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We propose a method for computing space-resolved correlation properties ofthe two-dimensional Hubbard model within a quantum-classical embedding strategythat uses a Noisy, Intermediate Scale Quantum (NISQ) computer to solve theembedded model. While previous approaches were limited to purely local,one-impurity embedded models, requiring at most four qubits and relativelyshallow circuits, we solve a two-impurity model requiring eight qubits with anadvanced hybrid scheme on top of the Variational Quantum Eigensolver algorithm.This iterative scheme, dubbed Natural Orbitalization (NOization), graduallytransforms the single-particle basis to the approximate Natural-Orbital basis,in which the ground state can be minimally expressed, at the cost of measuringthe one-particle reduced density-matrix of the embedded problem. We show thatthis transformation tends to make the variational optimization of existing (buttoo deep) ansatz circuits faster and more accurate, and we propose an ansatz,the Multireference Excitation Preserving (MREP) ansatz, that achieves greatexpressivity without requiring a prohibitive gate count. The one-impurityversion of the ansatz has only one parameter, making the ground statepreparation a trivial step, which supports the optimal character of ourapproach. Within a Rotationally Invariant Slave Boson embedding scheme thatrequires a minimal number of bath sites and does not require computing the fullGreen's function, the NOization combined with the MREP ansatz allow us tocompute accurate, space-resolved quasiparticle weights and static self-energiesfor the Hubbard model even in the presence of noise levels representative ofcurrent NISQ processors. This paves the way to a controlled solution of theHubbard model with larger and larger embedded problems solved by quantumcomputers.

physical review. b./physical review. b

Unraveling correlated material properties with noisy quantum computers:  Natural orbitalized variational quantum eigensolving of extended impurity  models within a slave-boson approach