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Real-Time Adaptive Filtering and the Boxcar Limit in Superconducting Qubit Readout

Hans Johnson, Tanay Roy, Leonardo Bove, David van Zanten, Silvia Zorzetti, Jafar Saniie

arXiv:2610.00783v1quant-pheess.SP

TL;DR

The paper asks when digital processing improves dispersive qubit readout beyond boxcar integration, and evaluates an on-fabric adaptive FIR alongside offline readout analyses. It finds that frozen FIR filtering cleans traces without systematic decision improvement, while readout-window and weighting choices yield gains in tested conditions.

  • Problem

    The paper asks when adaptive or sequential processing improves on boxcar integration, noting that readout methods often freeze the statistic or adapt acquisition and control instead.

    Source: §I · p. 2

  • Method

    The authors implement an on-fabric frozen FIR whose accumulated output collapses to a rescaled boxcar statistic apart from a finite-record edge, and compare readout methods offline.

    Source: §II · p. 2, §I · p. 2

  • Results

    The frozen filter showed no systematic fidelity gain over full-window integration, while tuned windows and per-sample weighting produced gains; at RL = 8 µs, weighting added +0.33% beyond the tuned window.

    Source: §VI · p. 14

  • Takeaways & Limitations

    The boxcar limit applies to the tested frozen-FIR-plus-accumulator path, motivating future tests of direct decision-weight and assignment-time control in situ.

    Source: §VI · p. 15

    The boxcar limit is specific to the tested frozen-FIR-plus-accumulator path, and the proposed in-situ decision and feedback path remains future work.

    Source: §VI · p. 15

Abstract

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In dispersive readout of superconducting qubits, the common baseline is a boxcar averager: a uniformly weighted average over a fixed window followed by threshold-based state assignment. We ask when additional digital processing improves fidelity. We evaluated an adaptive finite-impulse-response (FIR) filter trained in real time by the least-mean-squares (LMS) algorithm on an FPGA quantum controller, and analyzed measured readout shots offline to compare the frozen filter with boxcar averaging and to test per-sample weighting and sequential detection. For the fixed FIR filters tested, summing the filtered samples gives the boxcar sum multiplied by one complex number, apart from a small edge correction (the kernel collapse). This scales state separation and noise equally, so discrimination cannot improve (the boxcar limit). The frozen LMS filter reduces trace noise without a resolved fidelity improvement at the tested readout lengths. Replayed on the same shots offline, each filtered shot carries 99.4% of the boxcar shot's discrimination signal-to-noise ratio at the 8 $\mu$s operating point of the 2D transmon qubit (Q1). On Q1, optimizing the readout window's start and duration improves contrast readout fidelity by +2.4% to +5.6% across four readout lengths. Per-sample weighting adds up to +3.0% over full-window integration, and only +0.33% beyond the tuned window at 8 $\mu$s. Remaining results are from a 3D ancilla qubit (Q2), which sits above the early-decision crossover that Q1 sits below. Hardware sweeps locate the crossover window near 1 $\mu$s. Offline, the sequential test decided most shots early, with fidelity within 0.5 percentage points of the boxcar. About 30 labeled shots per class build a matched-filter template nearly as good as one from hundreds. The results form an operating-point record that separates waveform denoising from decision improvement.

I. INTRODUCTION

The paper asks when adaptive or sequential readout processing improves on equal-weight boxcar integration, against prior methods that typically freeze readout weights or adapt acquisition and control. It derives why a frozen FIR followed by uniform accumulation collapses to a rescaled boxcar statistic, then distinguishes trace cleanup from improved state discrimination.

I. INTRODUCTION

  • The study asks whether adaptive or sequential methods improve on boxcar integration, which weights every sample in the selected window equally.Prior approaches typically use host-computed frozen weights or adapt acquisition and control rather than the readout statistic itself.Source: §I · pp. 1–2

II. THE GOVERNING LAW: KERNEL COLLAPSE AND THE MATCHED-FILTER CEILING

  • For a frozen FIR followed by uniform accumulation, the summed output is a rescaled boxcar statistic apart from a finite-record edge, the kernel collapse.The scalar-rescaling limit scales and rotates the I/Q clouds without improving normalized separation, termed the boxcar limit.Source: §II · p. 2

