73 citations · 301 across the 13 of their papers we have counts for
13 papers
Learning many-body Hamiltonians with Heisenberg-limited scaling
Hsin-Yuan Huang, Yu Tong, Di Fang +1
Learning a many-body Hamiltonian from its dynamics is a fundamental problem in physics. In this work, we propose the first algorithm to achieve the Heisenberg limit for learning an…
Uniform observable error bounds of Trotter formulae for the semiclassical Schrödinger equation
Yonah Borns-Weil, Di Fang
Known as no fast-forwarding theorem in quantum computing, the simulation time for the Hamiltonian evolution needs to be in the worst case, which essentially states tha…
Time-marching based quantum solvers for time-dependent linear differential equations
Di Fang, Lin Lin, Yu Tong
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 compu…
Asymptotic analysis of diabatic surface hopping algorithm in the adiabatic and non-adiabatic limits
Zhenning Cai, Di Fang, Jianfeng Lu
Surface hopping algorithms, as an important class of quantum dynamics simulation algorithms for non-adiabatic dynamics, are typically performed in the adiabatic representation, whi…
Efficient quantum algorithm for nonlinear reaction-diffusion equations and energy estimation
Dong An, Di Fang, Stephen Jordan +3
Nonlinear differential equations exhibit rich phenomena in many fields but are notoriously challenging to solve. Recently, Liu et al. [1] demonstrated the first efficient quantum a…
Time-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schrödinger Equation
Dong An, Di Fang, Lin Lin
We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operat…
Observable Error Bounds of the Time-splitting Scheme for Quantum-Classical Molecular Dynamics
Di Fang, Albert Tres
Quantum-classical molecular dynamics, as a partial classical limit of the full quantum Schrödinger equation, is a widely used framework for quantum molecular dynamics. The underlyi…
Parallel transport dynamics for mixed quantum states with applications to time-dependent density functional theory
Dong An, Di Fang, Lin Lin
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 func…
Time-dependent unbounded Hamiltonian simulation with vector norm scaling
Dong An, Di Fang, Lin Lin
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 Ha…
Numerical study of ergodicity for the overdamped Generalized Langevin Equation with fractional noise
Di Fang, Lei Li
The Generalized Langevin Equation, in history, arises as a natural fix for the rather traditional Langevin equation when the random force is no longer memoryless. It has been prove…
Emergent behaviors of the Cucker-Smale ensemble under attractive-repulsive couplings and Rayleigh frictions
Di Fang, Seung-Yeal Ha, Shi Jin
In this paper, we revisit an interaction problem of two homogeneous Cucker-Smale (in short C-S) ensembles with attractive-repulsive couplings, possibly under the effect of Rayleigh…
A Diabatic Surface Hopping Algorithm based on Time Dependent Perturbation Theory and Semiclassical Analysis
Di Fang, Jianfeng Lu
Surface hopping algorithms are popular tools to study dynamics of the quantum-classical mixed systems. In this paper, we propose a surface hopping algorithm in diabatic representat…
An Efficient Time-splitting Method for the Ehrenfest Dynamics
Di Fang, Shi Jin, Christof Sparber
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-sp…