Linear-combination-of-unitaries decomposition for the Laplace operator
Physical Review A 114, 012455 (2026).
Research
Quantum algorithms.
Nonlinear mathematics.
I study how the structure of differential equations can inform quantum algorithms—and how nonlinear models behave beyond perturbative regimes.
Current research
Quantum computing for PDEs
My postdoctoral research at the U.S. Naval Research Laboratory focuses on quantum algorithms for discretized partial differential equations arising in physics and fluid dynamics. Problems of interest include Poisson’s equation, the viscous Burgers’ equation, and discrete velocity and lattice Boltzmann models.
I work on matrix decompositions, block encoding of unitary and non-unitary operators, and quantum circuit constructions. I also analyze resource requirements for near-term and fault-tolerant frameworks, alongside the accuracy, convergence, and stability of the underlying numerical schemes.
My broader interests include numerical linear algebra, optimization, and the simulation of complex physical systems.
Publications & preprints
Selected research papers
Efficient decomposition of the Carleman linearized Burgers’ equation
Physical Review A 113, 032408 (2026).
Quantum data loading for Carleman linearized systems: Application to the lattice-Boltzmann equation
arXiv:2605.00302 (2026). Preprint.
Broadening global families of anti-plane shear equilibria
SIAM Journal on Mathematical Analysis 53, 5853–5879 (2021).
Talks & posters
Selected presentations
September 18, 2026 · Scheduled
Linear Combination of Non-Unitaries: Theory, Computation and Applications
IEEE Quantum Week 2026 · Toronto, Canada
Tutorial co-organizer and presenter. Tutorial information
August 2026
A Linear Combination of Unitaries Decomposition for the Laplace Operator
US CLIVAR Quantum Computing and Sensing for Weather and Climate Applications Workshop · Boulder, Colorado
Poster presentation.
April 2022
Nonlinear evolution equations and wave phenomena
Twelfth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory
Conference talk.
2021
KUMUNU-ISU Conference on PDE, Dynamical Systems, and Applications
Poster presentation.
Doctoral research
Bifurcation theory and nonlinear PDEs
My dissertation at the University of Missouri–Columbia studied nonlinear elliptic equations motivated by elasticity and gas dynamics. A central theme was the global behavior of solution families: what happens as solutions move far from a small-amplitude or perturbative regime?
In Broadening global families of anti-plane shear equilibria, I constructed families of equilibria for classes of nonlinear elastic materials. Depending on the material model, these families exhibit broadening or a loss of ellipticity.
I am interested in how classical elliptic tools—including maximum principles, the Hopf lemma, and regularity theory—adapt when ellipticity degenerates. Related questions arise in transonic flow and nonlinear wave problems.