87 citations · 179 across the 21 of their papers we have counts for
23 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…
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 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…
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…
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…
Schrödingerisation based computationally stable algorithms for ill-posed problems in partial differential equations
Shi Jin, Nana Liu, Chuwen Ma
We introduce a simple and stable computational method for ill-posed partial differential equation (PDE) problems. The method is based on Schrödingerization, introduced in [S. Jin,…
Quantum Circuits for partial differential equations via Schrödingerisation
Junpeng Hu, Shi Jin, Nana Liu +1
Quantum computing has emerged as a promising avenue for achieving significant speedup, particularly in large-scale PDE simulations, compared to classical computing. One of the main…
On Schrödingerization based quantum algorithms for linear dynamical systems with inhomogeneous terms
Shi Jin, Nana Liu, Chuwen Ma
We analyze the Schrödingerization method for quantum simulation of a general class of non-unitary dynamics with inhomogeneous source terms. The Schrödingerization technique, introd…
Quantum simulation for time-dependent Hamiltonians -- with applications to non-autonomous ordinary and partial differential equations
Yu Cao, Shi Jin, Nana Liu
Non-autonomous dynamical systems appear in a very wide range of interesting applications, both in classical and quantum dynamics, where in the latter case it corresponds to having…
Dilation theorem via Schrödingerisation, with applications to the quantum simulation of differential equations
Junpeng Hu, Shi Jin, Nana Liu +1
Nagy's unitary dilation theorem in operator theory asserts the possibility of dilating a contraction into a unitary operator. When used in quantum computing, its practical implemen…
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…