Scholars@Duke
Di Fang

Di Fang

Assistant Professor of Mathematics
Mathematics
di.fang@duke.edu
515 S Mangum St, #5302, Durham, NC 27701

Selected Publications

Mixing Time of Open Quantum Systems via Hypocoercivity.

Journal Article Physical review letters · April 2025 Understanding the mixing of open quantum systems is a fundamental problem in physics and quantum information science. Existing approaches for estimating the mixing time often rely on the spectral gap estimation of the Lindbladian generator, which can be ch ... Full text Cite

UNIFORM OBSERVABLE ERROR BOUNDS OF TROTTER FORMULAE FOR THE SEMICLASSICAL SCHRÖDINGER EQUATION

Journal Article Multiscale Modeling and Simulation · January 1, 2025 Known as the no fast-forwarding theorem in quantum computing (see, e.g., Theorem 3 in [D. W. Berry et al., Comm. Math. Phys., 270 (2007), pp. 359-371], Theorem 5 in [A. M. Childs, Comm. Math. Phys., 294 (2010), pp. 581-603], and [R. Kothari, Efficient Simu ... Full text Cite

Efficient Quantum Algorithm for Nonlinear Reaction–Diffusion Equations and Energy Estimation

Journal Article Communications in Mathematical Physics · December 1, 2023 Nonlinear differential equations exhibit rich phenomena in many fields but are notoriously challenging to solve. Recently, Liu et al. (in: Proceedings of the National Academy of Sciences 118(35), 2021) demonstrated the first efficient quantum algorithm for ... Full text Cite

Learning Many-Body Hamiltonians with Heisenberg-Limited Scaling.

Journal Article Physical review letters · May 2023 Learning a many-body Hamiltonian from its dynamics is a fundamental problem in physics. In this Letter, we propose the first algorithm to achieve the Heisenberg limit for learning an interacting N-qubit local Hamiltonian. After a total evolution time of O( ... Full text Cite

Observable Error Bounds of the Time-Splitting Scheme for Quantum-Classical Molecular Dynamics

Journal Article SIAM Journal on Numerical Analysis · February 28, 2023 Full text Cite

Time-marching based quantum solvers for time-dependent linear differential equations

Journal Article Quantum · January 1, 2023 The time-marching strategy, which propagates the solution from one time step to the next, is a natural strategy for solving time-dependent differential equations on classical computers, as well as for solving the Hamiltonian simulation problem on quantum c ... Full text Cite

Parallel transport dynamics for mixed quantum states with applications to time-dependent density functional theory

Journal Article Journal of Computational Physics · February 15, 2022 Direct simulation of the von Neumann dynamics for a general (pure or mixed) quantum state can often be expensive. One prominent example is the real-time time-dependent density functional theory (rt-TDDFT), a widely used framework for the first principle de ... Full text Cite

Time-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schrödinger Equation

Journal Article Quantum · January 1, 2022 We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm that is both inse ... Full text Cite

Time-dependent unbounded Hamiltonian simulation with vector norm scaling

Journal Article Quantum · January 1, 2021 The accuracy of quantum dynamics simulation is usually measured by the error of the unitary evolution operator in the operator norm, which in turn depends on certain norm of the Hamiltonian. For unbounded operators, after suitable discretization, the norm ... Full text Cite

Numerical approximation and fast evaluation of the overdamped generalized Langevin equation with fractional noise

Journal Article ESAIM: Mathematical Modelling and Numerical Analysis · March 1, 2020 The generalized Langevin equation (GLE) is a stochastic integro-differential equation that has been used to describe the movement of microparticles with sub-diffusion phenomenon. It has been proved that with fractional Gaussian noise (fGn) mostly considere ... Full text Cite

Emergent behaviors of the Cucker-Smale ensemble under attractive-repulsive couplings and Rayleigh frictions

Journal Article Mathematical Models and Methods in Applied Sciences · June 30, 2019 In this paper, we revisit an interaction problem of two homogeneous Cucker-Smale (in short CS) ensembles with attractive-repulsive couplings, possibly under the effect of Rayleigh friction, and study three sufficient frameworks leading to bi-cluster flocki ... Full text Cite

Implicit and Semi-implicit Numerical Schemes for the Gradient Flow of the Formation of Biological Transport Networks

Journal Article SMAI Journal of Computational Mathematics · January 1, 2019 Implicit and semi-implicit time discretizations are developed for the Cai–Hu model describing the formation of biological transport networks. The model couples a nonlinear elliptic equation for the pressure with a nonlinear reaction-diffusion equation for ... Full text Cite

A diabatic surface hopping algorithm based on time dependent perturbation theory and semiclassical analysis

Journal Article Multiscale Modeling and Simulation · January 1, 2018 Surface hopping algorithms are popular tools to study dynamics of the quantumclassical mixed systems. In this paper, we propose a surface hopping algorithm in diabatic representations, based on time dependent perturbation theory and semiclassical analysis. ... Full text Open Access Cite

An efficient time-splitting method for the ehrenfest dynamics

Journal Article Multiscale Modeling and Simulation · January 1, 2018 The Ehrenfest dynamics, representing a quantum-classical mean-field type coupling, is a widely used approximation in quantum molecular dynamics. In this paper, we propose a time-splitting method for an Ehrenfest dynamics, in the form of a nonlinearly coupl ... Full text Cite