Quantum simulation of partial differential equations via Schrodingerisation

S. Chandrasekhar, Radiative transfer (Dover Publications, Inc., New York, 1960) pp. xiv+393

1960

Earlier work this paper cites.

S. Lloyd, Universal quantum simulators, Science 273

1996

Earlier work this paper cites.

L. Ryzhik, G. Papanicolaou, and J. B. Keller, Transport equations for elastic and other waves in random media, Wave Motion 24

1996

Earlier work this paper cites.

L. Erdős and H.-T. Yau, Linear boltzmann equation as the weak coupling limit of a random schrödinger equation, Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences 53

2000

Earlier work this paper cites.

H. Buhrman, R. Cleve, J. Watrous, and R. De Wolf, Quantum fingerprinting, Physical Review Letters 87

2001

Earlier work this paper cites.

G. Brassard, P. Hoyer, M. Mosca, and A. Tapp, Quantum amplitude amplification and estimation, Contemporary Mathematics 305

2002

Earlier work this paper cites.

C. Mouhot and L. Neumann, Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus, Nonlinearity 19

2006

Earlier work this paper cites.

L. Lehtovaara, J. Toivanen, and J. Eloranta, Solution of time-independent schrödinger equation by the imaginary time propagation method, Journal of Computational Physics 221

2007

Earlier work this paper cites.

D. Poulin and P. Wocjan, Sampling from the thermal quantum gibbs state and evaluating partition functions with a quantum computer, Physical review letters 103

2009

Earlier work this paper cites.

A. W. Harrow, A. Hassidim, and S. Lloyd, Quantum algorithm for linear systems of equations, Physical review letters 103

2009

Earlier work this paper cites.

R. A. Horn and C. R. Johnson, Matrix analysis (Cambridge university press, 2012)

2012

Cited alongside, same era.

D. W. Berry, A. M. Childs, and R. Kothari, Hamiltonian simulation with nearly optimal dependence on all parameters, in 2015 IEEE 56th annual symposium on foundations of computer science (IEEE, 2015) pp. 792–809

2015

Cited alongside, same era.

A. Montanaro and S. Pallister, Quantum algorithms and the finite element method, Physical Review A 93

2016

Cited alongside, same era.

G. H. Low, T. J. Yoder, and I. L. Chuang, Methodology of resonant equiangular composite quantum gates, Physical Review X 6

2016

Cited alongside, same era.

A. M. Childs, R. Kothari, and R. D. Somma, Quantum algorithm for systems of linear equations with exponentially improved dependence on precision, SIAM Journal on Computing 46

2017

Cited alongside, same era.

L. Lin and Y. Tong, Near-optimal ground state preparation, Quantum 4

2020

Later among the works it cites.

M. Motta, C. Sun, A. T. Tan, M. J. O’Rourke, E. Ye, A. J. Minnich, F. G. Brandão, and G. K. Chan, Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution, Nature Physics 16

2020

Later among the works it cites.

A. M. Childs, J.-P. Liu, and A. Ostrander, High-precision quantum algorithms for partial differential equations, Quantum 5

2021

Later among the works it cites.

J.-P. Liu, H. Ø. Kolden, H. K. Krovi, N. F. Loureiro, K. Trivisa, and A. M. Childs, Efficient quantum algorithm for dissipative nonlinear differential equations, Proceedings of the National Academy of Sciences 118

2021

Later among the works it cites.

S. Jin and N. Liu, Quantum algorithms for computing observables of nonlinear partial differential equations, arXiv:2202.07834 (2022)