A. Trace SNR, Discrimination SNR, and Fidelity Uncertainty

  • Trace SNR describes signal relative to noise in one trace, whereas discrimination SNR measures squared class-mean separation relative to pre-threshold score-noise variance.The paper also distinguishes these quantities from the standard error of fidelity estimated with labeled shots.Source: A. Trace SNR, Discrimination SNR, and… · p. 2
  • At measured operating points, the deployed filter improved trace SNR without systematic improvement in discrimination SNR or fewer validation shots for a given fidelity standard error.The generalized matched filter sets the maximum complex-output SNR for positive-definite noise covariance.Source: A. Trace SNR, Discrimination SNR, and… · p. 2
  • Adaptive noise cancellation would require an independent correlated noise-only reference input, which the setup did not include.The authors expect little advantage because amplifier-added noise dominating the averager passband has no signal-free copy to cancel.Source: A. Trace SNR, Discrimination SNR, and… · p. 2

B. The Kernel Collapse

For the tested frozen FIR-plus-accumulator path, kernel collapse makes the decision statistic a scaled boxcar statistic except for a finite-record edge. The filter’s measurable trace-noise reduction therefore does not produce a systematic discrimination gain at the tested operating points.

B. The Kernel Collapse

  • The filter-and-sum composition gives the same coefficient W to nearly every input sample, so its accumulated output is the boxcar statistic scaled by W.The coefficient origin does not matter; the identity follows from the composition itself.Source: B. The Kernel Collapse · p. 3
  • The scaling cannot improve discrimination because it multiplies state separation and noise variance by the same factor.For the uniform window, only the final T −1 samples can differ from W because their filter responses extend past the accumulation window.Source: B. The Kernel Collapse · pp. 3–4
  • At RL = 8 µs, 0.0256 of effective-weight entries differed from W, matching (T −1)/N = 63/2458.For fixed tap count, the potentially affected fraction decreases as record length increases.Source: B. The Kernel Collapse · p. 4
  • At RL = 8 µs, 93% of measured class-difference spectral power lay within ±125 kHz, where the boxcar averager’s two-sided ENBW is 125 kHz.The FIR mainly removed high-frequency trace noise already strongly attenuated in the decision statistic; matching the accumulator ENBW would require at least 2458 taps.Source: B. The Kernel Collapse · p. 4
  • The frozen 64-tap LMS/Wiener filter showed no systematic gain over boxcar averaging at any live readout length.A 64-tap moving average removed 16.2–16.3 dB of trace noise while its RL8 fidelity change was consistent with zero (−0.16%, 95% CI [−0.48, +0.13]).Source: B. The Kernel Collapse · p. 4
  • Escaping collapse requires changing the composition, such as using one designated FIR output sample or directly controlling sample-indexed accumulation weights.Either approach avoids summing the complete filtered output record uniformly.Source: B. The Kernel Collapse · p. 4

C. The Equivalent-Shot Currency

Equivalent-shot ratios express how many readouts are needed to match the boxcar’s accumulated discrimination SNR, not how many labeled shots estimate a classifier’s fidelity.

C. The Equivalent-Shot Currency

  • At RL = 8 µs, the frozen-filter detector’s equivalent-shot ratio was 0.9945 (95% CI [0.9931, 0.9960]), with ratios at RL = 4, 6, and 13 µs of 1.0192, 0.9910, and 0.9934.Values stayed within two percent of unity, and departures changed sign with readout length, consistent with a finite-window edge rather than systematic gain.Source: C. The Equivalent-Shot Currency · p. 4
  • For independent repetitions at equal accumulated deflection, required readouts scale as 1/Meq relative to the boxcar; this is not the labeled-shot count for estimating fixed-classifier fidelity.The frozen-filter ratios were near unity, while the per-sample matched filter gave Meq = 1.20 at the shortest window and 0.977 at the longest.Source: C. The Equivalent-Shot Currency · p. 4

D. Escaping the Collapse: The Matched-Filter Ceiling

Linear readout can exceed boxcar performance when its weights exploit time-varying state differences or in-band noise structure. The available gains are operating-point dependent, and a mismatched training direction can still impose a penalty.

