Full Specification Sheet · Methodology & Sources

Have we found quantum advantage? The five-scoreboard answer

Nature Campaign summary (5 scoreboards) Hardware IBM Heron · 2026 campaign Experiments ~110 · F01–F118 Every number a job ID

◇ FOUND ON FOUR OF FIVE · theorem ceilings cleared 21σ to 341σ

↓ Read this sheet as plain-text Markdown

This is the methodology sheet behind the visual scoreboard. The exhibit answers one question — have we found quantum advantage? — across five scoreboards, each cleared against an exact theorem ceiling, and it states plainly what is not claimed. Every σ below is transcribed verbatim from the exhibit (the tiles and the enumerated rows array); nothing is invented. Sources in §5.

1The verdict, in one line

Yes — measurably, on four of five scoreboards, against exact theorem ceilings cleared by 21σ to 341σ. On the fifth — computational — the wall against a brute-force speedup is measured (F54), and the constant-depth solver that the only depth-separation theorem is built on now runs on silicon at 90%. No shortcut is claimed that the hardware does not hold.

2The five scoreboards

Games & correlations — FOUND. 216.8σ causal-order game; the three great no-go theorems in one court — Bell, indefinite causal order, contextuality (8/9 at 196σ). F82 · F106
Communication & sensing — FOUND. 341σ superdense coding; a ladder including 2→1 QRAC (110σ) and GHZ metrology beating the standard quantum limit (168σ). F87 · F107 · F108/9
Thermodynamics — FOUND. 21.1σ ICO refrigeration: population inversion from passive baths, a full cycle, negative local energy. F86 · F94/5 · F97
Information — FOUND. 42σ negative conditional entropy S(B|A)<0 — a sign classical physics forbids — plus zero-capacity transmission. F103 · F105
Computational — WALL + BRIDGE. No brute-force speedup (F54's wall), but the constant-depth 2D-HLF solver runs at 0.90 (438σ over chance) and persists to n=9. F113 · F114

3The theorem ceilings — clearance over the classical / theorem bound

Each headline clears an exact, pre-registered bound. The flagship σ values, transcribed from the exhibit's enumerated table with the null each is measured against:

Campaign headline clearances over classical theorem bounds across five scoreboards
scoreboard headline	clearance	over the bound
Superdense coding	341σ	over 0.5 (unassisted)
Causal-order game	216.8σ	over 0.8695 (SDP)
Magic-square contextuality	196σ	over 8/9 (enumerated)
GHZ metrology	168σ	over executed SQL
One-sided-DI steering	96σ	over LHS bound 1
Capacity activation	55.6σ	over 0
Negative conditional entropy	42σ	S(B\|A) < 0
ICO refrigeration	21.1σ	over 0

The through-line

The classical hardness of the computational problem (F113) is the magic-square contextuality (F106), certified at 196σ — the correlation advantage and the computational instrument are the same resource. (The Race-6 runtime claim that briefly sat on this scoreboard was superseded by our own red-team pre-submission, C4996 — see the exhibit.)

4What is NOT claimed

The boundary column — each an explicit limit printed on the exhibit:

✕No brute-force speedup — F54's 10× depth wall, measured. ✕No on-chip QNC⁰≠NC⁰ proof — the separation is asymptotic; the apparatus is real. ✕No loophole-free device-independence — the randomness certificate (F117, 0.65 bit/use) is one-sided-DI; locality open. ✕Same Heron generation only — a cross-generation exam is the harder unclaimed test.

5Sources & provenance

Exhibit: demo/scoreboard/index.html — the five tiles, the log-scale σ bars, the through-line, and the "what is not claimed" list. All σ values on this sheet are transcribed from it (tiles + rows array).
Campaign ledger: docs/campaign-arcs.md (F01–F118) — per-finding rows corroborate each headline: F82 (216.8σ), F106 (196σ), F87 (341σ), F108 (168σ), F83 (55.6σ), F86 (21.1σ), F113/F114 (438σ / n=9), F117 (0.65 bit/use, one-sided-DI).
Scope of the whole board: ~110 experiments · 3 Heron dies (marrakesh · kingston · fez), certified across all three (F112) · 2 standing tools (SDP-randomness, QPU-weather). Every number traces to a pre-registered job with a public ID.
Full argument: docs/quantum-advantage-the-complete-answer-whisper-c4682.md.

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