Probing Many-Body Bell Correlation Depth with Superconducting Qubits

Quantum nonlocality describes a stronger form of quantum correlation than that of entanglement. It refutes Einstein’s belief of local realism and is among the most distinctive and enigmatic features of quantum mechanics. It is a crucial resource for achieving quantum advantages in a variety of practical applications, ranging from cryptography and certified random number generation via self-testing to machine learning. Nevertheless, the detection of nonlocality, especially in quantum many-body systems, is notoriously challenging. Here, we report an experimental certification of genuine multipartite Bell-operator correlations, which signal nonlocality in quantum many-body systems, up to 24 qubits with a fully programmable superconducting quantum processor. In particular, we employ energy as a Bell-operator correlation witness and variationally decrease the energy of a many-body system across a hierarchy of thresholds, below which an increasing Bell-operator correlation depth can be certified from experimental data. We variationally prepare the low-energy state of a two-dimensional honeycomb model with 73 qubits and certify its Bell-operator correlations by measuring an energy that surpasses the corresponding classical bound with up to 48 standard deviations. In addition, we variationally prepare a sequence of low-energy states and certify their genuine multipartite Bell-operator correlations up to 24 qubits via energies measured efficiently by parity oscillation and multiple quantum coherence techniques. Our results establish a viable approach for preparing and certifying multipartite Bell-operator correlations, which provide not only a finer benchmark beyond entanglement for quantum devices, but also a valuable guide toward exploiting multipartite Bell correlations in a wide spectrum of practical applications. Published by the American Physical Society 2025