A rare-event envelope, not a hardware-advantage claim.

A Bayes update divides by the probability of the observed evidence. When that event is very rare, direct accepted-event sampling needs many trials before the estimator has enough useful observations. QANTIS targets this inference-side bottleneck rather than moving the entire planner onto a quantum processor.

Amplitude amplification changes the logical sampling relationship toward inverse-square-root evidence scaling. The paper tests whether a bounded schedule can raise the accepted-event probability close to its analytic target on present Heron hardware across a sweep that reaches one-in-a-million evidence.

The sequential Tiger study uses all-step fixed-point amplitude amplification with phase-shifted reflections and one iterate per listen step. The rare-event envelope uses bounded-length standard Grover-Brassard reflections on a one-qubit logical oracle.

Keeping the circuit families separate prevents an attractive but incorrect shortcut. The 971,832x figure belongs to the rare-event logical sweep; it is not the amplification measured in the sequential Tiger posterior loop and it is not an end-to-end system acceleration factor.

For the rarest tested evidence probability, one in one million, the Kingston Heron R2 run reports accepted-event probability 0.9718 against an analytic prediction of 0.9714. The paper labels the corresponding ratio 971,832x logical amplification.

The word logical carries the claim boundary. It describes the ratio between the original evidence probability and the measured accepted-event probability under the tested logical schedule. It does not include compilation overhead, queue time, execution latency, repeated calibration, classical orchestration, or the complete cost of a belief update.

After transpilation at the reported default optimization level, the rare-event source circuit collapses to at most six single-qubit basis gates. That makes the row useful for validating the logical sample-complexity envelope, but it does not validate long or deep rare-event circuits.

The paper includes a barrier-fenced depth sweep to expose this boundary. Merged circuits track the logical prediction; deliberately unmerged deeper circuits become physical-depth frontier markers. The result therefore supports a shallow operating map and identifies depth as the next hardware constraint.

The primary claim remains sequential Tiger POMDP belief updating in the reported 8-step and 12-step runs. The rare-event sweep is supporting evidence that maps the logical sampling regime the service wants to exploit. Heron R3 transfer and longer horizons provide other supporting controls.

Four-state and UCGate/QSD pilots are exploratory. Hardware advantage, wall-clock speedup, full policy optimization, downstream MTDA advantage, and end-to-end autonomy are out of scope.

An operating envelope is useful when it changes what a system does. A research workflow can route an evidence update to hardware only when the estimated event probability, scheduled iterate count, compiled depth, calibration state, and fallback path remain inside the tested corridor.

Outside that corridor, the correct action is to use classical sampling, redesign the oracle, reduce depth, or gather more evidence. The map becomes an engineering control only when its caveats travel with every decision.

Rare observations are difficult because direct sampling may wait a long time for enough accepted events. Amplitude amplification changes the probability of measuring that accepted event, so the useful first question is whether the measured acceptance follows the analytic target as the original evidence becomes very small.

At evidence probability 0.000001, the reported hardware row measures 0.9718 acceptance against 0.9714 analytically. The resulting 971,832x ratio is striking, but its unit matters: it is logical amplification of event probability. It says nothing by itself about compilation, queueing, control overhead, or total elapsed time.

The envelope is therefore a map for engineering. It identifies a rare-evidence regime worth investigating and, alongside separate depth sweeps, shows where physical circuit depth begins to break the logical picture. A future speed claim would need complete timing records and an end-to-end baseline that this preprint does not provide.

The rare-event values come from arXiv:2607.06760, submitted 7 July 2026. The source calls the figure an operating map and a logical sample-complexity envelope. It also explains that the one-qubit bounded-length Grover-Brassard circuits are distinct from the phase-shifted FPAA circuits used in the sequential Tiger loop.

For that reason this guide never converts 971,832x into a latency, throughput, cost, or end-to-end autonomy claim. The paper reports none of those outcomes.