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Fermionic reduced density matrices summarize the key observables in fermionicsystems. In electronic systems, the two-particle reduced density matrix (2-RDM)is sufficient to determine the energy and most physical observables ofinterest. Here, we consider the possibility of using matrix completion toreconstruct the two-particle reduced density matrix to chemical accuracy frompartial information. We consider the case of noiseless matrix completion, wherethe partial information corresponds to a subset of the 2-RDM elements, as wellas noisy completion, where the partial information corresponds to both a subsetof elements, as well as statistical noise in their values. Through experimentson a set of 24 molecular systems, we find that the 2-RDM can be efficientlyreconstructed from a reduced amount of information. In the case of noisycompletion, this results in multiple orders of magnitude reduction in thenumber of measurements needed to determine the 2-RDM to chemical accuracy.These techniques can be readily applied to both classical and quantumalgorithms for quantum simulations.

Fermionic reduced density low-rank matrix completion, noise filtering, and measurement reduction in quantum simulations