Playing Quantum Nonlocal Games with Six Noisy Qubits on the Cloud

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, the minimal implementation of the nonlocal game proposed in Science 362, 308 (2018) is considered. This game is tested by preparing a 6-qubit cluster state using quantum computers on the cloud by IBM, IonQ, and Honeywell. The present implementation 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. The quantum nature of the cluster state is further studied by a Bell inequality that allows us to observe quantum advantage in less accurate quantum computers, at the expense of probing a larger number of circuits.