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Applied and Computational Math Seminar

Variational embedding for quantum ground-state energy problems

Bowen Li (Duke University)

Location:  Hill 525
Date & time: Tuesday, 17 October 2023 at 11:00AM - 12:00PM

In this talk, we consider the quantum many body problems and introduce a sum-of-squares SDP hierarchy approximating the ground-state energy from below with a natural quantum embedding interpretation. We establish the connections between our approach and other variational methods for lower bounds, including the RDM method in quantum chemistry and the Anderson bounds. Additionally, inspired by the quantum information theory, we propose efficient strategies 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 investigation, we find that quantum entanglement has the potential to capture the underlying graph of the many-body Hamiltonian.

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