Braiding fractional quantum Hall quasiholes on a superconducting quantum processor

Direct experimental detection of anyonic exchange statistics in fractional quantum Hall systems by braiding the excitations and measuring the wave-function phase is an enormous challenge. Here, we use a small, noisy quantum computer to emulate direct braiding within the framework of a simplified model applicable to a thin cylinder geometry and measure the topological phase. Our algorithm first prepares the ground state with two quasiholes. It then applies a unitary operation controlled by an ancilla, corresponding to a sequence of adiabatic evolutions that take one quasihole around the other. We finally extract the phase of the wave function from measuring the ancilla with a compound error mitigation strategy. Our results point out an avenue for studying braiding statistics in fractional Hall states.