Testing complementarity on a transmon quantum processor
We propose quantum circuits to test interferometric complementarity using
symmetric two-way interferometers coupled to a which-path detector. First, we
consider the two-qubit setup in which the controlled transfer of path
information to the detector subsystem depletes interference on the probed
subspace, testing the visibility-distinguishability trade-off via minimum-error
state discrimination measurements. Next, we consider the quantum eraser setup,
in which reading out path information in the right basis recovers an
interference pattern. These experiments are then carried out in an IBM
superconducting transmon processor. A detailed analysis of the results is
provided. Despite finding good agreement with theory at a coarse level, we also
identify small but persistent systematic deviations preventing the observation
of full particle-like and wave-like statistics. We understand them by carefully
modeling two-qubit gates, showing that even small coherent errors in their
implementation preclude the observation of Bohr's strong formulation of
complementarity.
Pedro M. Q. Cruz J. Fernández-Rossier