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DOE OSTI · 3024752

Is the Matrix Completion of Reduced Density Matrices Unique?

Massaccesi, Gustavo E. [Univ. of Buenos Aires (Argentina)] (ORCID:0000000173905255)·Oña, Ofelia B. [National Univ. of La Plata (Argentina)] (ORCID:0000000224825109)·Lain, Luis [Univ. of the Basque Country (Spain)] (ORCID:000000027260049X)·Torre, Alicia [Univ. of the Basque Country (Spain)] (ORCID:0000000256817074)·Peralta, Juan E. [Central Michigan Univ., Mount Pleasant, MI (United States)] (ORCID:0000000328498472)·Alcoba, Diego R. [Univ. of Buenos Aires (Argentina); National Scientific and Technical Research Council (CONICET) (Argentina)] (ORCID:0000000151651127)·Scuseria, Gustavo E. [Rice Univ., Houston, TX (United States)]
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Abstract

Reduced density matrices are central to describing observables in many-body quantum systems. In electronic structure theory, the two-particle reduced density matrix (2-RDM) suffices to determine the energy and other key properties. Recent work has used matrix completion, leveraging the low-rank structure of RDMs and approximate theoretical models, to reconstruct the 2-RDM from partial data and thus reduce the computational cost. However, matrix completion is, in general, an under-determined problem. Revisiting Rosina’s theorem (Rosina, M. Queen’s Papers on Pure and Applied Mathematics , 1968, No. 11, 369), we here show that the matrix completion is unique under certain conditions, identifying the subset of 2-RDM elements that enables its exact reconstruction from incomplete information. Building on this, we introduce a hybrid quantum–stochastic algorithm that achieves exact matrix completion, demonstrated through applications to the Fermi–Hubbard model.

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Massaccesi, Gustavo E. [Univ. of Buenos Aires (Argentina)] (ORCID:0000000173905255), Oña, Ofelia B. [National Univ. of La Plata (Argentina)] (ORCID:0000000224825109), Lain, Luis [Univ. of the Basque Country (Spain)] (ORCID:000000027260049X), Torre, Alicia [Univ. of the Basque Country (Spain)] (ORCID:0000000256817074), Peralta, Juan E. [Central Michigan Univ., Mount Pleasant, MI (United States)] (ORCID:0000000328498472), Alcoba, Diego R. [Univ. of Buenos Aires (Argentina); National Scientific and Technical Research Council (CONICET) (Argentina)] (ORCID:0000000151651127), Scuseria, Gustavo E. [Rice Univ., Houston, TX (United States)]. 2026-03-13. Is the Matrix Completion of Reduced Density Matrices Unique?. https://doi.org/10.1021/acs.jpclett.6c00296

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