14 citations · 42 across the 12 of their papers we have counts for
18 papers
Enabling Quantum Speedup of Markov Chains using a Multi-level Approach
Xiantao Li
Quantum speedup for mixing a Markov chain can be achieved based on the construction of slowly-varying Markov chains where the initial chain can be easily prepared and the spect…
A Local Convergence Theory for the Stochastic Gradient Descent Method in Non-Convex Optimization With Non-isolated Local Minima
Taehee Ko, Xiantao Li
Loss functions with non-isolated minima have emerged in several machine learning problems, creating a gap between theory and practice. In this paper, we formulate a new type of loc…
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…
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…