  The possibility of interaction-free measurements and counterfactual
computations is a striking feature of quantum mechanics pointed out around 20
years ago. We implement such phenomena in actual 5-qubit, 15-qubit and 20-qubit
IBM quantum computers by means of simple quantum circuits. The results are in
general close to the theoretical expectations. For the larger circuits (with
numerous gates and consequently larger errors) we implement a simple error
mitigation procedure which improve appreciably the performance.
