  Neuroevolution, a field that draws inspiration from the evolution of brains
in nature, harnesses evolutionary algorithms to construct artificial neural
networks. It bears a number of intriguing capabilities that are typically
inaccessible to gradient-based approaches, including optimizing neural-network
architectures, hyperparameters, and even learning the training rules. In this
paper, we introduce a quantum neuroevolution algorithm that autonomously finds
near-optimal quantum neural networks for different machine learning tasks. In
particular, we establish a one-to-one mapping between quantum circuits and
directed graphs, and reduce the problem of finding the appropriate gate
sequences to a task of searching suitable paths in the corresponding graph as a
Markovian process. We benchmark the effectiveness of the introduced algorithm
through concrete examples including classifications of real-life images and
symmetry-protected topological states. Our results showcase the vast potential
of neuroevolution algorithms in quantum machine learning, which would boost the
exploration towards quantum learning supremacy with noisy intermediate-scale
quantum devices.
