A constructive solution to the n-representability problem
Abstract
We present an instantiation of the constructive solution to the fermionic quantum marginal problem by building the complete family of two-body witnesses at each level of a weighted sum-of-squares hierarchy. Our construction combines positive-semidefinite Gram matrices with explicit linear nullspace constraints that exactly cancel all higher-body contributions following a similar idea to the existing solution but made explicit in open source software. We demonstrate the weighted sum-of-squares construction numerically by solving the associated semidefinite program and recovering the exact ground-state energy of a Richardson Hamiltonian in the three-fermion sector. We further prove that higher-degree particle-number multipliers are unnecessary when the full sum-of-squares generating algebra is used.
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BibTeX
@misc{rubin2026constructive,
title = {{A constructive solution to the $n$-representability problem}},
author = {Nicholas C. Rubin and A. Eugene DePrince III},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20737},
eprint = {2610.20737},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20737},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A constructive solution to the n-representability problem
AU - Nicholas C. Rubin
AU - A. Eugene DePrince III
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.20737
UR - https://arxiv.org/abs/2610.20737
AB - We present an instantiation of the constructive solution to the fermionic quantum marginal problem by building the complete family of two-body witnesses at each level of a weighted sum-of-squares hierarchy. Our construction combines positive-semidefinite Gram matrices with explicit linear nullspace constraints that exactly cancel all higher-body contributions following a similar idea to the existing solution but made explicit in open source software. We demonstrate the weighted sum-of-squares construction numerically by solving the associated semidefinite program and recovering the exact ground-state energy of a Richardson Hamiltonian in the three-fermion sector. We further prove that higher-degree particle-number multipliers are unnecessary when the full sum-of-squares generating algebra is used.
ER -