D. Escaping the Collapse: The Matched-Filter Ceiling

  • A general sample-indexed linear readout exceeds the boxcar matched-filter ceiling only when the state-difference waveform is not proportional to noise covariance times the all-ones vector.The boxcar reaches the ceiling exactly when that proportionality holds.Source: D. Escaping the Collapse: The… · p. 4
  • At the transmon operating point, the calculated full matched-filter ceiling was approximately +1.6% over boxcar, while the measured comparison was +0.12%.These values are operating-point scoped; spur-rich noise or strongly nonstationary waveforms change both the calculated ceiling and measured comparison.Source: D. Escaping the Collapse: The… · p. 4

1) Colored Noise:

  • On Q2, the pre-registered whitening test gave +0.23% (95% CI [+0.12, +0.35]) against a +1.0% threshold.A planted +1.8% synthetic effect survived the same analysis pipeline.Source: 1) Colored Noise · p. 4

2) Time-Varying State Difference:

  • When the state-difference waveform varies through ring-up or T1 decay, per-sample weights can outperform a flat profile; live gains were +3.00/+1.90/+2.62% at RL = 4/6/8 µs and +0.02% at RL = 13 µs.An earlier sweep reported +3.26% at RL = 4 µs, a CI including zero at RL = 10 µs, and a negative result at RL = 13 µs.Source: 2) Time-Varying State Difference · pp. 4–5
  • At RL = 8 µs, per-sample weighting added +0.33% beyond the tuned boxcar, so most gain over full-window integration came from window placement.The tuned boxcar omitted early samples before the resonator response developed; integrating only the relaxation tail gave a negative change at RL = 6 and 8 µs.Source: 2) Time-Varying State Difference · p. 5
  • A per-state average-waveform MMSE objective can mismatch discrimination direction, with a computed penalty of approximately 0.96 dB at χ/κ = 1.0 and 1.0–12 dB over χ/κ ∈[0.1, 1.0].This direction penalty applies to the per-sample escape path; on the collapsed FIR path scalar invariance makes direction irrelevant.Source: 3) Training-Objective Mismatch and the… · p. 5

E. Empirical Closure

The on-fabric filter reduced trace noise but showed no resolved fidelity improvement, consistent with the predicted absence of systematic LMS/Wiener gains. The empirical closure also finds unchanged leading shot-count scaling, while model-based calibration estimates templates from tens of labeled shots.

E. Empirical Closure

  • Empirical closure uses real-score δ/σ for equivalent-shot ratios and checks held-out time-domain projections under an additive-noise, within-session-stationarity model.The analysis retains I/Q correlations, the measured finite window, and checks the frozen linear model against the fixed-point implementation.Source: E. Empirical Closure · p. 5

F. The Conjecture’s Verdict

  • The on-fabric filter reduced trace noise but produced no resolved fidelity improvement on replay, matching the predicted absence of systematic LMS/Wiener gain.The replay used read-back coefficients on the same measured shots.Source: F. The Conjecture’s Verdict · p. 5, §III · p. 5
  • All sixteen fitted log-log slope CIs contain −1/2, consistent with unchanged leading model-free shot-count scaling; model-based calibration instead estimates templates from tens of labeled shots.The remaining claims about calibration visibility, threshold stability, and drift tracking are left for future work.Source: F. The Conjecture’s Verdict · p. 5

III. THE ON-FABRIC ADAPTIVE FILTER AS A MEASUREMENT INSTRUMENT

  • The QICK readout-1 path sends downconverted, decimated samples through LMS filtering and accumulation before the tProc; labeled measured traces train the filter for same-shot offline replay.The filter coefficients are read back from the fabric and frozen for replay against the boxcar averager.Source: §III · p. 5, Figure 2 · p. 6

A. The Instrument Model

The instrument trains a complex FIR filter against an ensemble-average target using normalized LMS updates, then routes its output in adaptive, frozen, or bypass mode. For the frozen filter tested, accumulation scales state separation and noise equally, leaving discrimination fidelity unchanged.

