87 citations · 179 across the 30 of their papers we have counts for
32 papers
Wavelength-Uniform Quantum Algorithms for Mixed-State Quantum Dynamics
Shi Jin, Chuwen Ma
One of the main challenges in numerical simulation of quantum dynamics is the prohibitive cost in the semi-classical regime, in which the de Broglie wave length is small compared w…
Quantum Simulation of Stokes Flow via Schrödingerisation and Artificial Compressibility
Shi Jin, Jiaqi Tang, Qilong Zhai +1
Simulating incompressible Stokes flow is essential for studies in microfluidics and low-Reynolds number hydrodynamics. However, the computational cost of resolving the associated s…
Schrödingerization based quantum algorithms for regularized Wasserstein proximal operators
Shi Jin, Nana Liu, Yue Yu
We develop a quantum algorithm for the regularized Wasserstein proximal operator, which is a fundamental tool in optimal transport and mean-field games. The regularization introduc…
Quantum simulation of the Liouville equation in classical mechanics with discontinuous potential via Schrödingerization
Shi Jin, Shuyi Zhang
We develop quantum simulation algorithms for the Liouville equation of classical mechanics with discontinuous potential. Such discontinuities represent potential barriers at which…
Young Measure Based Quantum Linear Programming Algorithms for Nonlinear/Stochastic Multiscale Partial Differential Equations and Homogenization
Siqi Chen, Shi Jin, Lei Zhang
We study quantum algorithms for nonlinear and stochastic homogenization via a Young-measure based linear programming (LP) formulation, which lifts the nonlinear problem to a linear…
Analog photonic simulator for large-scale transport
Mengyu Zhao, Xuezhi Zhu, Nikita Guseynov +9
Transport equations describe how physical quantities -- such as mass, energy, momentum, concentration, probability, or fields -- are carried, propagated, or redistributed through s…
Quantum Implicit-Explicit Schemes for Multiscale Ordinary and Partial Differential Equations via Schrödingerization
Qitong Hu, Xiaoyang He, Shi Jin +1
In this paper, we present a quantum implicit-explicit (IMEX) scheme for multiscale ordinary and partial differential equations whose discretization parameters are independent of th…
Hybrid quantum-classical algorithms for complex nonlinear partial differential equations with Ginzburg-Landau potential and vortex motion laws
Shi Jin, Nana Liu, Chuwen Ma
We propose quantum algorithms for complex-valued nonlinear partial differential equations in the strongly nonlinear regime, where the dynamics is governed by vortex cores, phase si…
Quantum algorithms for Young measures: applications to nonlinear partial differential equations
Shi Jin, Nana Liu, Maria Lukacova-Medvidova +1
Many nonlinear PDEs have singular or oscillatory solutions or may exhibit physical instabilities or uncertainties. This requires a suitable concept of physically relevant generaliz…
Quantum simulation of Liouville equation in geometrical optics with partial transmission and reflection via Schrödingerization
Shi Jin, Shuyi Zhang
This paper investigates quantum simulation algorithms for the Liouville equation in geometrical optics with partial transmission and reflection at sharp interfaces, based on the Sc…
Quantum algorithms for viscosity solutions to nonlinear Hamilton-Jacobi equations based on an entropy penalisation method
Shi Jin, Nana Liu
We present a framework for efficient extraction of the viscosity solutions of nonlinear Hamilton-Jacobi equations with convex Hamiltonians. These viscosity solutions play a central…
Quantum Random Feature Method for Solving Partial Differential Equations
Junpeng Hu, Shi Jin, Nana Liu +1
Quantum computing holds significant promise for scientific computing due to its potential for polynomial to even exponential speedups over classical methods, which are often hinder…
Schrodingerization based quantum algorithms for the time-fractional heat equation
Shi Jin, Nana Liu, Yue Yu
We develop a quantum algorithm for solving high-dimensional time-fractional heat equations. By applying the dimension extension technique from [FKW23], the -dimensional time-f…
Quantum Neural Ordinary and Partial Differential Equations
Yu Cao, Shi Jin, Nana Liu
We introduce a unified framework -- Quantum Neural Ordinary and Partial Differential Equations (QNODEs and QNPDEs) -- which extends the continuous-time formalism of classical neura…
Schrödingerization based quantum algorithms for the fractional Poisson equation
Shi Jin, Nana Liu, Yue Yu
We develop a quantum algorithm for solving high-dimensional fractional Poisson equations. By applying the Caffarelli-Silvestre extension, the -dimensional fractional equation is…
Quantum preconditioning method for finite difference discretizations of the Poisson equation via Schrödingerization
Shi Jin, Nana Liu, Chuwen Ma +1
We present a quantum preconditioning framework for solving linear systems arising from a finite difference discretization of the Poisson equation. It is based on the combination of…
On the Schrödingerization method for linear non-unitary dynamics with optimal dependence on matrix queries
Shi Jin, Nana Liu, Chuwen Ma +2
The Schrödingerization method converts linear partial and ordinary differential equations with non-unitary dynamics into systems of Schrödinger-type equations with unitary evolutio…
A quantum gradient descent algorithm for optimizing Gaussian Process models
Junpeng Hu, Jinglai Li, Lei Zhang +1
Gaussian Process Regression (GPR) is a nonparametric supervised learning method, widely valued for its ability to quantify uncertainty. Despite its advantages and broad application…
Quantum simulation of a class of highly-oscillatory transport equations via Schrödingerisation
Anjiao Gu, Shi Jin
In this paper, we present quantum algorithms for a class of highly-oscillatory transport equations, which arise in semiclassical computation of surface hopping problems and other r…
Quantum Algorithms for Stochastic Differential Equations: A Schrödingerisation Approach
Shi Jin, Nana Liu, Wei Wei
Quantum computers are known for their potential to achieve up-to-exponential speedup compared to classical computers for certain problems. To exploit the advantages of quantum comp…
Schrödingerization based Quantum Circuits for Maxwell's Equation with time-dependent source terms
Chuwen Ma, Shi Jin, Nana Liu +2
The Schrödingerisation method combined with the autonomozation technique in \cite{cjL23} converts general non-autonomous linear differential equations with non-unitary dynamics int…
Unifying framework for quantum simulation algorithms for time-dependent Hamiltonian dynamics
Yu Cao, Shi Jin, Nana Liu
Recently, there has been growing interest in simulating time-dependent Hamiltonians using quantum algorithms, driven by diverse applications, such as quantum adiabatic computing. W…
Analog quantum simulation of parabolic partial differential equations using Jaynes-Cummings-like models
Shi Jin, Nana Liu
We present a simplified analog quantum simulation protocol for preparing quantum states that embed solutions of parabolic partial differential equations, including the heat, Black-…
Quantum Circuits for the heat equation with physical boundary conditions via Schrodingerisation
Shi Jin, Nana Liu, Yue Yu
This paper explores the explicit design of quantum circuits for quantum simulation of partial differential equations (PDEs) with physical boundary conditions. These equations and/o…