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SUMMARY:The sum-of-squares for fermionic systems\, and the SYK model - Mat
 thew Hastings (Microsoft Research)
DTSTART:20230228T160000Z
DTEND:20230228T170000Z
UID:TALK197791@talks.cam.ac.uk
CONTACT:Sergii Strelchuk
DESCRIPTION: The central problem in physics and quantum chemistry is to de
 termine properties of the ground state of an interacting system of fermion
 s.  As a quantum mechanical problem\, there may be no efficient classical 
 witness to the ground state energy\, or even to an approximation of that e
 nergy.  A commonly considered witness is a so-called “Gaussian state”\
 , or free fermion wavefunction.  As a prominent example \, the Sachdev-Ye-
 Kitaev (SYK) model has no Gaussian state which achieves a good approximati
 on to the energy\; this model is sometimes considered as one of the “mos
 t entangled” or “most strongly interacting” models possible.  I will
  discuss applications of the sum-of-squares method to this model.  Sum-of-
 squares is a semidefinite programming relaxation.  I will show that this m
 ethod can give classically efficient constant-factor lower bounds on the e
 nergy\, and it inspires a quantum algorithm which gives constant-factor up
 per bounds.  Joint work with R. O’Donnell.\n\nThis talk is part of the C
 ambridge-Warwick Quantum Computing Colloquium\n \nZoom link: https://maths
 -cam-ac-uk.zoom.us/j/95558689595?pwd=US9uSDlvdnFIVGJOZ3NKSzJpTTFEZz09
LOCATION: Via Zoom
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