Benchmarks of Nonclassicality for Qubit Arrays

We present a set of practical benchmarks for N-qubit arrays that economically test the fidelity of achieving multi-qubit nonclassicality. The benchmarks are measurable correlators similar to 2-qubit Bell correlators, and are derived from a particular set of geometric structures from the N-qubit Pauli group. These structures prove the Greenberger-Horne-Zeilinger (GHZ) theorem, while the derived correlators witness genuine N-partite entanglement and establish a tight lower bound on the fidelity of particular stabilizer state preparations. The correlators need only M leq N+1 distinct measurement settings, as opposed to the 2^2N-1 settings that would normally be required to tomographically verify their associated stabilizer states. We optimize the measurements of these correlators for a physical array of qubits that can be nearest-neighbor-coupled using a circuit of controlled-Z gates with constant gate depth to form N-qubit linear cluster states. We numerically simulate the provided circuits for a realistic scenario with N=3,...,9 qubits, using ranges of T₁ energy relaxation times, T₂ dephasing times, and controlled-Z gate-fidelities consistent with Google's 9-qubit superconducting chip. The simulations verify the tightness of the fidelity bounds and witness nonclassicality for all nine qubits, while also showing ample room for improvement in chip performance.