Is the matrix completion of reduced density matrices unique?

• URL: http://arxiv.org/abs/2603.13087v1
• Date: Fri, 13 Mar 2026 15:38:47 GMT
• Title: Is the matrix completion of reduced density matrices unique?
• Abstract summary: In electronic structure theory, the two-particle reduced density matrix (2-RDM) suffices to determine the energy and other key properties.<n>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.<n>We introduce a hybrid quantum-stochastic algorithm that achieves exact matrix completion, demonstrated through applications to the Fermi-Hubbard model.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 computational cost. However, matrix completion is, in general, an under-determined problem. Revisiting Rosina's theorem [M. Rosina, Queen's Papers on Pure and Applied Mathematics No. 11, 369 (1968)], 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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