152 citations · 506 across the 51 of their papers we have counts for
52 papers
Simulating Open Quantum Systems Using Hamiltonian Simulations
Zhiyan Ding, Xiantao Li, Lin Lin
We present a novel method to simulate the Lindblad equation, drawing on the relationship between Lindblad dynamics, stochastic differential equations, and Hamiltonian simulations.…
Random coordinate descent: a simple alternative for optimizing parameterized quantum circuits
Zhiyan Ding, Taehee Ko, Jiahao Yao +2
Variational quantum algorithms rely on the optimization of parameterized quantum circuits in noisy settings. The commonly used back-propagation procedure in classical machine learn…
Stochastic Quantum Sampling for Non-Logconcave Distributions and Estimating Partition Functions
Guneykan Ozgul, Xiantao Li, Mehrdad Mahdavi +1
We present quantum algorithms for sampling from non-logconcave probability distributions in the form of . Here, can be written as a finite sum $f(x):…
Implementation of the Density-functional Theory on Quantum Computers with Linear Scaling with respect to the Number of Atoms
Taehee Ko, Xiantao Li, Chunhao Wang
Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science. A faithful implementation of the theory requires self-consistent calculat…
Simulation-assisted learning of open quantum systems
Ke Wang, Xiantao Li
Models for open quantum systems, which play important roles in electron transport problems and quantum computing, must take into account the interaction of the quantum system with…
Quantum Simulation for Partial Differential Equations with Physical Boundary or Interface Conditions
Shi Jin, Xiantao Li, Nana Liu +1
This paper explores the feasibility of quantum simulation for partial differential equations (PDEs) with physical boundary or interface conditions. Semi-discretisation of such prob…
Quantum Simulation for Quantum Dynamics with Artificial Boundary Conditions
Shi Jin, Nana Liu, Xiantao Li +1
Quantum dynamics, typically expressed in the form of a time-dependent Schrödinger equation with a Hermitian Hamiltonian, is a natural application for quantum computing. However, wh…
Efficient Quantum Algorithms for Quantum Optimal Control
Xiantao Li, Chunhao Wang
In this paper, we present efficient quantum algorithms that are exponentially faster than classical algorithms for solving the quantum optimal control problem. This problem involve…
Simulating Markovian open quantum systems using higher-order series expansion
Xiantao Li, Chunhao Wang
We present an efficient quantum algorithm for simulating the dynamics of Markovian open quantum systems. The performance of our algorithm is similar to the previous state-of-the-ar…
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…
The Mori-Zwanzig formulation of deep learning
Daniele Venturi, Xiantao Li
We develop a new formulation of deep learning based on the Mori-Zwanzig (MZ) formalism of irreversible statistical mechanics. The new formulation is built upon the well-known duali…
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…
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…
Random Batch Algorithms for Quantum Monte Carlo simulations
Shi Jin, Xiantao Li
Random batch algorithms are constructed for quantum Monte Carlo simulations. The main objective is to alleviate the computational cost associated with the calculations of two-body…
Markovian Embedding Procedures for Non-Markovian Stochastic Schrödinger Equations
Xiantao Li
We present embedding procedures for the non-Markovian stochastic Schrödinger equations, arising from studies of quantum systems coupled with bath environments. By introducing auxil…
Estimating linear response statistics using orthogonal polynomials: An RKHS formulation
He Zhang, John Harlim, Xiantao Li
We study the problem of estimating linear response statistics under external perturbations using time series of unperturbed dynamics. Based on the fluctuation-dissipation theory, t…