Controllable logic gate on the basis of a four-node linear hybrid cluster state

In the case of a large number of quantum calculations, a situation may arise when the intermediate results of the calculations need to be stored for a given time. This work shows how to create a hybrid atom-light cluster state and realize a $CZ$ gate in such a way that the results of its implementation are stored on long-lived degrees of freedom of the atomic ensemble and can be preserved for a long time.