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CATEGORIES:CQIF Seminar
SUMMARY:Classical approximations of quantum Hamiltonian dy
namics with the Nyström method - Andrea Rocchetto
(University of Oxford and UCL)
DTSTART;TZID=Europe/London:20181011T141500
DTEND;TZID=Europe/London:20181011T151500
UID:TALK111601AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/111601
DESCRIPTION:Simulating the time-evolution of quantum mechanica
l systems is BQP-hard and expected to be one of th
e foremost applications of quantum computers. Duri
ng this talk I will present a method to approximat
e Hamiltonian dynamics using subsampling methods f
rom randomized numerical linear algebra and propos
e conditions for the efficient approximation of st
ate vectors evolving under a given Hamiltonian. As
an immediate application\, I will show that sampl
e based quantum simulation\, a type of evolution w
here the Hamiltonian is a density matrix\, can be
efficiently classically simulated under specific s
tructural conditions. The main technical contribut
ion of our method is a randomized algorithm for ap
proximating Hermitian matrix exponentials. The pro
of leverages the Nyström method to obtain low-rank
approximations of the Hamiltonian\, a tool common
ly used in the statistical machine learning litera
ture. \n\nThe talk is based on joint work with Car
lo Ciliberto\, Massimiliano Pontil\, Alessandro Ru
di\, Simone Severini and Leonard Wossnig
LOCATION:MR4\, Centre for Mathematical Sciences\, Wilberfor
ce Road\, Cambridge
CONTACT:Johannes Bausch
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