A. The Instrument Model

  • The 64-tap complex FIR is trained against the ensemble-average target d[n], with its error driving a block-normalized LMS weight update.The firmware stores direct complex coefficients and uses the LMS branch to update them.Source: A. The Instrument Model · p. 6
  • The normalized step is formed once per pulse from accumulated window power, and the firmware commits updated coefficients between pulses.Mean convergence requires 0 < αeff < 2/λmax.Source: A. The Instrument Model · p. 6
  • Mode-0 adapts the weights, Mode-1 freezes them for Wiener filtering, and bypass passes the unfiltered signal through.The FIR and LMS blocks share a tapped delay line in the firmware design.Source: A. The Instrument Model · p. 6, Figure 3 · p. 6
  • The frozen Wiener filter scales the accumulated output by W, so state separation and noise spread scale together and single-shot fidelity does not improve.The reported effect is trace-noise reduction without fidelity improvement at the tested operating points.Source: A. The Instrument Model · p. 7

B. Implementation Footprint

The parallel 64-tap LMS update uses substantial FPGA resources, and the three-instance configuration would exceed device capacity before other QICK logic is added. The filtered path’s latency is dominated by the vendor FIR cores rather than by the LMS update.

B. Implementation Footprint

  • The filtered path has 280-ns latency at 307.2 MHz, with vendor FIR cores contributing 79 of its 86 clocks.The custom LMS update takes 18 clocks and runs in parallel with filtering.Source: B. Implementation Footprint · p. 7
  • The parallel 64-tap complex LMS update uses 512 DSP48E2 slices, and three 1,558-slice instances exceed the ZCU216’s 4,272-slice capacity before remaining QICK logic.Most remaining DSP use comes from the two vendor FIR cores.Source: Table I · p. 7, B. Implementation Footprint · p. 7
  • The packaged IP separates sample and coefficient streams on AXI4-Stream from AXI4-Lite user-variable access, with separate clock/reset pairs.A tProc trigger coordinates pulse-boundary operations.Source: Figure 4 · p. 7

C. Experimental Verification on the Qubit

The Q1 sweep mapped where fixed-point LMS training converges, while measured noise reduction confirmed that filtering cleans single-shot traces. The remaining noise and fidelity results show that denoising does not itself improve state assignment.

C. Experimental Verification on the Qubit

  • A shift-set amplitude floor can silently leave zero-initialized coefficients all-zero when updates fall below one LSB; every operating point tested was above it.Coefficient read-back, rather than the loss curve, is the ground truth for what the instrument applies.Source: C. Experimental Verification on the… · pp. 7–8
  • 657 of 4824 Q1 training configurations converged in a narrow diagonal band, with a maximum 84.06% fidelity, +1.44% over the unfiltered baseline.That maximum was mechanism evidence, not a deployable gain; the operating filter tied the boxcar comparison.Source: C. Experimental Verification on the… · p. 8, Figure 5 · p. 8
  • Across converged configurations, mean fidelity rose with coefficient energy from 69.1% to 76.6%, contrary to the proposed weight-quantization collapse explanation.The four log-spaced coefficient-energy bins had mean fidelities of 69.1%, 70.9%, 73.7%, and 76.6%.Source: C. Experimental Verification on the… · p. 8

D. Removable Noise for the Estimation Objective

  • 16.2–16.3 dB: the Q1 offline replays achieved this reduction against 18.06 dB predicted for the 64-tap average; correlated Q2 residual noise reduced its filtering benefit.Q1 residual noise was only mildly correlated, while Q2 residual noise was strongly correlated.Source: D. Removable Noise for the Estimation… · pp. 8–9
  • The Q1 hardware filter reduced residual power by 7.9 dB over 20–120 MHz, while fixed-point flooring and a widened passband limited its performance.The trained filter’s two-sided ENBW was about 39 MHz at RL = 8 µs, versus 4.8 MHz for the 64-tap average.Source: D. Removable Noise for the Estimation… · p. 9, Figure 6 · p. 9
  • 27.1–29.4 dB: the unit-DC Kalman filter reached this measured-shot noise reduction, 0.8–3.0 dB below the available budget.Mixed-ensemble training cost the templates at most 0.11 dB, and conditional-mean denoising changed no decision.Source: D. Removable Noise for the Estimation… · p. 9

IV. THE MEASURED OPERATING-POINT RECORD

This section records readout operating points across several qubits and acquisition protocols, with fidelity measures and comparison conditions that constrain how the results can be interpreted.

