  We study a quantum walk of a single particle that is subject to stroboscopic
projective measurements on a graph with two sites. This two-level system is the
minimal model of a measurement induced quantum walk. The mean first detected
transition and return time are computed on an IBM quantum computer as a
function of the hopping matrix element between the sites and the on-site
potential. The experimentally monitored quantum walk reveals the theoretically
predicted behavior, such as the quantization of the first detected return time
and the strong increase of the mean first detected transition time near
degenerate points, with high accuracy.
