Simulating a Mach-Zehnder interferometer on a quantum computer for detecting mutual fractional statistics

Quantum spin liquids (QSL) are phases of matter that have recently gathered significant interests due to their unique properties that cannot be captured by the Landau theory and spontaneous symmetry breaking. Their ground states lack magnetic order but display long-range entanglement and topological order. In particular, quasi-particles with fractional statistics emerge in the QSL. We propose to use digital quantum devices to simulate a Mach-Zehnder interferometer for probing the quasiparticles mutual fractional statistics. We design a quasi-1D $mathbb Z_2$ ladder architecture in the case of $mathbb Z_2$ QSL, and show the signature of mutual fractional statistics from the data obtained from IonQ quantum devices and analyze the robustness of the signature to noises.