A. The Record and Its Disclosures

  • The section defines per-window deflection as accumulated state separation in units of single-shot noise spread, with δ/σ = 3.50 and 4.65 marking early-decision thresholds.These thresholds correspond to 92% and 98% contrast fidelity, respectively.Source: A. The Record and Its Disclosures · p. 10
  • Q1 was a fixed-frequency 2D transmon and the only qubit running the adaptive-filter firmware; Q2 and Q3 used different qubit and controller setups.Q2 was a 3D-style ancilla on a separate testbed; Q3 used an OPX1000 controller, and its captures were not controlled architecture or controller comparisons.Source: A. The Record and Its Disclosures · p. 10
  • The Q1 LMS/Wiener comparisons used separate acquisitions, while boxcar and per-sample matched-filter comparisons used held-out shots and tuned-boxcar results used nested cross-validation.The per-sample matched filter was an offline reference detector with knowledge of class templates.Source: A. The Record and Its Disclosures · p. 10
  • The frozen-filter replay showed no resolved fidelity difference from full-window boxcar integration; window tuning accounts for much of the observed improvement.Fig. 7 contrasts hardware acquisitions with offline analyses and shows 95% bootstrap confidence intervals.Source: Figure 7 · p. 10
  • The retained Q1 readout lengths were 4, 6, 8, and 13 µs, but their amplitudes also changed, so trends reflect operating-point changes as well as readout length.Other lengths were excluded for instrument fault, a Mode-0 artifact, or incomplete captures; 2 µs was not acquired.Source: A. The Record and Its Disclosures · p. 10

B. The Frozen-Filter Tie and the Per-Sample Escape

With frozen coefficients and uniform accumulation, the FIR output is approximately a complex rescaling of the boxcar sum, so trace denoising does not improve accumulated discrimination. The reported gains instead come from changing sample weights, motivating offline template-calibration and sequential-decision benchmarks.

B. The Frozen-Filter Tie and the Per-Sample Escape

  • Per-sample SNR values do not add to the full-window SNR because neighboring FIR outputs share inputs and their summed variance includes covariance.Fig. 9 plots per-sample squared deflection, whereas Table II reports deflection for the full-window sum.Source: B. The Frozen-Filter Tie and the… · p. 11, Figure 9 · p. 11
  • At RL = 8 µs, the deployed filter retained Meq = 0.9945, leaving shot requirements essentially unchanged at equal accumulated discrimination SNR.For frozen coefficients, uniform full-window accumulation scales state separation and noise equally, apart from a finite-record edge correction.Source: B. The Frozen-Filter Tie and the… · p. 11
  • +0.33%: the matched filter added this beyond the tuned window under the common nested RL8 evaluation; gains came from changing decision weights.Tuned boxcar windows improved fidelity at all four retained readout lengths.Source: B. The Frozen-Filter Tie and the… · p. 11

V. WHAT SURVIVES THE COLLAPSE

  • Offline Q2 studies benchmarked labeled-shot costs for template calibration and per-shot decision time; an on-fabric path’s performance and feedback latency remain untested in hardware.Q1 and Q3 supplied operating-point comparisons.Source: §V · p. 12

A. Template Estimation from Fewer Labeled Shots

Model-based template estimation reaches the matched-filter reference with substantially fewer labeled calibration shots than direct averaging. The estimator’s shot savings depend on the allowed template family, and calibration efficiency is distinct from the shots needed to validate a fixed classifier.

A. Template Estimation from Fewer Labeled Shots

  • 89.8% fewer labeled shots for the constant pulse and 87.5% fewer for fast ring-up reached the target versus direct averaging.The target was within 0.50% of the full-training-subset matched-filter reference; the savings varied across splits.Source: A. Template Estimation from Fewer… · p. 12
  • The model-based estimator fits a ring-up waveform to each M-shot mean, and its savings depend on the allowed linewidth search range.The fitted linewidth specifies template shape, not a physical linewidth measurement.Source: A. Template Estimation from Fewer… · p. 12
  • Computed sequencer time for template shots fell from ∼0.95 s with direct averaging to ∼0.097 s with the fit, excluding spectroscopy, software, and transfer overhead.The fast-ring-up pulse added a 0.20-µs pre-pulse without shortening the acquisition window; its matched-filter reference was 93.60%, versus 95.62% for the constant pulse.Source: A. Template Estimation from Fewer… · p. 12
  • Fig. 10 compares four template estimators against the full-training-subset matched-filter reference as labeled shots per class increase.It shows contrast fidelity on a fixed test subset for constant-amplitude and fast-ringup pulses.Source: Figure 10 · p. 12, A. Template Estimation from Fewer… · p. 12
  • The physics fit’s fidelity-estimate standard deviation was 1.39× the reference square root at M = 16, and at or below it from M = 32 onward.This comparison uses the full-rate dataset and the Cramer–Rao reference.Source: A. Template Estimation from Fewer… · p. 12
  • A three-way split changed the primary-acquisition saving from 89.8% to 90.0%, but tested template calibration rather than independent shots for fixed-classifier fidelity estimation.The split separates training, target definition, and testing.Source: A. Template Estimation from Fewer… · p. 13

