  We employ a machine learning-enabled approach to quantum state engineering
based on evolutionary algorithms. In particular, we focus on superconducting
platforms and consider a network of qubits -- encoded in the states of
artificial atoms with no direct coupling -- interacting via a common
single-mode driven microwave resonator. The qubit-resonator couplings are
assumed to be in the resonant regime and tunable in time. A genetic algorithm
is used in order to find the functional time-dependence of the couplings that
optimise the fidelity between the evolved state and a variety of targets,
including three-qubit GHZ and Dicke states and four-qubit graph states. We
observe high quantum fidelities (above 0.96 in the worst case setting of a
system of effective dimension 96) and resilience to noise, despite the
algorithm being trained in the ideal noise-free setting. These results show
that the genetic algorithms represent an effective approach to control quantum
systems of large dimensions.
