Research

My research asks a common question across several domains: how can mathematical structure and advanced computational technologies deepen our understanding of complex quantum systems while making their simulation more accurate, efficient, and interpretable? I work at the intersection of computational mathematics, numerical and applied analysis, fault-tolerant quantum algorithms, quantum error correction, quantum many-body systems, mathematical physics, multiscale quantum materials, and scientific machine learning.

Quantum algorithms & implementation

Structure-preserving quantum algorithms and practical circuits

I develop algorithms and explicit circuits for representing, preparing, and evolving quantum many-body systems 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 end to end, builds low-gate-count block encodings for second-quantized Hamiltonians, and studies Hamiltonian simulation and higher-dimensional circuit synthesis. The aim is a practical theory of quantum scientific computing: mathematically controlled algorithms whose costs reflect the machines we can plausibly build.

Representative papers State-preparation resource estimation Low-gate-count block encoding Pairing Hamiltonian circuits

Applied analysis & mathematical physics

Quantum dynamics across scales

I study quantum dynamics using tools from numerical and applied analysis, multiscale analysis, and mathematical physics. These interests include open quantum systems and Magnus expansions for time-dependent Hamiltonian simulation, alongside multiscale models for quantum many-body systems and materials.

Twisted two-dimensional materials provide a central testbed: their atomic models become aperiodic at generic twist angles. I analyze how infinite, incommensurate systems can be approximated on finite domains and when reduced continuum models faithfully reproduce their electronic structure and dynamics. This work connects spectral theory, partial differential equations, and computation, supporting reliable models that move between atomic-scale mechanisms and experimentally relevant moiré scales.

Representative papers Magnus expansion & superconvergence High-order Magnus expansion Electronic dynamics in twisted bilayer graphene Seeing moiré

AI for Quantum

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.

Representative papers Learning local density of states Convolutional learning for twistronics

Fault tolerance & quantum error correction

Protecting quantum computation with codes and resource-aware design

Reliable quantum computation requires more than low gate counts: physical operations must become protected logical operations without losing sight of the resulting overhead. I study fault-tolerant primitives and higher-dimensional quantum error-correcting codes, emphasizing how their algebraic structure shapes both reliability and implementation.

One direction develops magic-state distillation from asymptotically good codes on qudits, extending fault-tolerance ideas beyond standard qubit constructions. A complementary direction connects circuit synthesis and end-to-end logical resource estimation to the costs imposed by error correction in practice. The goal is to make quantum error correction part of the full algorithmic analysis, from mathematical design to compiled workload.

Representative papers Magic-state distillation on qudits Single-qutrit circuit synthesis Logical resource estimation

Looking ahead

A unified program in computational mathematics for quantum science

I am building a research program in computational mathematics and theoretical applied mathematics that moves ideas in both directions between classical and quantum computation: using numerical and applied analysis to make quantum algorithms and error correction practical, and using quantum many-body systems to motivate new mathematics for multiscale models, dynamics, and scientific machine learning.