89 citations · 388 across the 18 of their papers we have counts for
18 papers
Laplace transform based quantum eigenvalue transformation via linear combination of Hamiltonian simulation
Dong An, Andrew M. Childs, Lin Lin +1
Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computati…
Quantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters
Dong An, Andrew M. Childs, Lin Lin
We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian s…
Linear combination of Hamiltonian simulation for nonunitary dynamics with optimal state preparation cost
Dong An, Jin-Peng Liu, Lin Lin
We propose a simple method for simulating a general class of non-unitary dynamics as a linear combination of Hamiltonian simulation (LCHS) problems. LCHS does not rely on convertin…
Quantum differential equation solvers: limitations and fast-forwarding
Dong An, Jin-Peng Liu, Daochen Wang +1
We study the limitations and fast-forwarding of quantum algorithms for linear ordinary differential equation (ODE) systems with a particular focus on non-quantum dynamics, where th…
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…
Optimal scaling quantum linear systems solver via discrete adiabatic theorem
Pedro C. S. Costa, Dong An, Yuval R. Sanders +3
Recently, several approaches to solving linear systems on a quantum computer have been formulated in terms of the quantum adiabatic theorem for a continuously varying Hamiltonian.…
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…
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…
Quantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance
Dong An, Noah Linden, Jin-Peng Liu +3
Inspired by recent progress in quantum algorithms for ordinary and partial differential equations, we study quantum algorithms for stochastic differential equations (SDEs). Firstly…
Towards sharp error analysis of extended Lagrangian molecular dynamics
Dong An, Lin Lin, Michael Lindsey
The extended Lagrangian molecular dynamics (XLMD) method provides a useful framework for reducing the computational cost of a class of molecular dynamics simulations with constrain…
Fast inversion, preconditioned quantum linear system solvers, and fast evaluation of matrix functions
Yu Tong, Dong An, Nathan Wiebe +1
Preconditioning is the most widely used and effective way for treating ill-conditioned linear systems in the context of classical iterative linear system solvers. We introduce a qu…
Stochastic Constrained Extended System Dynamics for Solving Charge Equilibration Models
Songchen Tan, Itai Leven, Dong An +2
We present a new stochastic extended Lagrangian solution to charge equilibration that eliminates self-consistent field (SCF) calculations, eliminating the computational bottleneck…
Split representation of adaptively compressed polarizability operator
Dong An, Lin Lin, Ze Xu
The polarizability operator plays a central role in density functional perturbation theory and other perturbative treatment of first principle electronic structure theories. The co…
Quantum linear system solver based on time-optimal adiabatic quantum computing and quantum approximate optimization algorithm
Dong An, Lin Lin
We demonstrate that with an optimally tuned scheduling function, adiabatic quantum computing (AQC) can readily solve a quantum linear system problem (QLSP) with $\mathcal{O}(κ~\tex…
Convergence of Stochastic-extended Lagrangian molecular dynamics method for polarizable force field simulation
Dong An, Sara Y. Cheng, Teresa Head-Gordon +2
Extended Lagrangian molecular dynamics (XLMD) is a general method for performing molecular dynamics simulations using quantum and classical many-body potentials. Recently several n…
Fast real-time time-dependent density functional theory calculations with the parallel transport gauge
Weile Jia, Dong An, Lin-Wang Wang +1
Real-time time-dependent density functional theory (RT-TDDFT) is known to be hindered by the very small time step (attosecond or smaller) needed in the numerical simulation due to…
Quantum Dynamics with the Parallel Transport Gauge
Dong An, Lin Lin
The dynamics of a closed quantum system is often studied with the direct evolution of the Schrodinger equation. In this paper, we propose that the gauge choice (i.e. degrees of fre…