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The development of various dynamic ansatz-constructing techniques has usheredin a new era, rendering the practical exploitation of Noisy Intermediate-ScaleQuantum (NISQ) hardware for molecular simulations increasingly viable. However,they exhibit substantial measurement costs during their execution. This workinvolves the development of a novel protocol that capitalizes on regenerativemachine learning methodologies and many-body perturbation theoretic measures toconstruct a highly expressive and shallow ansatz within the variational quantumeigensolver (VQE) framework. The machine learning methodology is trained withthe basis vectors of a low-rank expansion of the N-electron Hilbert space toidentify the dominant high-rank excited determinants without requiring a largenumber of quantum measurements. These selected excited determinants areiteratively incorporated within the ansatz through their low-rankdecomposition. The reduction in the number of quantum measurements and ansatzdepth manifests in the robustness of our method towards hardware noise, asdemonstrated through numerical applications. Furthermore, the proposed methodis highly compatible with state-of-the-art neural error mitigation techniques.This approach significantly enhances the feasibility of quantum simulations inmolecular systems, paving the way for impactful advancements in quantumcomputational chemistry.

Machine Learning Assisted Cognitive Construction of a Shallow Depth Dynamic Ansatz for Noisy Quantum Hardware