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Register a new userBenchmarks of Nonclassicality for Qubit Arrays
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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 $T_1$ energy relaxation times, $T_2$ dephasing times, and controlled-$Z$ gate-fidelities consistent with Googles 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.
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In a recent paper [R. Alicki and N. Van Ryn, J. Phys. A: Math. Theor., 41, 062001 (2008)] a test of nonclassicality for a single qubit was proposed. Here, we discuss the class of local realistic theories to which this test applies and present an experimental realization.
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