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SUMMARY:Towards polynomial convergence for variational quantum algorithms 
 using Langevin dynamics - Pablo Paez Velasco\, Universidad Complutense de 
 Madrid
DTSTART:20241114T141500Z
DTEND:20241114T151500Z
UID:TALK224470@talks.cam.ac.uk
CONTACT:Subhayan Roy Moulik
DESCRIPTION:One of the most promising types of algorithms to run on noisy 
 intermediate-scale quantum computers are variational optimization algorith
 ms (VQAs). In those algorithms one deals with a parametrized quantum circu
 it whose outputs are then a parametrized family of n-particle quantum stat
 es. One common problem to solve using VQAs is\, given an n-body observable
  H that can be efficiently implemented (e.g. a locally interacting Hamilto
 nian)\, obtain an approximation of the ground state and its associated ene
 rgy.\n\nThe aim of our work is to study the continuous Langevin dynamics i
 n U(n). Proving convergence results in such a setting may potentially lead
  to poly-time algorithms to solve the problem introduced in the previous p
 aragraph\, when considering depth-2 quantum circuits with gates acting on 
 a logarithmic number of sites. Moreover\, our results should be applicable
  to other circuits\, under certain assumptions on their structure and the 
 Hamiltonian considered. \n\nWe generalize some of the results from [1] to 
 the Lie group U(n)\; proving that the Gibbs distribution associated to the
  dynamics does indeed “find” the ground state of H. Furthermore\, we p
 rove that our setting satisfies a logarithmic Sobolev inequality\, which g
 uarantees exponential convergence of the process to its associated Gibbs d
 istribution. \n\nReferences: \n[1] M.B. Li\, and M.A. Erdogdu\, arXiv:2010
 .11176\, (2020).
LOCATION:MR2
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