BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Classical approximations of quantum Hamiltonian dynamics with the 
 Nyström method - Andrea Rocchetto (University of Oxford and UCL)
DTSTART:20181011T131500Z
DTEND:20181011T141500Z
UID:TALK111601@talks.cam.ac.uk
CONTACT:Johannes Bausch
DESCRIPTION:Simulating the time-evolution of quantum mechanical systems is
  BQP-hard and expected to be one of the foremost applications of quantum c
 omputers. During this talk I will present a method to approximate Hamilton
 ian dynamics using subsampling methods from randomized numerical linear al
 gebra and propose conditions for the efficient approximation of state vect
 ors evolving under a given Hamiltonian. As an immediate application\, I wi
 ll show that sample based quantum simulation\, a type of evolution where t
 he Hamiltonian is a density matrix\, can be efficiently classically simula
 ted under specific structural conditions. The main technical contribution 
 of our method is a randomized algorithm for approximating Hermitian matrix
  exponentials. The proof leverages the Nyström method to obtain low-rank 
 approximations of the Hamiltonian\, a tool commonly used in the statistica
 l machine learning literature. \n\nThe talk is based on joint work with Ca
 rlo Ciliberto\, Massimiliano Pontil\, Alessandro Rudi\, Simone Severini an
 d Leonard Wossnig 
LOCATION:MR4\, Centre for Mathematical Sciences\, Wilberforce Road\, Cambr
 idge
END:VEVENT
END:VCALENDAR