11 papers
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…
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…
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…
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),…
Quantum simulation of Helmholtz equations via Schr{ö}dingerization
Anjiao Gu, Shi Jin, Chuwen Ma
The Helmholtz equation is a prototypical model for time-harmonic wave propagation. Numerical solutions become increasingly challenging as the wave number grows, due to the equa…
Quantum simulation of multiscale linear transport equations via Schrödingerization and exponential integrators
Xiaoyang He, Shi Jin
In this paper, we present two Hamiltonian simulation algorithms for multiscale linear transport equations, combining the Schrödingerization method [S. Jin, N. Liu and Y. Yu, Phys.…
Quantum simulation of elastic wave equations via Schrödingerisation
Shi Jin, Chundan Zhang
In this paper we study quantum simulation algorithms on the elastic wave equations using the Schrödingerisation method. The Schrödingerisation method transforms any linear PDEs int…
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…
AP-MIONet: Asymptotic-preserving multiple-input neural operators for capturing the high-field limits of collisional kinetic equations
Tian-ai Zhang, Shi Jin
In kinetic equations, external fields play a significant role, particularly when their strength is sufficient to balance collision effects, leading to the so-called high-field regi…
The Random Batch Method for -Body Quantum Dynamics
François Golse, Shi Jin, Thierry Paul
This paper discusses a numerical method for computing the evolution of large interacting system of quantum particles. The idea of the random batch method is to replace the total in…