Improved classical optimization of fermionic Hamiltonians beyond Gaussian states

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 $\sqrt{2^{-n}\operatorname{Tr}(H^2)}$.

Quantum Physics (quant-ph); Data Structures and Algorithms (cs.DS)

arXiv:2610.12844 [quant-ph]

(or arXiv:2610.12844v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.12844 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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