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Center for Nonlinear Studies |
In this talk, I will present a new classical algorithm to approximate the free energy of dense, local quantum many-body systems in thermal equilibrium. Our algorithm is based on the variational characterization of the free energy, and uses techniques from semidefinite programming hierarchies. The main idea is to solve a relaxed convex optimization program over sets of reduced density matrices and then "round" these reduced density matrices to a valid quantum state. Our work simultaneously generalizes results in efficient algorithms for the free energy of dense classical Ising models, and product-state approximation algorithms for the ground-state energy of dense quantum Hamiltonians.Reference: Sergey Bravyi, Anirban Chowdhury, David Gosset and Pawel Wocjan, On the complexity of quantum partition functions, arXiv:2110.15466
Host: Gopikrishnan Muraleedharan