IAS HET Seminar | Matthew Hastings, Microsoft| “The Sum-of-Squares for Fermionic Systems, and the SYK Model” | Zoom Only

May 15, 2023, 2:30 pm2:30 pm
Zoom Only


Event Description

Perhaps the most important problem in physics or quantum chemistry is to determine properties of the ground state of an interacting system of fermions.  As a quantum mechanical problem, there may be no efficient classical witness to the ground state energy, or even to an approximation of that energy.  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 approximation to the energy; this model is sometimes considered as one of the “most 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 method can give classically efficient constant-factor lower bounds on the energy, and it inspires a quantum algorithm which gives constant-factor upper bounds.  Joint work with R. O’Donnell.