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SUMMARY:The complexity of steady states of detailed balance Lindbladians -
  Raz Firanko\, Technion
DTSTART:20240822T131500Z
DTEND:20240822T141500Z
UID:TALK220129@talks.cam.ac.uk
CONTACT:Angela Capel
DESCRIPTION:For the past two decades\, there have been great advances in o
 ur understanding of the complexity of quantum Hamiltonian systems. Tools l
 ike Lieb-Robinson bounds\, tensor-networks\, computational complexity redu
 ctions\, and entanglement theory have helped us to answer questions like w
 hat the complexity of approximating the ground states of various classes o
 f local Hamiltonians is\, or whether or not there exists an efficient clas
 sical representation for such states.\n\nMost physical systems\, however\,
  are open\, and are often governed by local Lindbladians rather than local
  Hamiltonians. It is therefore natural to ask if we could use the same too
 ls to study the complexity of such systems\, and in particular the complex
 ity of their steady states. The biggest obstacle in bridging these two wor
 lds is Hermiticity: while Hamiltonians are Hermitian and induce unitary dy
 namics\, Lindbladians are not\, and their dynamics is dissipative. \n\nIn 
 this talk\, I will use the quantum detailed-balance condition to overcome 
 this problem. I will present a mapping between local Lindbldadians that sa
 tisfy the quantum detailed-balance condition to local Hamiltonians. This w
 ill enable me to identify sufficient conditions under which the steady sta
 tes of these systems satisfies exponential decay of correlations\, satisfi
 es an area law\, and can be efficiently represented by a tensor-network. I
  will also discuss the implications of this mapping for numerical simulati
 ons\, as well as to the complexity of the local Hamiltonian problem.
LOCATION:MR2
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