26 citations · 27 across the 7 of their papers we have counts for
9 papers
An Efficient Explicit Implementation of a Quantum Algorithm with Quantum Advantage for Nonlinear Scalar Conservation Laws
Kezhen Wang, Junpeng Hu, Lei Zhang
Quantum algorithms for nonlinear partial differential equations remain challenging because nonlinear dynamics are not directly amenable to unitary quantum simulation. Building on t…
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…
On Optimal Convergence Rates for the Nonlinear Schrödinger Equation with a Wave Operator via Localized Orthogonal Decomposition
Hanzhang Hu, Zetao Ma, Lei Zhang
In this paper, we develop a Localized Orthogonal Decomposition (LOD) method for the two-dimensional time-dependent nonlinear Schrödinger equation with a wave operator. We prove tha…
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…
Quantum Circuits for the Black-Scholes equations via Schrödingerisation
Shi Jin, Zihao Tang, Xu Yin +1
In this paper, we construct quantum circuits for the Black-Scholes equations, a cornerstone of financial modeling, based on a quantum algorithm that overcome the cure of high dimen…
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…
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…
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…
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…