Fermionic Reduced Density Low-Rank Matrix Completion, Noise Filtering, and Measurement Reduction in Quantum Simulations

Peng, Linqing; Zhang, Xing; Chan, Garnet Kin-Lic

doi:10.1021/acs.jctc.3c00851

Title: Fermionic Reduced Density Low-Rank Matrix Completion, Noise Filtering, and Measurement Reduction in Quantum Simulations

Journal Article · 14 December 2023 · Journal of Chemical Theory and Computation

DOI: https://doi.org/10.1021/acs.jctc.3c00851 · OSTI ID:2229975

^[1]; Zhang, Xing ^[1];

^[1]

California Institute of Technology, Pasadena, CA (United States)

Fermionic reduced density matrices summarize the key observables in Fermionic systems. In electronic systems, the two-particle reduced density matrix (2-RDM) is sufficient to determine the energy and most physical observables of interest. Here, we consider the possibility of using matrix completion to reconstruct the two-particle reduced density matrix to chemical accuracy from partial information. We consider the case of noiseless matrix completion, where the partial information corresponds to a subset of the 2-RDM elements, as well as noisy completion, where the partial information corresponds to both a subset of elements and statistical noise in their values. Through experiments on a set of 24 molecular systems, we find that 2-RDM can be efficiently reconstructed from a reduced amount of information. In the case of noisy completion, this results in a multiple orders of magnitude reduction in the number of measurements needed to determine the 2-RDM with chemical accuracy. These techniques can be readily applied to both classical and quantum algorithms for quantum simulations.

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Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE

Grant/Contract Number:: SC0019330; SC0019374

OSTI ID:: 2229975

Alternate ID(s):: OSTI ID: 2263343

Journal Information:: Journal of Chemical Theory and Computation, Vol. 19, Issue 24; ISSN 1549-9618

Publisher:: American Chemical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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