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SUMMARY:Quantum algorithms for computing observables of nonlinear partial 
 differential equations - Shi Jin (Shanghai Jiao Tong University)
DTSTART:20220523T090000Z
DTEND:20220523T100000Z
UID:TALK173408@talks.cam.ac.uk
DESCRIPTION:Nonlinear partial differential equations (PDEs) are crucial to
  modelling important problems in science but they are computationally expe
 nsive and suffer from the curse of dimensionality. Since quantum algorithm
 s have the potential to resolve the curse of dimensionality in certain ins
 tances\, some quantum algorithms for nonlinear PDEs have been developed. H
 owever\, they are fundamentally bound either to weak nonlinearities\, vali
 d to only short times\, or display no quantum advantage. We construct new 
 quantum algorithms--based on level sets --for nonlinear Hamilton-Jacobi an
 d scalar hyperbolic PDEs that can be performed with quantum advantages on 
 various critical numerical parameters\, even for computing the physical ob
 servables\, for arbitrary nonlinearity and are valid globally in time. &nb
 sp\;These PDEs are important for many applications 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\, i
 t can &nbsp\;display up to exponential advantage in both the dimension of 
 the PDE and the error in computing its observables. &nbsp\;For general non
 linear PDEs\, quantum advantage with respect to $M$\, for computing the en
 semble averages of solutions corresponding to $M$ different initial data\,
  is possible in the large $M$ limit.This is a joint work with Nana Liu.
LOCATION:Seminar Room 1\, Newton Institute
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