Experimental test of Mermin inequalities on a five-qubit quantum computer

Violation of Mermin inequalities is tested on the five-qubit IBM quantum computer. For three, four, and five parties, quantum states that violate the corresponding Mermin inequalities are constructed using quantum circuits on superconducting qubits. Measurements on different bases are included as additional final gates in the circuits. The experimental results obtained using the quantum computer show violation of all Mermin inequalities, with a clear degradation of the results in the five-qubit case. Though this quantum computer is not competitive to test Mermin inequalities as compared to other techniques when applied to a few qubits, it does offer the opportunity to explore multipartite entanglement for four and five qubits beyond the reach of other alternative technologies.

Figure 1

The two circuits used for the three-qubit Mermin inequality. The first circuit corresponds to the ${\sigma }_x{\sigma }_x{\sigma }_y$ experiment, and the second circuit corresponds to the ${\sigma }_y{\sigma }_y{\sigma }_y$ experiment. The $S^{†}$ gates make the difference between a ${\sigma }_x$ measurement and a ${\sigma }_y$ measurement.

Figure 2

Two of the circuits used for the four-qubit and five-qubit Mermin inequalities. The first circuit corresponds to the ${\sigma }_y{\sigma }_y{\sigma }_x{\sigma }_x$ experiment, whereas the second corresponds to the ${\sigma }_x{\sigma }_y{\sigma }_x{\sigma }_x{\sigma }_y$ experiment. The $S^{†}$ gates make the difference between a ${\sigma }_x$ measurement and a ${\sigma }_y$ measurement. In order to change from ${\sigma }_x$ to ${\sigma }_y$, one has to add an $S^{†}$ gate, or remove it to do the opposite. With this technique one can obtain all the circuits needed to test the inequalities.