  The development of various dynamic ansatz-constructing techniques has ushered
in a new era, rendering the practical exploitation of Noisy Intermediate-Scale
Quantum (NISQ) hardware for molecular simulations increasingly viable. However,
they exhibit substantial measurement costs during their execution. This work
involves the development of a novel protocol that capitalizes on regenerative
machine learning methodologies and many-body perturbation theoretic measures to
construct a highly expressive and shallow ansatz within the variational quantum
eigensolver (VQE) framework. The machine learning methodology is trained with
the basis vectors of a low-rank expansion of the N-electron Hilbert space to
identify the dominant high-rank excited determinants without requiring a large
number of quantum measurements. These selected excited determinants are
iteratively incorporated within the ansatz through their low-rank
decomposition. The reduction in the number of quantum measurements and ansatz
depth manifests in the robustness of our method towards hardware noise, as
demonstrated through numerical applications. Furthermore, the proposed method
is highly compatible with state-of-the-art neural error mitigation techniques.
This approach significantly enhances the feasibility of quantum simulations in
molecular systems, paving the way for impactful advancements in quantum
computational chemistry.
