Boundary-aware BIQAE where amplitudes become fragile.

QANTIS uses BIQAE to estimate the accepted-event amplitude after the amplification step. BIQAE maintains a Bayesian posterior over the amplitude angle, selects a Grover depth, observes success or failure, and updates the distribution. The sequential service then converts that amplitude estimate into evidence for an ordinary Bayes update.

The hardware problem appears near zero and one, exactly where rare observations and concentrated beliefs can place the service. An estimator that is accurate in the middle but biased at the boundaries can corrupt the posterior even when the amplifier behaves as designed.

On the reported IBM Pittsburgh paired run, the baseline boundary error at target amplitude 0.01 is 0.6317 and the boundary-aware protocol returns 0.00224. At target amplitude 0.95, the corresponding errors are 0.4890 and 0.00773.

The protocol does not fit a generic correction curve. A coarse scan selects an informative prior for the appropriate boundary regime, then BIQAE proceeds with that prior and the recorded hardware context. The result should not be generalized across devices, calibration windows, circuit families, or untested amplitude schedules.

The service is sequential: the posterior returned at one listen step becomes the prior at the next. This makes systematic estimator bias more dangerous than a one-off noisy measurement because it can propagate through the trajectory.

Boundary-aware calibration is therefore connected to the primary claim even though it sits in the supporting evidence tier. It helps explain how all-step amplification can remain usable when the Tiger belief becomes highly concentrated instead of relying on a guard that skips difficult steps.

The paper separately reports a 24-row Kingston boundary sweep in which 21 rows remain below Hellinger distance 0.02. That sweep validates the adaptive guard around standard Grover amplification; it is not the dataset used to produce the paired Pittsburgh BIQAE results.

Both controls help map the service boundary, but they answer different questions and should retain separate records. The Kingston sweep tests when to amplify or skip, while boundary-aware BIQAE tests how the estimator behaves near zero and one.

The primary evidence remains the 8-step and 12-step sequential Tiger posterior on Heron. Boundary-aware BIQAE is a supporting control that explains estimator stability near zero and one. The separate adaptive-guard sweep, rare-event envelope, and longer trajectories add operating context without becoming one calibration dataset.

Larger-state corridor and synthesis pilots remain exploratory. Wall-clock speedup, quantum advantage, full policy optimization, end-to-end autonomy, and downstream MTDA performance remain outside the paper's claim boundary.

A production research record should bind the coarse result, selected prior, visibility model, backend, job window, circuit family, amplitude schedule, mitigation state, shot budget, and software version together. The posterior should retain that provenance so a reviewer can reconstruct why the estimate was accepted.

When a boundary gate fails, the safe response is not to stretch the claim. The service should return to a classical estimator, request more evidence, or mark the update for review. The boundary-aware protocol is valuable because it makes that decision explicit.

The boundary failure is structural. A diffuse prior is reasonable in the interior but wasteful when the true amplitude lies near zero or one. If the estimator begins in the wrong regime, it can chase the boundary with deeper circuits just as hardware noise becomes more damaging.

The two-phase protocol uses a shallow first look to choose the prior family, then runs the ordinary BIQAE update. That small architectural change turns calibration into a service guardrail: it routes the hard boundary case before expensive estimation rather than trying to repair a drifting posterior afterward.

The paired Pittsburgh measurements make the effect concrete. At amplitude 0.01, absolute error moves from 0.6317 to 0.00224; at 0.95, it moves from 0.4890 to 0.00773. The responsible systems interpretation is that endpoint-aware initialization stabilized those tested cases, not that amplitude estimation is now solved universally.

The figures come from the boundary-aware BIQAE section of arXiv:2607.06760, submitted 7 July 2026. The preprint distinguishes same-backend boundary pairs from moderate-boundary supporting context and reports both baseline and calibrated errors for auditability.

The study frames the protocol as a lightweight calibration layer for a repeated belief-update service. It does not claim quantum advantage, wall-clock speedup, or validated performance across arbitrary probability models.