  We introduce a synthetic Mach-Zehnder interferometer for digitized quantum
computing devices to probe fractional exchange statistics of anyonic
excitations that appear in quantum spin liquids. Employing an IonQ quantum
computer, we apply this scheme to the toric ladder, a quasi-one-dimensional
reduction of the toric code. We observe interference patterns resulting from
the movement of `electric' excitations in the presence and absence of
`magnetic' ones. We model the noise in IonQ via depolarizing Lindbladian
dynamics, and find quantitative agreement with the measurements obtained from
the quantum device. The synthetic Mach-Zehnder interferometer can thus also
serve as an effective means to probe the coherence length and time scales of
multi-qubit noisy quantum devices.
