  Nonlocal games are extensions of Bell inequalities, aimed at demonstrating
quantum advantage. These games are well suited for noisy quantum computers
because they only require the preparation of a shallow circuit, followed by the
measurement of non-commuting observable. Here, we consider the minimal
implementation of the nonlocal game proposed in Science 362, 308 (2018). We
test this game by preparing a 6-qubit cluster state using quantum computers on
the cloud by IBM, Ionq, and Honeywell. Our approach includes several levels of
optimization, such as circuit identities and error mitigation and allows us to
cross the classical threshold and demonstrate quantum advantage in one quantum
computer. We conclude by introducing a different inequality that allows us to
observe quantum advantage in less accurate quantum computers, at the expense of
probing a larger number of circuits.
