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 two-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 2N stabilizer state preparations.

The correlators need only M ≤ N + 1 distinct measurement settings, as opposed to the 2 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.