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We investigate fully self-consistent multiscale quantum-classical algorithmson current generation superconducting quantum computers, in a unified approachto tackle the correlated electronic structure of large systems in both quantumchemistry and condensed matter physics. In both of these contexts, a stronglycorrelated quantum region of the extended system is isolated andself-consistently coupled to its environment via the sampling of reduceddensity matrices. We analyze the viability of current generation quantumdevices to provide the required fidelity of these objects for a robust andefficient optimization of this subspace. We show that with a simple errormitigation strategy and optimization of compact tensor product bases tominimize the number of terms to sample, these self-consistent algorithms areindeed highly robust, even in the presence of significant noises on quantumhardware. Furthermore, we demonstrate the use of these density matrices for thesampling of non-energetic properties, including dipole moments and Fermi liquidparameters in condensed phase systems, achieving a reliable accuracy withsparse sampling. It appears that uncertainties derived from the iterativeoptimization of these subspaces is smaller than variances in the energy for asingle subspace optimization with current quantum hardware. This boosts theprospect for routine self-consistency to improve the choice of correlatedsubspaces in hybrid quantum-classical approaches to electronic structure forlarge systems in this multiscale fashion.

Reduced Density Matrix Sampling: Self-consistent Embedding and Multiscale Electronic Structure on Current Generation Quantum Computers