This page states what the task is, why we use the Mermin–Peres state-dependent test rather than a full Kochen–Specker (state-independent) proof, and how QPC demonstrates capability in quantum contextuality research—from formal definition to hardware execution on 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 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 cannot be predetermined independent of which other compatible observables are measured. Demonstrating it on real hardware validates that (1) the quantum signal survives NISQ noise, 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 experimental feasibility.
Rationale. We chose Mermin–Peres because it is the minimal, well-established contextuality test that (a) runs cleanly on IBM Fez 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 would require more qubits, non-Pauli bases, and many more circuits—possible in principle, but not necessary to demonstrate QPC’s ability to execute contextuality research from theory to praxis.
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 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. Contextuality sign preserved; reducer recovers structure from noisy hardware. Noise Reducer. |
Evaluation. QPC shows that it can (1) adopt a standard contextuality test from the literature, (2) implement it correctly on real hardware, and (3) interpret results in line with the quantum contextures research field. This complements holographic memory, structure recovery, and other QPC demos—all on the same IBM backend—demonstrating breadth from foundational contextuality to application-oriented tasks.
The contextuality task shares the same noise ceiling as holographic, SWR, and other tests.
Universal restriction. Gate errors, decoherence, and readout noise cap everyone's circuits on current machines—not only QPC. Raw col3 product −0.72 (vs ideal −1) reflects NISQ noise. The QPC reducer (readout mitigation + constraint projection) recovers ideal row/col products. The task definition remains: demonstrate contextuality by the sign structure; implementation benefits from QPC-level noise reduction.
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 achieved (Tier C-level outcome on sign structure).
→ KS Fez results (numbers, protocol, script)
→ Holographic quantum-native task framing (parallel conceptual page for holographic line)