  The variational quantum eigensolver (VQE) algorithm recently became a popular
method to compute quantum chemical properties of molecules on noisy
intermediate scale quantum (NISQ) devices. In order to avoid noise accumulation
from the NISQ device in the circuit, it is important to keep the so-called
quantum depth of the circuit at a minimum, defined as the minimum number of
quantum gates that need to be operated sequentially. In the present work, we
introduce a modular 2-qubit cluster circuit that allows for the design of a
shallow-depth quantum circuit compared to previously proposed architectures
without loss of chemical accuracy. Moreover, by virtue of the simplicity of the
cluster circuit, it is possible to assign a valence bond chemical
interpretation to the cluster circuit. The design was tested on the H2, (H2)2
and LiH molecules, as well as the finite-size transverse-field Ising model, as
the latter provides additional insights in the construction of the circuit in a
resonating valence bond picture.
