Simulating Adiabatic Braiding of Fractional Hall Anyons on Quantum Computers

Intermediate-scale quantum technologies provide new opportunities for scientific discovery, yet they also pose the challenge of identifying suitable problems that can take advantage of such devices despite their present-day limitations. In solid-state materials, fractional quantum Hall (FQH) states support fractionally charged quasi-hole excitations, which have fractional exchange statistics. We will use quantum computers to create FQH quasi-hole excited states with a positive fractional charge. Next, we simulate the adiabatic process of exchanging two anyons and measure the anyonic braiding statistics on NISQ devices. Our results open a new avenue for studying the braiding statistics in fractional Hall models on the existing quantum hardware.