  Efficient quantum circuits are necessary for realizing quantum algorithms on
noisy intermediate-scale quantum devices. Fermionic excitations entering
unitary coupled-cluster (UCC) ans\"atze give rise to quantum circuits
containing CNOT "staircases" whose number scales exponentially with the
excitation rank. Recently, Yordanov et al. [Phys. Rev. A 102, 062612 (2020);
Commun. Phys. 4, 228 (2021)] constructed CNOT-efficient quantum circuits for
both fermionic- (FEB) and qubit-excitation-based (QEB) singles and doubles and
illustrated their usefulness in adaptive derivative-assembled
pseudo-Trotterized variational quantum eigensolver (ADAPT-VQE) simulations. In
this work, we extend these CNOT-efficient quantum circuits to arbitrary
excitation ranks. To illustrate the benefits of these compact FEB and QEB
quantum circuits, we perform numerical simulations using the recently developed
selected projective quantum eigensolver (SPQE) approach, which relies on an
adaptive UCC ansatz built from arbitrary-order particle-hole excitation
operators. We show that both FEB- and QEB-SPQE decrease the number of CNOT
gates compared to traditional SPQE by factors as large as 15. At the same time,
QEB-SPQE requires, in general, more ansatz parameters than FEB-SPQE, in
particular those corresponding to higher-than-double excitations, resulting in
quantum circuits with larger CNOT counts. Although ADAPT-VQE generates quantum
circuits with fewer CNOTs than SPQE, SPQE requires orders of magnitude less
residual element evaluations than gradient element evaluations in ADAPT-VQE.
