  The near-term utility of quantum computers is hindered by hardware
constraints in the form of noise. One path to achieving noise resilience in
hybrid quantum algorithms is to decrease the required circuit depth -- the
number of applied gates -- to solve a given problem. This work demonstrates how
to reduce circuit depth by combining the transcorrelated (TC) approach with
adaptive quantum ans\"atze and their implementations in the context of
variational quantum imaginary time evolution (AVQITE). The combined TC-AVQITE
method is used to calculate ground state energies across the potential energy
surfaces of H$_4$, LiH, and H$_2$O. In particular, H$_4$ is a notoriously
difficult case where unitary coupled cluster theory, including singles and
doubles excitations, fails to provide accurate results. Adding TC yields
energies close to the complete basis set (CBS) limit while reducing the number
of necessary operators -- and thus circuit depth -- in the adaptive ans\"atze.
The reduced circuit depth furthermore makes our algorithm more noise-resilient
and accelerates convergence. Our study demonstrates that combining the TC
method with adaptive ans\"atze yields compact, noise-resilient, and
easy-to-optimize quantum circuits that yield accurate quantum chemistry results
close to the CBS limit.
