  Quantum architecture search (QAS) involves optimizing both the quantum
parametric circuit configuration but also its parameters for a variational
quantum algorithm. Thus, the problem is known to be multi-level as the
performance of a given architecture is unknown until its parameters are tuned
using classical routines. Moreover, the task becomes even more complicated
since well-known trainability issues, e.g., barren plateaus (BPs), can occur.
In this paper, we aim to achieve two improvements in QAS: (1) to reduce the
number of measurements by an online surrogate model of the evaluation process
that aggressively discards architectures of poor performance; (2) to avoid
training the circuits when BPs are present. To detect the presence of the BPs,
we employed a recently developed metric, information content, which only
requires measuring the energy values of a small set of parameters to estimate
the magnitude of cost function's gradient. The main idea of this proposal is to
leverage a recently developed metric which can be used to detect the onset of
vanishing gradients to ensure the overall search avoids such unfavorable
regions. We experimentally validate our proposal for the variational quantum
eigensolver and showcase that our algorithm is able to find solutions that have
been previously proposed in the literature for the Hamiltonians; but also to
outperform the state of the art when initializing the method from the set of
architectures proposed in the literature. The results suggest that the proposed
methodology could be used in environments where it is desired to improve the
trainability of known architectures while maintaining good performance.
