Optimizing fermionic Hamiltonians with classical interactions

• URL: http://arxiv.org/abs/2510.02122v1
• Date: Thu, 02 Oct 2025 15:31:55 GMT
• Title: Optimizing fermionic Hamiltonians with classical interactions
• Authors: Maarten Stroeks, Barbara M. Terhal, Yaroslav Herasymenko,
• Abstract summary: We consider the optimization problem (ground energy search) for fermionic Hamiltonians with classical interactions.<n>We prove that fermionic Gaussian states achieve an approximation ratio of at least 1/3 for such Hamiltonians, independent of sparsity.
• Score: 0.0509780930114934
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the optimization problem (ground energy search) for fermionic Hamiltonians with classical interactions. This QMA-hard problem is motivated by the Coulomb electron-electron interaction being diagonal in the position basis, a fundamental fact that underpins electronic-structure Hamiltonians in quantum chemistry and condensed matter. We prove that fermionic Gaussian states achieve an approximation ratio of at least 1/3 for such Hamiltonians, independent of sparsity. This shows that classical interactions are sufficient to prevent the vanishing Gaussian approximation ratio observed in SYK-type models. We also give efficient semi-definite programming algorithms for Gaussian approximations to several families of traceless and positive-semidefinite classically interacting Hamiltonians, with the ability to enforce a fixed particle number. The technical core of our results is the concept of a Gaussian blend, a construction for Gaussian states via mixtures of covariance matrices.

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