Optimal Nonclassicality-based Benchmarks for Linear Qubit Arrays

A special class of sets of M ≤N + 1 mutually commuting N-qubit Pauli operators can be used to simultaneously witness N-partite entanglement, violate a Bell inequality associated with the N-qubit Greenberger-Horne-Zeilinger theorem, and place a tight lower bound on the fidelity of particular stabilizer state preparations. This fidelity bound is tight in the sense that if the true fidelity is 1, then the lower bound obtained from M measurement settings also goes to 1, but it grows worse as the true fidelity degrades.

Example sets are given for N= 3,...,9 qubits, along with the corresponding circuit designs, which are optimized to require only nearest-neighbor controlled-Z operations on a linear array of physical qubits, with a uniform gate depth of four - local rotations to initialize each qubit, two rounds of staggered nearest neighbor controlled-Z gates, and local rotations to set the readout basis. These circuits were simulated to estimate their practicality with a range of state-of-the art T₁ decoherence times, T₂ dephasing times, and gate fidelities.

The paper was presented at: Proceedings of: 'APS March Meeting 2018, abstract id.L28.012

This work was supported (in part) by the Fetzer Franklin Fund of the John E. Fetzer Memorial Trust.