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07/13/2023
Implementation of the Density-functional Theory on Quantum Computers with Linear Scaling with respect to the Number of Atoms
Density-functional theory (DFT) has revolutionized computer simulations ...
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04/05/2023
Efficient Quantum Algorithms for Quantum Optimal Control
In this paper, we present efficient quantum algorithms that are exponent...
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10/25/2022
Enabling Quantum Speedup of Markov Chains using a Multi-level Approach
Quantum speedup for mixing a Markov chain can be achieved based on the c...
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09/12/2022
The Mori-Zwanzig formulation of deep learning
We develop a new formulation of deep learning based on the Mori-Zwanzig ...
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04/20/2022
Stability Preserving Data-driven Models With Latent Dynamics
In this paper, we introduce a data-driven modeling approach for dynamics...
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03/21/2022
A Local Convergence Theory for the Stochastic Gradient Descent Method in Non-Convex Optimization With Non-isolated Local Minima
Non-convex loss functions arise frequently in modern machine learning, a...
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11/19/2021
Some Error Analysis for the Quantum Phase Estimation Algorithms
This paper is concerned with the phase estimation algorithm in quantum c...
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07/03/2021
Stochastic Algorithms for Self-consistent Calculations of Electronic Structures
The convergence property of a stochastic algorithm for the self-consiste...
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06/06/2021
A Projection-based Reduced-order Method for Electron Transport Problems with Long-range Interactions
Long-range interactions play a central role in electron transport. At th...
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05/21/2021
Error Bounds of the Invariant Statistics in Machine Learning of Ergodic Itô Diffusions
This paper studies the theoretical underpinnings of machine learning of ...
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01/28/2021
Projection based model reduction for the immersed boundary method
Fluid-structure interactions are central to many bio-molecular processes...
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01/14/2021
A Machine-Learning Method for Time-Dependent Wave Equations over Unbounded Domains
Time-dependent wave equations represent an important class of partial di...
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08/29/2020
Random Batch Algorithms for Quantum Monte Carlo simulations
Random batch algorithms are constructed for quantum Monte Carlo simulati...
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12/23/2019
Kernel Embedding Linear Response
In the paper, we study the problem of estimating linear response statist...
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10/30/2019