9 papers
Transmutation based Quantum Simulation for Non-unitary Dynamics
Shi Jin, Chuwen Ma, Enrique Zuazua
We present a quantum algorithm for simulating dissipative diffusion dynamics generated by positive semidefinite operators of the form , a structure that arises natur…
Quantum Simulation of Non-Unitary Dynamics via Amplitude-Phase Separation
Qitong Hu, Shi Jin
Linear non-unitary dynamics arise in open quantum systems, non-Hermitian models, and numerical evolution problems, yet current quantum algorithms do not cleanly separate coherent a…
Time-asymptotic behavior of the Boltzmann equation with random inputs in whole space and its stochastic Galerkin approximation
Shi Jin, Qi Shao, Haitao Wang
We consider the Boltzmann equation with random uncertainties arising from the initial data and collision kernel in the {\it whole space}, along with their stochastic Galerkin (SG)…
How Particle-System Random Batch Methods Enhance Graph Transformer: Memory Efficiency and Parallel Computing Strategy
Hanwen Liu, Yixuan Ma, Shi Jin +1
Attention mechanism is a significant part of Transformer models. It helps extract features from embedded vectors by adding global information and its expressivity has been proved t…
Asymptotic uniform estimate of random batch method with replacement for the Cucker-Smale model
Shi Jin, Yuelin Wang, Yuliang Wang
The Random Batch Method (RBM) [S. Jin, L. Li and J.-G. Liu, Random Batch Methods (RBM) for interacting particle systems, J. Comput. Phys. 400 (2020) 108877] is not only an efficien…
Quantum Algorithms for Solving Generalized Linear Systems via Momentum Accelerated Gradient and Schrödingerization
Qitong Hu, Xiaoyang He, Shi Jin +1
In this paper, we propose a quantum algorithm that combines the momentum accelerated gradient method with Schrödingerization [S. Jin, N. Liu and Y. Yu, Phys. Rev. Lett, 133 (2024)…