  Quantum Machine Learning (QML) is a recent and rapidly evolving field where
the theoretical framework and logic of quantum mechanics are employed to solve
machine learning tasks. Various techniques with different levels of
quantum-classical hybridization have been proposed. Here we focus on
variational quantum circuits (VQC), which emerged as the most promising
candidates for the quantum counterpart of neural networks in the noisy
intermediate-scale quantum (NISQ) era. Although showing promising results, VQCs
can be hard to train because of different issues, e.g., barren plateau,
periodicity of the weights, or choice of architecture. This paper focuses on
this last problem for finding optimal architectures of variational quantum
circuits for various tasks. To address it, we propose a gradient-free algorithm
inspired by natural evolution to optimize both the weights and the architecture
of the VQC. In particular, we present a version of the well-known
neuroevolution of augmenting topologies (NEAT) algorithm and adapt it to the
case of variational quantum circuits. We refer to the proposed architecture
search algorithm for VQC as QNEAT. We test the algorithm with different
benchmark problems of classical fields of machine learning i.e. reinforcement
learning and combinatorial optimization.
