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UID:dd6c0ac23507cb2e27aefe2f5791f86b
CATEGORIES:Applied and Computational Math Seminar
CREATED:20231004T222306
SUMMARY:Variational embedding for quantum ground-state energy problems
LOCATION:Hill 525
DESCRIPTION:In this talk, we consider the quantum many body problems and introduce a su
 m-of-squares SDP hierarchy approximating the ground-state energy from below
  with a natural quantum embedding interpretation. We establish the connecti
 ons between our approach and other variational methods for lower bounds, in
 cluding the RDM method in quantum chemistry and the Anderson bounds. Additi
 onally, inspired by the quantum information theory, we propose efficient st
 rategies for optimizing cluster selection to tighten SDP relaxations while 
 staying within a computational budget. Numerical experiments are presented 
 to demonstrate the effectiveness of our strategy. As a by-product of our in
 vestigation, we find that quantum entanglement has the potential to capture
  the underlying graph of the many-body Hamiltonian.\n
X-ALT-DESC;FMTTYPE=text/html:<p><span style="color: #212529; font-family: 'Open Sans', sans-serif; font-
 size: 16px; font-style: normal; font-weight: 400; letter-spacing: normal; o
 rphans: 2; text-align: start; text-indent: 0px; text-transform: none; widow
 s: 2; word-spacing: 0px; white-space: normal; background-color: #ffffff; fl
 oat: none;">In this talk, we consider the quantum many body problems and in
 troduce a sum-of-squares SDP hierarchy approximating the ground-state energ
 y from below with a natural quantum embedding interpretation. We establish 
 the connections between our approach and other variational methods for lowe
 r bounds, including the RDM method in quantum chemistry and the Anderson bo
 unds. Additionally, inspired by the quantum information theory, we propose 
 efficient strategies for optimizing cluster selection to tighten SDP relaxa
 tions while staying within a computational budget. Numerical experiments ar
 e presented to demonstrate the effectiveness of our strategy. As a by-produ
 ct of our investigation, we find that quantum entanglement has the potentia
 l to capture the underlying graph of the many-body Hamiltonian.</span></p>
CONTACT:Bowen Li (Duke University)
DTSTAMP:20260827T115846
DTSTART;TZID=America/New_York:20231017T110000
DTEND;TZID=America/New_York:20231017T120000
SEQUENCE:0
TRANSP:OPAQUE
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