What did the GHZ cloud benchmark measure?
Nine processors prepared an entangled GHZ target through their cloud workflows. A result could pass the study’s search rule at an estimated fidelity of 0.40. Certifying genuine multipartite entanglement under the study’s uncertainty bound required at least 0.60. The gap changes how to read the reported qubit counts.
Version 1.0.0 · source checked · JSON records · CSV records · Manifest and checksums
Main cloud workflow
Each row gives the fidelity estimate at the largest size encountered that passed the authors’ permissive search rule, Y + 0.10 ≥ 0.50. The other two columns describe boundaries from the same search, not additional measurements.
| Observation | Physical qubits | Fidelity Y | Y ≥ 0.50 boundary | Certification boundary | Experiment date and source |
|---|---|---|---|---|---|
| ibm_phoenix Nighthawk r2 | 27 | 0.438 | 23–26 | 16–22 | Table 2, ibm_phoenix, Y(N*) Observation conditionsQiskit optimization level 3 · Qiskit noise-aware layout Tested sizes: 16, 23, 27, 28, 29. One execution per tested size. The boundary comes from the tested search path. |
| ibm_basquecountry Heron r2 | 24 | 0.430 | 16–22 | 16–22 | Table 2, ibm_basquecountry, Y(N*) Observation conditionsQiskit optimization level 3 · Qiskit noise-aware layout Tested sizes: 16, 23, 24, 25, 27. One execution per tested size. The boundary comes from the tested search path. |
| ibm_pittsburgh Heron r3 | 21 | 0.510 | 21 | <16 | Table 2, ibm_pittsburgh, Y(N*) Observation conditionsQiskit optimization level 3 · Qiskit noise-aware layout Tested sizes: 16, 19, 21, 22, 23. One execution per tested size. The boundary comes from the tested search path. |
| iqm_emerald Crystal 54 | 20 | 0.421 | 16–18 | <16 | Table 2, iqm_emerald, Y(N*) Observation conditionsDefault Braket provider compilation · Provider-selected physical qubits Tested sizes: 16, 19, 20, 21, 23. One execution per tested size. The boundary comes from the tested search path. |
| ibm_miami Nighthawk r1 | 18 | 0.423 | 17 (non-monotonic) | <16 | Table 2, ibm_miami, Y(N*) Observation conditionsQiskit optimization level 3 · Qiskit noise-aware layout Tested sizes: 16, 17, 18, 19, 23. The hardware was exploratory during this run. Fidelity at N=17 crossed 0.50 after N=16 did not. |
| iqm_garnet Crystal 20 | 13 | 0.437 | 8–11 | 8–11 | Table 2, iqm_garnet, Y(N*) Observation conditionsDefault Braket provider compilation · Provider-selected physical qubits Tested sizes: 8, 12, 13, 14, 16. One execution per tested size. The boundary comes from the tested search path. |
| aqt_ibex_q1 IBEX Q1 | 12 | 0.711 | ≥12 (register limit) | ≥12 (register limit) | Table 2, aqt_ibex_q1, Y(N*) Observation conditionsDefault Braket provider compilation · Provider-selected physical qubits Tested sizes: 7, 10, 11, 12. Device register bounds the result. The experiment has no higher tested size. |
| rigetti_cepheus Cepheus-1-108Q | 4 | 0.491 | <4 | <4 | Table 2, rigetti_cepheus, Y(N*) Observation conditionsDefault Braket provider compilation · Provider-selected physical qubits Tested sizes: 4, 5, 6, 8, 16. AWS ran ten shots per stabilizer; only the first informed fidelity. This was the default workflow. |
| qmio Revision not reported | 3 | 0.513 | 3 | <3 | Table 2, qmio, Y(N*) Observation conditionsQiskit optimization level 3 · Qiskit noise-aware layout Tested sizes: 3, 4, 5, 8, 16. Qmio ran N=3 on 22 July. The 4-qubit check on 27 July contributes to the boundary; the precise processor revision is not named. |
A range such as 16–22 means 16 passed and the next tested size, 23, failed. It does not mean every intervening size ran. A value below the smallest tested size means that none of the tested sizes passed. IBEX Q1 reached its full register. Miami’s point estimates crossed 0.50 non-monotonically.
