Measurement
A logical Bell state, certified in three bases.
How our 99.94% logical Bell fidelity was measured in three mutually incompatible bases, re-derived from archived raw arrays, and published with its conditions.
Key takeaways
- We prepared the logical Bell state of the [[4,2,2]] error-detecting code and measured all three logical correlators, each in its own circuit at 20,000 shots.
- The three correlators came out at 〈ZZ〉 = +0.99969, 〈XX〉 = +0.99896, 〈YY〉 = −0.99885 — each within 0.2% of its ideal value.
- Together they give a logical Bell fidelity of 99.94%, 95% CI [0.9991, 0.9996], post-selected on the code’s detection check (~96% acceptance).
- Raw per-shot arrays are archived; a re-decode from them on 2026-08-15 tightened the confidence interval. The circuit is depth 7 and re-runs for $0 on a free account.
Why three bases?
A high number in one basis proves correlation, and classical systems correlate perfectly well. Entanglement only shows when the same state holds up in mutually incompatible bases at once. For the Bell state, ZZ and XX should read +1 while YY reads −1 — and faking all three simultaneously is what no classical state can do. That is why we treat single-basis memory results as classical until proven otherwise, our own included.
What did we measure?
Four physical qubits encode two logical qubits in the [[4,2,2]] error-detecting code — a textbook construction, published on several platforms before us. We prepared the logical Bell pair, then measured each logical correlator in its own circuit at 20,000 shots, with topology-aware placement on native couplers. Shots failing the code’s detection check are discarded before scoring — post-selection, with the ~96% acceptance rate published beside the number, the way a spec sheet carries its test conditions.
What did the numbers show?
The fidelity assembles from the three correlators: F = (1 + 〈ZZ〉 + 〈XX〉 − 〈YY〉)/4 = 0.9994, with a 95% confidence interval of [0.9991, 0.9996]. Every number re-derives offline from the archived per-shot arrays; a raw-array re-decode two weeks after the run tightened the interval and is dated on the ledger.
How can you check it?
The circuit is depth 7 with two entangling gates — among the cheapest experiments that run on real quantum hardware. With a free account on the open plan, anyone can rebuild it from the published decode conventions, run it, and compare their three correlators against ours. If your number differs, we want to hear it first.
Conditions. [[4,2,2]] error-detecting code (distance 2 — encoded and detected, not error correction), post-selected at ~96% acceptance per circuit; Heron-class processor; 20,000 shots per basis; bootstrap 95% intervals from archived per-shot counts; re-decoded from raw arrays 2026-08-15. Conditions and job IDs: the ledger.