Nonlocal quantum games using deformed topologically ordered states

We introduce a nonlocal quantum game for which toric code ground states are a resource. Players who share a fixed-point state beforehand win with unit probability, whereas the optimal classical strategy only wins three quarters of the time. Unlike previous examples, the fixed-point strategy continues to surpass the optimal classical strategy away from the fixed point, leading to robust quantum advantage throughout an appreciable fraction of the toric code phase. We demonstrate this robustness experimentally on the Quantinuum H1-1 quantum computer by playing the game with a continuous family of randomly deformed toric code states created by applying weak measurements to every qubit.