Fetching the paper…
Reading the bibliography…
This paper explores the feasibility of quantum simulation for partial differential equations (PDEs) with physical boundary or interface conditions.
The Stefan Problem
LI Rubinshtein · 1971
Earlier work this paper cites.
The immersed interface method for elliptic equations with discontinuous coefficients and singular sources
R. J. Leveque and Z. Li · 1994
Earlier work this paper cites.
The immersed interface method for acoustic wave equations with discontinuous coefficients
C. Zhang and R. J. Leveque · 1997
Earlier work this paper cites.
The immersed boundary method
Charles S Peskin · 2002
Earlier work this paper cites.
Computational high frequency wave propagation
B. Engquist and O. Runborg · 2003
Earlier work this paper cites.
A level set method for the computation of multivalued solutions to quasi-linear hyperbolic PDEs and Hamilton-Jacobi equations
S. Jin and S. Osher · 2003
Earlier work this paper cites.
Hamiltonian-preserving schemes for the Liouville equation with discontinuous potentials
S. Jin and X. Wen · 2005
Earlier work this paper cites.
A Hamiltonian-preserving scheme for the Liouville equation of geometrical optics with discontinuous local wave speeds
S. Jin and X. Wen · 2006
Earlier work this paper cites.
A Hamiltonian-preserving scheme for the Liouville equation of geometrical optics with partial transmissions and reflections
S. Jin and X. Wen · 2006
Earlier work this paper cites.
Covergence of an immersed interface upwind scheme for linear advection equations with piecewise constant coefficients I: L 1 L^{1} -error estimates
X. Wen and S. Jin · 2008
Earlier work this paper cites.
Quantum algorithm for linear systems of equations
A. W. Harrow, A. Hassidim, and S. Lloyd · 2009
Earlier work this paper cites.
Numerical methods for hyperbolic systems with singular coefficients: well-balanced scheme, Hamiltonian preservation, and beyond
S. Jin · 2009
Earlier work this paper cites.
Quantum algorithm and circuit design solving the Poisson equation
Y. Cao, A. Papageorgiou, I. Petras, et al · 2013
Cited alongside, same era.
High-order quantum algorithm for solving linear differential equations
D. W. Berry · 2014
Cited alongside, same era.
Quantum algorithms and the finite element method
A. Montanaro and S. Pallister · 2016
Cited alongside, same era.
Quantum algorithm for linear differential equations with exponentially improved dependence on precision
D. W. Berry, A. M. Childs, A. Ostrander, and G. Wang · 2017
Cited alongside, same era.
Quantum algorithm for systems of linear equations with exponentially improved dependence on precision
A. M. Childs, R. Kothari, and R. D. Somma · 2017
Cited alongside, same era.
Optimal scaling quantum linear systems solver via discrete adiabatic theorem
P. C. S. Costa, D. An, Y. A. Sanders, Y. Su, R. Babbush, and D. W. Berry · 2021
Later among the works it cites.
High-precision quantum algorithms for partial differential equations
A. M. Childs, J. P. Liu, and A. Ostrander · 2021
Later among the works it cites.
A theory of quantum differential equation solvers: limitations and fast-forwarding
D. An, J. Liu, D. Wang, and Q. Zhao · 2022
Later among the works it cites.
Quantum algorithms for uncertainty quantification: application to partial differential equations
F. Golse, S. Jin, and N. Liu · 2022
Later among the works it cites.
Quantum algorithms for computing observables of nonlinear partial differential equations
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
G. Low and N. Wiebe · 2018
Cited alongside, same era.
Quantum algorithm for simulating the wave equation
P. C. S. Costa, S. Jordan, and A. Ostrander · 2019
Cited alongside, same era.
Quantum algorithm for the Vlasov equation
A. Engel, G. Smith, and S. E. Parker · 2019
Cited alongside, same era.
Quantum algorithms for systems of linear equations inspired by adiabatic quantum computing
Y. Subasi and R. D. Somma · 2019
Cited alongside, same era.
Time-dependent Hamiltonian simulation with l 1 l^{1} -norm scaling
D. W. Berry, A. M. Childs, Y. Su, X. Wang, and N. Wiebe · 2020
Cited alongside, same era.
Quantum spectral methods for differential equations
A. W. Childs and J. Liu · 2020
Cited alongside, same era.
Quantum vs. classical algorithms for solving the heat equation
N. Linden, A. Montanaro, and C. Shao · 2020
Cited alongside, same era.
S. Jin and N. Liu · 2022
Later among the works it cites.
Quantum simulation of partial differential equations via Schrödingerisation
S. Jin, N. Liu, and Y. Yu · 2022
Later among the works it cites.
Quantum simulation of partial differential equations via Schrödingerisation: technical details
S. Jin, N. Liu, and Y. Yu · 2022
Later among the works it cites.
Time complexity analysis of quantum difference methods for linear high dimensional and multiscale partial differential equations
S. Jin, N. Liu, and Y. Yu · 2022
Later among the works it cites.
S. Jin and N. Liu · 2023
Closest in time.
Quantum simulation for quantum dynamics with artificial boundary conditions
S. Jin, X. Li, N. Liu, and Y. Yu · 2023
Closest in time.
Time complexity analysis of quantum algorithms via linear representations for nonlinear ordinary and partial differential equations
S. Jin, N. Liu, and Y. Yu · 2023
Closest in time.