Which-path experiments on a transmon quantum processor

We propose quantum circuits to test the complementarity principle through which-path experiments on symmetric two-way interferometers coupled to a single detector. First, we consider the bipartite setup in which the controlled transfer of quantum information to a detector subsystem depletes interference on the probed subspace, testing the trade-off between which-path information and interference visibility. Next, we consider the quantum eraser setup, in which properly reading-out the which-path information recovers an interference pattern. Finally, we construct an N-qubit two-way interferometer to explore the quantum-to-classical transition. We start by conceiving abstract quantum circuits and discuss the problem in the quantum computing language. Then, we perform these experiments in the transmon superconducting quantum processors by IBM Q. A detailed analysis of the results is provided. Despite finding good agreement with theory, we also observe slight systematic deviations shown to be due to cross-talking.