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CATEGORIES:CQIF Seminar
SUMMARY:The sum-of-squares for fermionic systems\, and the
SYK model - Matthew Hastings (Microsoft Research)
DTSTART;TZID=Europe/London:20230228T160000
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UID:TALK197791AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/197791
DESCRIPTION: The central problem in physics and quantum chemis
try is to determine properties of the ground state
of an interacting system of fermions. As a quant
um mechanical problem\, there may be no efficient
classical witness to the ground state energy\, or
even to an approximation of that energy. A common
ly considered witness is a so-called “Gaussian sta
te”\, or free fermion wavefunction. As a prominen
t example \, the Sachdev-Ye-Kitaev (SYK) model has
no Gaussian state which achieves a good approxima
tion to the energy\; this model is sometimes consi
dered as one of the “most entangled” or “most stro
ngly interacting” models possible. I will discuss
applications of the sum-of-squares method to this
model. Sum-of-squares is a semidefinite programm
ing relaxation. I will show that this method can
give classically efficient constant-factor lower b
ounds on the energy\, and it inspires a quantum al
gorithm which gives constant-factor upper bounds.
Joint work with R. O’Donnell.\n\nThis talk is par
t of the Cambridge-Warwick Quantum Computing Collo
quium\n \nZoom link: https://maths-cam-ac-uk.zoom.
us/j/95558689595?pwd=US9uSDlvdnFIVGJOZ3NKSzJpTTFEZ
z09
LOCATION: Via Zoom
CONTACT:Sergii Strelchuk
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