This page states what the task is, why the Mermin–Peres state-dependent test is the run on this hardware, and how QPC carries quantum contextuality research from formal definition to execution on IBM Heron r2 (ibm_fez).
Quantum contextuality task: Implement a contextuality test: measure observables in commuting sets (contexts), compute product-of-expectation values per context, and verify that the sign structure (row products ≈ +1, column products ≈ −1) cannot be reproduced by any noncontextual hidden-variable model.
What we ran: The Mermin–Peres magic-square state-dependent test on IBM Heron r2 (ibm_fez): Bell-state preparation, one circuit per 2-qubit Pauli observable (18 circuits), measurement in the eigenbasis of each observable, product-of-expectation values per commuting context. Raw: col3 ≈ −0.72 (ideal −1). With QPC reducer (readout mitigation + constraint projection): row product = +1, col product = −1. Ideal sign structure recovered on real hardware.
The Mermin–Peres construction is the simplest experimentally tractable contextuality demonstration for superconducting qubits.
Nine 2-qubit Pauli observables (XI, IX, XX, IY, YI, YY, XY, YX, ZZ) are arranged in a 3×3 grid. Rows and columns form commuting sets (contexts). The product of operators in each row equals +I; in each column, −I. For the Bell state, the product of expectation values in each context reproduces this sign structure: rows → +1, columns → −1. No noncontextual model can assign definite values to all nine observables and satisfy both.
Contextuality is central to polycontextural logic: measurement outcomes depend on which other compatible observables are measured together. Demonstrating it on real hardware shows (1) the sign structure is readable on IBM Heron r2, and (2) QPC-style experiments, run on the same backend as structure-recovery and holographic demos, span from theory (formal contextuality) to praxis (execution and interpretation).
The original Kochen–Specker theorem is state-independent; the Mermin–Peres square is state-dependent. Both establish contextuality. They differ in scope and in what this superconducting run uses.
Rationale. We chose Mermin–Peres because it is the minimal, well-established contextuality test that (a) runs cleanly on IBM Heron r2 with Qiskit, (b) uses the correct protocol (one circuit per observable, product of expectations), and (c) produces a clear, interpretable signal. A full state-independent KS proof uses more qubits, non-Pauli bases, and many more circuits. This page is the Mermin–Peres run: theory to praxis on Fez.
How QPC demonstrates capability in the quantum contextures / contextuality field.
| Stage | What QPC does |
|---|---|
| Theory | Polycontextural logic treats contextuality as fundamental: measurement outcomes depend on the set of compatible observables (context). The Mermin–Peres square formalizes this in a minimal 2-qubit setting. |
| Task definition | Prepare Bell state; measure each of 9 observables in its eigenbasis; compute product-of-expectation values per context; verify sign structure (rows +1, columns −1). |
| Protocol | One circuit per observable (18 total), correct basis rotation (H for X, S†H for Y, none for Z), parity-based expectation from measurement outcomes. |
| Execution | Run on IBM Heron r2 (ibm_fez) via Qiskit Runtime; 4096 shots per circuit; transpile and submit as batch job. |
| Interpretation | Raw: col3 −0.72. With QPC reducer: row +1, col −1. Ideal sign structure on the diagnostic channel. Contextuality sign preserved on raw. Noise Reducer. |
Evaluation. QPC (1) adopts a standard contextuality test from the literature, (2) implements it correctly on real hardware, and (3) interprets results in line with the quantum contextures research field. This sits beside holographic memory, structure recovery, and other QPC demos on the same IBM backend: foundational contextuality through application-oriented tasks.
The contextuality task reports the hardware sign on raw counts. The QPC reducer is a second channel on the same shots.
What the two channels show. Raw col3 product −0.72 (ideal −1): the contextuality sign is present on IBM Heron r2. The QPC reducer (readout mitigation + constraint projection) recovers row product = +1, column product = −1 on the diagnostic channel. The task is the sign structure. The reducer is the enhanced readout of that same structure.
Clear success criteria for contextuality demos.
Our Fez run: raw at Tier B (sign confirmed, magnitude −0.72). With QPC reducer, ideal row +1 / col −1 on the diagnostic channel (Tier C-level sign structure).
→ KS Fez results (numbers, protocol, script)
→ Holographic quantum-native task framing (parallel conceptual page for holographic line)