152 citations · 506 across the 51 of their papers we have counts for
9 papers · 1 filter
On quantum algorithms for the Schrödinger equation in the semi-classical regime
Shi Jin, Xiantao Li, Nana Liu
Solving the time-dependent Schrödinger equation is an important application area for quantum algorithms. We consider Schrödinger's equation in the semi-classical regime. Here the s…
Some Error Analysis for the Quantum Phase Estimation Algorithms
Xiantao Li
This paper is concerned with the phase estimation algorithm in quantum computing algorithms, especially the scenarios where (1) the input vector is not an eigenvector; (2) the unit…
Succinct Description and Efficient Simulation of Non-Markovian Open Quantum Systems
Xiantao Li, Chunhao Wang
Non-Markovian open quantum systems represent the most general dynamics when the quantum system is coupled with a bath environment. The quantum dynamics arising from many important…
A Partially Random Trotter Algorithm for Quantum Hamiltonian Simulations
Shi Jin, Xiantao Li
Given the Hamiltonian, the evaluation of unitary operators has been at the heart of many quantum algorithms. Motivated by existing deterministic and random methods, we present a hy…
Stochastic Algorithms for Self-consistent Calculations of Electronic Structures
Taehee Ko, Xiantao Li
The convergence property of a stochastic algorithm for the self-consistent field (SCF) calculations of electron structures is studied. The algorithm is formulated by rewriting the…
A Projection-based Reduced-order Method for Electron Transport Problems with Long-range Interactions
Weiqi Chu, Xiantao Li
Long-range interactions play a central role in electron transport. At the same time, they present a challenge for direct computer simulations, since sufficiently large portions of…
Error Bounds of the Invariant Statistics in Machine Learning of Ergodic Itô Diffusions
He Zhang, John Harlim, Xiantao Li
This paper studies the theoretical underpinnings of machine learning of ergodic Itô diffusions. The objective is to understand the convergence properties of the invariant statistic…
Projection based model reduction for the immersed boundary method
Yushuang Luo, Xiantao Li, Wenrui Hao
Fluid-structure interactions are central to many bio-molecular processes, and they impose a great challenge for computational and modeling methods. In this paper, we consider the i…
A Machine-Learning Method for Time-Dependent Wave Equations over Unbounded Domains
Changjian Xie, Jingrun Chen, Xiantao Li
Time-dependent wave equations represent an important class of partial differential equations (PDE) for describing wave propagation phenomena, which are often formulated over unboun…