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SUMMARY:Pseudorandomness and random quantum circuits in different geometri
 es - Aram Harrow\, MIT
DTSTART:20190612T131500Z
DTEND:20190612T141500Z
UID:TALK123544@talks.cam.ac.uk
CONTACT:Francesca Chadha-Day
DESCRIPTION:Random unitary dynamics are a toy model for chaotic quantum dy
 namics\nand also have applications to quantum information theory and\ncomp
 uting.  A basic question about them is whether their first few\nmoments ap
 proximately match those of the Haar measure\; if so\, we call\nthem approx
 imate unitary designs.  It is natural to conjecture that\nthe time needed 
 for quantum dynamics to yield an approximate design is\ngiven by the time 
 for a signal to propagate from one side of the\nsystem to the other.  I wi
 ll describe the proof of this claim in one\nor more dimensions in Euclidea
 n geometry and will give examples where\nthis claim fails in more general 
 geometries\, including the\nSchwarzschild metric.  I will briefly discuss 
 two applications: (1)\nthe proposal by Google and other groups to use rand
 om quantum circuits\nfor "quantum supremacy\," meaning a quantum circuit p
 erforming a task\nthat is hard for a classical computer to simulate\; and 
 (2) the\nquestion of how quickly information is scrambled in black holes.\
 n\nThis is based on the following three papers.\narXiv:1208.0692 (with Fer
 nando Brandao and Michal Horodeck)\narXiv:1809.06957 (with Saeed Mehraban)
 \narXiv:1906.02219 (with Linghang Kong\, Zi-Wen Liu\, Saeed Mehraban\, and
  Peter Shor)
LOCATION:MR2\, Centre for Mathematical Sciences
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