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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Quantum algorithms for computing observables of no
nlinear partial differential equations - Shi Jin (
Shanghai Jiao Tong University)
DTSTART;TZID=Europe/London:20220523T100000
DTEND;TZID=Europe/London:20220523T110000
UID:TALK173408AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/173408
DESCRIPTION:Nonlinear partial differential equations (PDEs) ar
e crucial to modelling important problems in scien
ce but they are computationally expensive and suff
er from the curse of dimensionality. Since quantum
algorithms have the potential to resolve the curs
e of dimensionality in certain instances\, some qu
antum algorithms for nonlinear PDEs have been deve
loped. However\, they are fundamentally bound eith
er to weak nonlinearities\, valid to only short ti
mes\, or display no quantum advantage. We construc
t new quantum algorithms--based on level sets --fo
r nonlinear Hamilton-Jacobi and scalar hyperbolic
PDEs that can be performed with quantum advantages
on various critical numerical parameters\, even f
or computing the physical observables\, for arbitr
ary nonlinearity and are valid globally in time. &
nbsp\;These PDEs are important for many applicatio
ns like optimal control\, machine learning\, semi-
classical limit of Schrodinger equations\, mean-fi
eld games and many more.\nDepending on the details
of the initial data\, it can \;display up to
exponential advantage in both the dimension of th
e PDE and the error in computing its observables.
\;For general nonlinear PDEs\, quantum advant
age with respect to $M$\, for computing the ensemb
le averages of solutions corresponding to $M$ diff
erent initial data\, is possible in the large $M$
limit.This is a joint work with Nana Liu.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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