87 citations · 186 across the 11 of their papers we have counts for
12 papers
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…
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…
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…
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…
Quantum simulation of the Fokker-Planck equation via Schrodingerization
Shi Jin, Nana Liu, Yue Yu
This paper studies a quantum simulation technique for solving the Fokker-Planck equation. Traditional semi-discretization methods often fail to preserve the underlying Hamiltonian…
Quantum Simulation for Partial Differential Equations with Physical Boundary or Interface Conditions
Shi Jin, Xiantao Li, Nana Liu +1
This paper explores the feasibility of quantum simulation for partial differential equations (PDEs) with physical boundary or interface conditions. Semi-discretisation of such prob…
Quantum Simulation for Quantum Dynamics with Artificial Boundary Conditions
Shi Jin, Nana Liu, Xiantao Li +1
Quantum dynamics, typically expressed in the form of a time-dependent Schrödinger equation with a Hermitian Hamiltonian, is a natural application for quantum computing. However, wh…
Quantum simulation of partial differential equations via Schrodingerisation: technical details
Shi Jin, Nana Liu, Yue Yu
We study a new method - called Schrodingerisation introduced in [Jin, Liu, Yu, arXiv: 2212.13969] - for solving general linear partial differential equations with quantum simulatio…
Quantum simulation of partial differential equations via Schrodingerisation
Shi Jin, Nana Liu, Yue Yu
We present a simple new way - called Schrodingerisation - to simulate general linear partial differential equations via quantum simulation. Using a simple new transform, referred t…
Time complexity analysis of quantum algorithms via linear representations for nonlinear ordinary and partial differential equations
Shi Jin, Nana Liu, Yue Yu
We construct quantum algorithms to compute the solution and/or physical observables of nonlinear ordinary differential equations (ODEs) and nonlinear Hamilton-Jacobi equations (HJE…