Improved classical optimization of fermionic Hamiltonians beyond Gaussian states

2026-10-12 · arXiv Quantum Physics

arXiv:2610.12844v1 Announce Type: new

Abstract: We give a polynomial-time randomized classical algorithm that approximates the largest eigenvalue $\lambda_{\max}$ of a traceless quartic fermionic Hamiltonian $H$ on $n$ modes. The algorithm achieves energy at least $\lambda_{\max}/O(\sqrt n)$ and outputs either a fermionic Gaussian state or a polynomially sparse state in the Fock basis. This is achieved through a new upper bound on $\lambda_{\max}$ in terms of the maximum energy of a Gaussian state and $\sqrt{2^{-n}\operatorname{Tr}(H^2)}$.

原文链接：https://arxiv.org/abs/2610.12844

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