Interaction-free measurements and counterfactual computation in IBM quantum computers

The possibility of interaction-free measurements and counterfactual computations is a striking feature of quantum mechanics pointed out around 20 years ago. We have designed simple quantum circuits that realize both phenomena in real 5-qubit, 15-qubit and 20-qubit IBM quantum computers. In particular, counterfactual computation in its simplest form (Jozsa protocol) cannot be directly implemented in present quantum computers, requiring the design of a modified quantum circuit. 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.