics, quantum computation, and modern mathematics, helping bridge theory, simulation, and experiment.


Publications