  We investigate the potential of bio-inspired evolutionary algorithms for
designing quantum circuits with specific goals, focusing on two particular
tasks. The first one is motivated by the ideas of Artificial Life that are used
to reproduce stochastic cellular automata with given rules. We test the
robustness of quantum implementations of the cellular automata for different
numbers of quantum gates The second task deals with the sampling of quantum
circuits that generate highly entangled quantum states, which constitute an
important resource for quantum computing. In particular, an evolutionary
algorithm is employed to optimize circuits with respect to a fitness function
defined with the Mayer-Wallach entanglement measure. We demonstrate that, by
balancing the mutation rate between exploration and exploitation, we can find
entangling quantum circuits for up to five qubits. We also discuss the
trade-off between the number of gates in quantum circuits and the computational
costs of finding the gate arrangements leading to a strongly entangled state.
Our findings provide additional insight into the trade-off between the
complexity of a circuit and its performance, which is an important factor in
the design of quantum circuits.
