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This conference talk by Eugene De Prince from Florida State University explores "Lower Bounds in Quantum Chemistry" as part of IPAM's Optimal Transport for Density Operators workshop at UCLA. Discover how any electronic Hamiltonian can be decomposed into a sum of squares (SOS) of products of fermionic creation and annihilation operators plus a constant shift, with this constant shift serving as a lower-bound to the ground-state energy. Learn about the complementary relationship between the SOS decomposition problem and the variational optimization of the two-electron reduced density matrix (2RDM) approach in quantum chemistry. Understand how both methods approach the full configuration interaction energy from below as their respective conditions become more complete. The 46-minute presentation, recorded on March 31, 2025, offers valuable insights into the similarities and differences between these two quantum chemistry approaches.
