Is the Matrix Completion of Reduced Density Matrices Unique?
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- Univ. of Buenos Aires (Argentina)
- National Univ. of La Plata (Argentina)
- Univ. of the Basque Country (Spain)
- Central Michigan Univ., Mount Pleasant, MI (United States)
- Univ. of Buenos Aires (Argentina); National Scientific and Technical Research Council (CONICET) (Argentina)
- Rice Univ., Houston, TX (United States)
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.
- Research Organization:
- Emory Univ., Atlanta, GA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- Grant/Contract Number:
- SC0019374
- OSTI ID:
- 3024752
- Journal Information:
- Journal of Physical Chemistry Letters, Journal Name: Journal of Physical Chemistry Letters Journal Issue: 12 Vol. 17; ISSN 1948-7185
- Publisher:
- American Chemical SocietyCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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