PreprintarXiv licencearXiv
Improved classical optimization of fermionic Hamiltonians beyond Gaussian states
Abstract
We give a polynomial-time randomized classical algorithm that approximates the largest eigenvalue λmax of a traceless quartic fermionic Hamiltonian H on n modes. The algorithm achieves energy at least λmax/O(√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 λmax in terms of the maximum energy of a Gaussian state and √(2−nTr(H2)).
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BibTeX
@misc{parekh2026improved,
title = {{Improved classical optimization of fermionic Hamiltonians beyond Gaussian states}},
author = {Ojas Parekh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12844},
eprint = {2610.12844},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12844},
}
RIS
TY - UNPB
TI - Improved classical optimization of fermionic Hamiltonians beyond Gaussian states
AU - Ojas Parekh
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.12844
UR - https://arxiv.org/abs/2610.12844
AB - We give a polynomial-time randomized classical algorithm that approximates the largest eigenvalue λ_max of a traceless quartic fermionic Hamiltonian H on n modes. The algorithm achieves energy at least λ_max/O(√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 λ_max in terms of the maximum energy of a Gaussian state and √(2^−nTr(H^2)).
ER -