GHZ State Fidelity

GHZ state fidelity is the oldest whole-device entanglement benchmark still in routine use: prepare an N-qubit Greenberger–Horne–Zeilinger state spanning the processor, then measure how faithfully it was made. No single paper defines it. The prepare-and-certify protocol traces to Sackett et al.’s deterministic four-ion entanglement at NIST in 2000, was scaled to 14 ions by Monz et al., and is now a named system-level benchmark in Quantinuum’s hardware documentation alongside Quantum Volume. Because it engages every qubit and the entangling-gate set at once, the largest certified N is a community-tracked cross-platform record.

How it works

An N-qubit GHZ state, (|0…0⟩ + |1…1⟩)/√2, is prepared, typically via a logarithmic-depth entangling circuit. Fidelity is estimated as F = (P + C)/2: populations P come from computational-basis measurements of the all-zeros and all-ones weights, and coherences C from parity oscillations or multiple-quantum-coherence measurements, avoiding full tomography. F > 0.5 witnesses genuine N-partite entanglement, so results are reported as the fidelity at a given N and the largest N certified.

Strengths and limitations

The test stresses the whole machine at once (entangling gates, crosstalk, correlated decoherence) with verification cost that stays modest as N grows. But it is community practice, not a standard: preparation circuits, estimation methods (tomography, parity oscillations, MQC, direct fidelity estimation), and error-mitigation choices vary by group and materially change the score. Mooney et al.’s 27-qubit IBM result clears 0.5 only with quantum readout error mitigation, while Quantinuum reports without SPAM correction, so check methodology before comparing platforms. F > 0.5 is a sufficient, not necessary, witness; and the bare fidelity is just a metric: the prepare-N/certify protocol and largest-certified-N record are what function as the benchmark.

Notable results

Quantinuum’s system benchmarks documentation reports H2-1 at 56 qubits with fidelity 0.6156 ± 0.0082, uncorrected (see also the H2 racetrack paper); superconducting records reached 60 qubits with readout correction by 2024. At the Helios launch (November 2025), Quantinuum’s blog reported 94 logical qubits fully entangled via the Iceberg code, not directly comparable to physical-qubit fidelities. Application suites such as SupermarQ include GHZ preparation among their tests.