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Quantum Machine Learning (QML) is a recent and rapidly evolving field wherethe theoretical framework and logic of quantum mechanics are employed to solvemachine learning tasks. Various techniques with different levels ofquantum-classical hybridization have been proposed. Here we focus onvariational quantum circuits (VQC), which emerged as the most promisingcandidates for the quantum counterpart of neural networks in the noisyintermediate-scale quantum (NISQ) era. Although showing promising results, VQCscan be hard to train because of different issues, e.g., barren plateau,periodicity of the weights, or choice of architecture. This paper focuses onthis last problem for finding optimal architectures of variational quantumcircuits for various tasks. To address it, we propose a gradient-free algorithminspired by natural evolution to optimize both the weights and the architectureof the VQC. In particular, we present a version of the well-knownneuroevolution of augmenting topologies (NEAT) algorithm and adapt it to thecase of variational quantum circuits. We refer to the proposed architecturesearch algorithm for VQC as QNEAT. We test the algorithm with differentbenchmark problems of classical fields of machine learning i.e. reinforcementlearning and combinatorial optimization.

QNEAT: Natural Evolution of Variational Quantum Circuit Architecture