Optimizing fermionic Hamiltonians with classical interactions

Maarten Stroeks examines ground-energy optimisation for fermionic Hamiltonians whose interactions are classical in a suitable basis, a setting motivated by electronic structure in chemistry and condensed matter. Despite QMA hardness, fermionic Gaussian states achieve an approximation ratio of at least one third independent of sparsity. Semidefinite algorithms handle several traceless and positive-semidefinite families, including fixed particle number. A construction that mixes covariance matrices, called a Gaussian blend, provides the technical foundation.