Generating multipartite nonlocality to benchmark quantum computers

Abstract

We show that quantum computers can be used for producing large $n$-partite nonlocality, thereby providing a method to benchmark them. The main challenges to overcome are as follows: (i) The interaction topology might not allow arbitrary two-qubit gates. (ii) Noise limits the Bell violation. (iii) The number of combinations of local measurements grows exponentially with $n$. To overcome (i), we point out that graph states that are compatible with the two-qubit connectivity of the computer can be efficiently prepared. To mitigate (ii), we note that for specific graph states, there are $n$-partite Bell inequalities whose resistance to white noise increases exponentially with $n$. To address (iii) for any $n$ and any connectivity, we introduce an estimator that relies on random sampling. As a result, we propose a method for producing $n$-partite Bell nonlocality with unprecedented large $n$. This allows one, in return, to benchmark nonclassical correlations regardless of the number of qubits or the connectivity. We test our approach by using a simulation for a noisy IBM quantum computer, which predicts $n$-partite Bell nonlocality for at least $n=24$ qubits.