Di Fang

Research Interests

applied and numerical analysis, differential equations, quantum algorithms, quantum computing

Education

• Ph.D. University of Wisconsin, Madison, 2019

Trainings & Certifications

• Morrey Assistant Professor, DEPARTMENT OF MATHEMATICS, (2019 - 2022) University of California, Berkeley
• Simons Quantum Postdoctoral Fellow, SIMONS INSTITUTE FOR THE THEORY OF COMPUTING (2022 - 2023) University of California, Berkeley

Positions

• Assistant Professor of Mathematics
• Member of the Duke Quantum Center

Courses Taught

• MATH 799: Special Readings
• MATH 790-90: Minicourse in Advanced Topics
• MATH 690-70: Topics in Applied Mathematics
• MATH 555: Ordinary Differential Equations

Publications

• Borns-Weil Y, Fang D. UNIFORM OBSERVABLE ERROR BOUNDS OF TROTTER FORMULAE FOR THE SEMICLASSICAL SCHRu00d6DINGER EQUATION. Multiscale Modeling and Simulation. 2025 Jan 1;23(1):255u201377.
• Fang D, Liu D, Sarkar R. Time-dependent Hamiltonian Simulation via Magnus Expansion: Algorithm and Superconvergence. arXiv. 2024.
• Fang D, Lu J, Tong Y. Mixing Time of Open Quantum Systems via Hypocoercivity. 2024.
• Liu JP, An D, Fang D, Wang J, Low GH, Jordan S. Efficient Quantum Algorithm for Nonlinear Reactionu2013Diffusion Equations and Energy Estimation. Communications in Mathematical Physics. 2023 Dec 1;404(2):963u20131020.
• An D, Fang D, Jordan S, Liu J-P, Low GH, Wang J. Efficient quantum algorithm for nonlinear reaction-diffusion equations and energy estimation. Commun Math Phys. 2023 Oct 31;404:963u20131020.
• Borns-Weil Y, Fang D. Uniform observable error bounds of Trotter formulae for the semiclassical Schru00f6dinger equation. arXiv 2208.07957. 2023.
• Huang H-Y, Tong Y, Fang D, Su Y. Learning Many-Body Hamiltonians with Heisenberg-Limited Scaling. Physical review letters. 2023 May;130(20):200403.
• Fang D, Vilanova AT. Observable Error Bounds of the Time-Splitting Scheme for Quantum-Classical Molecular Dynamics. SIAM Journal on Numerical Analysis. 2023 Feb 28;61(1):26u201344.
• Fang D, Lin L, Tong Y. Time-marching based quantum solvers for time-dependent linear differential equations. Quantum. 2023 Jan 1;7.
• Cai Z, Fang D, Lu J. Asymptotic analysis of diabatic surface hopping algorithm in then adiabatic and non-adiabatic limits. 2022.
• An D, Fang D, Lin L. Parallel transport dynamics for mixed quantum states with applications to time-dependent density functional theory. Journal of Computational Physics. 2022 Feb 15;451.
• An D, Fang D, Lin L. Time-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schru00f6dinger Equation. Quantum. 2022 Jan 1;6.
• An D, Fang D, Lin L. Time-dependent unbounded Hamiltonian simulation with vector norm scaling. Quantum. 2021 Jan 1;5:1u201349.
• Fang D, Li L. Numerical approximation and fast evaluation of the overdamped generalized Langevin equation with fractional noise. ESAIM: Mathematical Modelling and Numerical Analysis. 2020 Mar 1;54(2):431u201363.
• Fang D, Ha SY, Jin S. Emergent behaviors of the Cucker-Smale ensemble under attractive-repulsive couplings and Rayleigh frictions. Mathematical Models and Methods in Applied Sciences. 2019 Jun 30;29(7):1349u201385.
• Fang D, Jin S, Markowich P, Perthame B. Implicit and Semi-implicit Numerical Schemes for the Gradient Flow of the Formation of Biological Transport Networks. SMAI Journal of Computational Mathematics. 2019 Jan 1;5:229u201349.
• Fang D, Jin S, Sparber C. An efficient time-splitting method for the ehrenfest dynamics. Multiscale Modeling and Simulation. 2018 Jan 1;16(2):900u201321.
• Fang D, Lu J. A diabatic surface hopping algorithm based on time dependent perturbation theory and semiclassical analysis. Multiscale Modeling and Simulation. 2018 Jan 1;16(4):1603u201322.

In The News

• New Math Faculty Represent New Wave of Computational Thinking (Oct 9, 2023 | Department of Mathematics)