Separate manual layout experiment
The authors also selected physical chains for Rigetti Cepheus-1 using calibration data. Keep these observations separate from the main default-compilation result. The four-qubit run has a different layout and no separately reported run date or shot accounting in Appendix B.
| Observation | Physical qubits | Fidelity Y | Experiment date and source |
|---|---|---|---|
| rigetti_cepheus Cepheus-1-108Q | 2 | 0.86 | Run date not reported in Appendix B Appendix B, Table 3, N=2, GHZ fidelity Y Observation conditionsSeparate calibration-aware chain experiment · Manual chain selected from calibration graph Tested sizes: 2, 3, 4, 8, 16. Appendix B does not give a run date or a separate shot-accounting manifest for this series. Keep this result separate from the main workflow. |
| rigetti_cepheus Cepheus-1-108Q | 3 | 0.42 | Run date not reported in Appendix B Appendix B, Table 3, N=3, GHZ fidelity Y Observation conditionsSeparate calibration-aware chain experiment · Manual chain selected from calibration graph Tested sizes: 2, 3, 4, 8, 16. Appendix B does not give a run date or a separate shot-accounting manifest for this series. Keep this result separate from the main workflow. |
| rigetti_cepheus Cepheus-1-108Q | 4 | 0.33 | Run date not reported in Appendix B Appendix B, Table 3, N=4, GHZ fidelity Y Observation conditionsSeparate calibration-aware chain experiment · Manual chain selected from calibration graph Tested sizes: 2, 3, 4, 8, 16. Appendix B does not give a run date or a separate shot-accounting manifest for this series. Keep this result separate from the main workflow. |
| rigetti_cepheus Cepheus-1-108Q | 8 | 0.25 | Run date not reported in Appendix B Appendix B, Table 3, N=8, GHZ fidelity Y Observation conditionsSeparate calibration-aware chain experiment · Manual chain selected from calibration graph Tested sizes: 2, 3, 4, 8, 16. Appendix B does not give a run date or a separate shot-accounting manifest for this series. Keep this result separate from the main workflow. |
| rigetti_cepheus Cepheus-1-108Q | 16 | 0.04 | Run date not reported in Appendix B Appendix B, Table 3, N=16, GHZ fidelity Y Observation conditionsSeparate calibration-aware chain experiment · Manual chain selected from calibration graph Tested sizes: 2, 3, 4, 8, 16. Appendix B does not give a run date or a separate shot-accounting manifest for this series. Keep this result separate from the main workflow. |
Read the conditions before comparing
- Denominator and statistic
- Y is a unitless estimate of overlap with the ideal GHZ target at the listed size. It is not per-gate error or the fraction of the processor that worked.
- Uncertainty
- The main experiment sampled 2,952 stabilizers per size. The authors’ ±0.10 bound at 90% confidence is a finite-sample guarantee, not run-to-run variation. Rigetti ran ten shots per sampled stabilizer and used the first for the estimate.
- Compilation and accounting
- The Qiskit route used optimization level 3. Braket used provider-managed default compilation. Those workflows differ in qubit selection. The results do not match compilation time, queue time, cost or total resource use.
- Missing context
- Blank download cells denote fields the review could not establish for that observation. The study’s shot-retention rule is recorded separately from outcome-dependent postselection. A classical performance baseline is inapplicable to the ideal-state overlap estimator.
Different target sizes, dates, compilation choices and missing context block numerical ordering in this edition. The corpus lets you inspect the same study’s measurements and see why its search boundary cannot identify a general hardware winner.
Sources, versions and corrections
QubitWire transcribed the selected numeric facts and added interpretation notes. Measurements are by Sergio Hernández and coauthors. Consult the November 10 arXiv preprint, version 1, especially methodology, Table 2 and Appendix B, Table 3. The authors’ source data carry CC BY 4.0. The preprint has its own arXiv license.
Version 1.0.0 records the first 14 observations. The downloads retain their source version and locator. Send a correction with the affected observation ID to contact@qubitwire.com.
Read why the study had two pass marks · Work through a benchmark mixture example · Explore QRank’s organization research