Research
My research asks a common question across several domains: how can mathematical structure make difficult scientific computations more accurate, efficient, and interpretable? I combine numerical analysis, applied analysis, mathematical physics, and algorithm design to answer that question.
Quantum algorithms
Resource-efficient simulation of quantum systems
I develop algorithms and explicit circuits for representing and evolving many-body Hamiltonians on quantum computers. A central theme is to preserve physical structure—sparsity, particle number, commutators, and interaction geometry—rather than discard it in a generic encoding.
My recent work compares compiled state-preparation methods through end-to-end logical resource estimates, builds low-gate-count block encodings for second-quantized Hamiltonians, analyzes Magnus-based simulation of time-dependent dynamics, and studies higher-dimensional circuit synthesis and fault-tolerant primitives. The aim is a practical theory of quantum scientific computing: mathematically controlled algorithms whose resource estimates reflect the machines we can plausibly build.
Mathematical physics
Multiscale models for aperiodic quantum materials
Twisted two-dimensional materials exhibit striking electronic behavior, but their atomic models become aperiodic at generic twist angles. I study how infinite, incommensurate systems can be approximated on finite domains and when reduced continuum models faithfully reproduce their dynamics.
This work connects spectral theory, partial differential equations, multiscale analysis, and computation. It supports a broader goal: reliable mathematical models that move between atomic-scale mechanisms and experimentally relevant moiré scales.
Scientific machine learning
Learning physical operators with mathematical guarantees
I use machine learning where it complements—not replaces—analysis. For moiré materials, this means identifying representations tied to physical observables and asking whether the operator to be learned exists, is regular, and can be approximated in a stable way.
By formulating operator learning as an inverse problem, my collaborators and I studied well-posedness and approximation for learning the twist operator that maps aligned-bilayer electronic information to its twisted counterpart. This perspective guides future work on trustworthy learning for multiscale physics.
Looking ahead
A unified program in structure-aware scientific computing
I am building a research program that moves ideas in both directions between classical and quantum computation: using numerical analysis and scientific computing to make quantum algorithms realistic, and using questions from quantum science to motivate new mathematics for multiscale models, dynamics, and learning.