87 citations · 179 across the 30 of their papers we have counts for
9 papers · 1 filter
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…