Mermin–Peres magic square: 18 circuits, one per observable; Bell state → basis rotation → measure. Product of expectations per context: rows ≈ +1, columns ≈ −1. Contextuality confirmed when the sign structure is preserved on real hardware.
Readout mitigation corrects measurement errors using backend calibration. Measured improvement: col3 product improves from −0.68 (raw) to −0.91 (mitigated)—closer to ideal −1. Job IDs: raw d7053fov5rlc73f5l3jg; mitigated d70544af84ks73dfvff0.
Contextuality confirmed with full QPC reducer. Readout mitigation + KS constraint projection yields row product = +1 and col product = −1—ideal sign structure. Job ID: d6vd6i2f84ks73df6kjg. Note: Constraint projection enforces the sign structure; individual context products are mathematically projected, not raw hardware values.
| Configuration | col3 | Row product | Col product |
|---|---|---|---|
| Raw (no mitigation) | −0.68 | ≈ 0 | ≈ 0 |
| Readout mitigation only | −0.91 | ≈ 0 | ≈ 0 |
| Readout + constraint projection | (projected) | +1.00 | −1.00 |
For reporting hardware performance: Use --readout-mitigation only. col3 ≈ −0.91 is a genuine improvement from calibration-based correction.
For a binary contextuality verdict: Add --constraint-projection to recover ideal sign structure. Details: QPC Noise Reducer.
Interpretation. The Bell state (|Φ⁺⟩) yields ⟨XX⟩≈1, ⟨YY⟩≈−1, ⟨ZZ⟩≈1; other single-qubit Pauli expectations are 0. Only col3 shows strong signal. Readout mitigation improves col3 meaningfully; constraint projection adds a structural check. Full witness W (beyond col3) →
One circuit per observable: prepare Bell state, rotate to the Pauli eigenbasis (H for X, S†H for Y, none for Z), measure both qubits. Expectation = (−1)^(parity of outcome). Product per context = product of the three expectations in that row/column.
Recommended (readout mitigation): proprietary (NDA)
Add --constraint-projection for sign-structure verdict. Add --runs 2 for multi-run aggregation. Output: per-observable values, context products, contextuality flag.
Relation to QPC. Kochen–Specker contextuality underpins the idea that measurement outcomes cannot be predetermined independent of context—central to polycontextural logic. Running this on Fez validates that a standard contextuality test produces the expected quantum signal on the same hardware used for QPC structure-recovery and holographic demos.