Separability falsification — is one IBM job really one quantum system?

The primary architecture claim for QPC: when K objective contextures run coupled in one circuit, the measurement statistics show cross-context correlation that K independent IBM jobs cannot reproduce. This page explains the task, the math in plain terms, and every IBM Fez result from June 2026.

The task (no jargon)

Build a quantum circuit with three objective blocks (e.g. carbon, biodiversity, social).
Coupled arm: connect blocks with transjunction gates → submit one job to IBM.
Control arm: run each block alone (no transjunctions) → submit three jobs, then pair samples as if they were independent.
Ask: does the coupled run show extra correlation between adjacent objectives that the control cannot match?

If yes → QPC is doing something quantum-joint, not “three cloud jobs + Python merge.”

This test does not ask who got the best portfolio score. Optimization is a separate benchmark.

How we compute ICC (inter-context correlation)

For each pair of adjacent contextures we look at the first decision qubit (municipality #1 in Cerrado, or decision bit 0 in toy tests):

ICC = | average(Z_left × Z_right) − average(Z_left) × average(Z_right) | Z is +1 if the qubit measured 0, −1 if it measured 1 (standard Pauli-Z expectation from shot counts). We average ICC over the three boundaries: • carbon ↔ biodiversity • biodiversity ↔ social • social ↔ carbon ICC gap = (mean ICC on coupled arm) − (mean ICC on separable control)

Load-bearing detail: without a post-coupling readout rotation RX(0.8) on decision qubits, ICC is invisible in raw Z measurements. Both arms use identical readout.

Pilot success (toy & small Cerrado)

Coupled ICC ≥ 0.02
ICC gap ≥ 0.05
Coupled ICC ≥ 3× separable ICC
Control runs on the same backend as coupled

Heron-scale criterion (n=28, depth ≥1000)

When mean gap falls below 0.05, we report per-boundary ICC. Pass if ≥1 transjunction boundary meets: coupled ICC ≥ 0.05, boundary gap ≥ 0.04, ratio ≥ 3×.

Toy soft-objective instance (15Q coupled, ibm_fez)

Synthetic three-contexture instance — fixed seeds for reproducibility. 4096 shots each.

Seed	ICC gap	Coupled ICC	Pass	Coupled job ID
7	0.106	0.114	✓	`d8i3vdtv8cos73f549cg`
11	0.052	0.062	✓ (rerun)	`d8i429dv8cos73f54e60`
42	0.104	0.112	✓	`d8i3vu66983c73drmk10`

Strong pass: 3/3 seeds. JSON: results/qpc_separability_ladder_ibm_fez.json

Cerrado real data (Goiás carbon portfolio)

Same open dataset as Ribeiro 2026 (arXiv:2602.09047). Three objective contextures in one 156Q Heron layout when noted.

Instance	Layout	Depth	Mean ICC gap	Verdict	Job ID
n=8, k=3	shared	~500	0.088	Pass	`d8i4065v8cos73f54a8g`
n=12, k=4	shared	474	0.088	Pass	`d8i42ic2upec739loi50`
n=28, k=7	heron156 morph5	1883	0.025	Mean fail	`d8i43g42upec739loja0`
n=28, k=7	heron156 morph2	1329	0.031	Heron pass*	`d8i44rc2upec739loktg`

*Heron pass = per-boundary, not mean. On morph2 uniform readout:

Transjunction boundary	Coupled ICC	Separable ICC	Gap	Per-boundary pass
carbon ↔ biodiversity	0.005	0.010	−0.005	✗
biodiversity ↔ social	0.110	0.012	0.098	✓
social ↔ carbon	0.003	0.001	0.001	✗

Honest read at full Heron width: NISQ depth washes two of three boundaries; the biodiversity↔social bridge still shows strong non-separability. More shots did not help (8192-shot gap 0.010). Boosting readout on carbon/social qubits hurt ICC — uniform RX 0.8 stays load-bearing.

What this demonstrates (value for reviewers)

Falsifiable architecture claim with IBM job IDs, not simulation-only.
Separates architecture from optimization — you can pass ICC and still score near greedy; both numbers are reported.
Independent review loop — external AI challenge → corrected parallel definition → proposed test → we ran it.
Negative results included — mean ICC at n=28, readout boost failure, Antenna closed (see architecture program page).

Reproduce (operator)

cd site_release_2025_11_15 .venv/bin/python3 vendor_benchmarks/qpc_separability/qpc_separability_fez.py --mode ibm --backend ibm_fez .venv/bin/python3 vendor_benchmarks/qpc_separability/qpc_separability_cerrado.py --mode ibm --n 28 --k 7 --layout heron156 --morph-depth 2 --backend ibm_fez

Criteria document (internal): docs/QPC_SEPARABILITY_CRITERIA.md

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