  The Adaptive Derivative-Assembled Pseudo-Trotter Variational Quantum
Eigensolver (ADAPT-VQE) has emerged as a pivotal promising approach for
electronic structure challenges in quantum chemistry with noisy quantum
devices. Nevertheless, to surmount existing technological constraints, this
study endeavors to enhance ADAPT-VQE's efficacy. Leveraging insights from
electronic structure theory, we concentrate on optimizing state preparation
without added computational burden and guiding ansatz expansion to yield more
concise wavefunctions with expedited convergence toward exact solutions. These
advancements culminate in shallower circuits and, as demonstrated, reduced
measurement requirements. This research delineates these enhancements and
assesses their performance across mono, di, and tridimensional arrangements of
H4 models, as well as in the water molecule. Ultimately, this work attests to
the viability of physically-motivated strategies in fortifying ADAPT-VQE's
efficiency, marking a significant stride in quantum chemistry simulations.
