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CATEGORIES:Wednesday HEP-GR Colloquium
SUMMARY:Pseudorandomness and random quantum circuits in di
fferent geometries - Aram Harrow\, MIT
DTSTART;TZID=Europe/London:20190612T141500
DTEND;TZID=Europe/London:20190612T151500
UID:TALK123544AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/123544
DESCRIPTION:Random unitary dynamics are a toy model for chaoti
c quantum dynamics\nand also have applications to
quantum information theory and\ncomputing. A basi
c question about them is whether their first few\n
moments approximately match those of the Haar meas
ure\; if so\, we call\nthem approximate unitary de
signs. It is natural to conjecture that\nthe time
needed for quantum dynamics to yield an approxima
te design is\ngiven by the time for a signal to pr
opagate from one side of the\nsystem to the other.
I will describe the proof of this claim in one\n
or more dimensions in Euclidean geometry and will
give examples where\nthis claim fails in more gene
ral geometries\, including the\nSchwarzschild metr
ic. I will briefly discuss two applications: (1)\
nthe proposal by Google and other groups to use ra
ndom quantum circuits\nfor "quantum supremacy\," m
eaning a quantum circuit performing a task\nthat i
s hard for a classical computer to simulate\; and
(2) the\nquestion of how quickly information is sc
rambled in black holes.\n\nThis is based on the fo
llowing three papers.\narXiv:1208.0692 (with Ferna
ndo Brandao and Michal Horodeck)\narXiv:1809.06957
(with Saeed Mehraban)\narXiv:1906.02219 (with Lin
ghang Kong\, Zi-Wen Liu\, Saeed Mehraban\, and Pet
er Shor)
LOCATION:MR2\, Centre for Mathematical Sciences
CONTACT:Francesca Chadha-Day
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