B. Sequential State Assignment

Offline sequential replay on Q2 shortened decision times for most shots, with the primary split’s contrast fidelity within the stated equivalence margin of boxcar integration. The evidence is limited to replayed decisions and measured operating points; the Q1 transmon did not reach the specified early-decision regime.

B. Sequential State Assignment

  • The replay uses a Wald SPRT with training-derived thresholds held fixed during testing, and assigns by the sign of the cumulative log-likelihood ratio at crossing or at the terminal sample.The threshold is the smallest training-derived candidate whose training error does not exceed the boxcar error on the same training shots.Source: B. Sequential State Assignment · p. 13
  • 85.0% of Q2 test shots crossed before the 2.60-µs deadline; mean decision time was 1.80 µs (69.2% of the window), with contrast fidelity 95.34% versus 95.20% for boxcar.The paired difference was +0.14 percentage points (95% CI [−0.18, +0.46]), within the retrospective ±0.5-percentage-point equivalence margin.Source: B. Sequential State Assignment · p. 13, Figure 11 · p. 13
  • Fig. 11 marks cumulative-score threshold crossings and replayed decision times, not measured hardware latency.Its shading gives the 10th–90th percentiles among shots crossing before the deadline; the dotted line is the median including terminal decisions.Source: Figure 11 · p. 13
  • Across three overlapping splits of the same Q2 capture, mean decision times were 1.69–1.80 µs and 85.0–89.8% of shots decided in-window, but equivalence was not established on every split.These were sensitivity checks, not independent replications; hardware feedback must account for processing latency and the decision-time tail.Source: B. Sequential State Assignment · p. 13
  • At the (0.05, 0.05) error budget, Q2 and Q3 met the δ/σ floor at 4.17 and 3.44, while Q1’s 1.33–2.68 fell short.This boundary applies to measured operating points and evaluated detectors, not planar qubits or stopping rules generally.Source: B. Sequential State Assignment · p. 13
  • Q2’s fidelity curve flattens inside its window, whereas Q1’s was still rising at its acquisition endpoint and did not establish early decisions at the (0.05, 0.05) target.The t95 marker is descriptive, not necessarily the fixed window matching the sequential detector; a stopping comparison should use a fixed-window baseline at the same target.Source: B. Sequential State Assignment · p. 14
  • Q2’s 2.6-µs capture contained a residual near 0.43 MHz, consistent with a fidelity peak near 2.4 µs as the boxcar attenuated a stable tone near 1/f ≈ 2.3 µs.Offline tone removal moved the floor crossing earlier, but its relevance to real-time stopping depends on estimating the tone without later samples.Source: B. Sequential State Assignment · p. 14
  • At tested Q2 operating points, delaying integration start improved short-window fidelity, while windows longer than 2.2 µs changed by at most 2%.For Q1, replay mean decision time was 73–81% of the window when the threshold matched the boxcar’s own error rate, not the registered (0.05, 0.05) budget.Source: B. Sequential State Assignment · p. 14

VI. CONCLUSION AND OUTLOOK

The tested frozen-FIR-plus-accumulator path did not improve discrimination over boxcar integration, despite reducing trace noise. The conclusion instead emphasizes window placement, per-sample weighting, and Q2 offline calibration and timing results, while identifying in-situ decision control as future work.

VI. CONCLUSION AND OUTLOOK

  • For a frozen FIR followed by uniform accumulation, the output is the boxcar statistic times one complex number, apart from finite-record and arithmetic corrections, scaling state separation and noise alike.The paper calls this the boxcar limit and confines it to the tested frozen-FIR-plus-accumulator path, not linear readout processing generally.Source: §VI · pp. 14–15
  • Same-shot replay of the 64-tap LMS/Wiener filter showed no resolved fidelity improvement over full-window boxcar integration at four retained Q1 operating points.Window placement and per-sample weighting produced gains that the frozen filter did not; at RL = 8 µs, matched filtering added +0.33% beyond the tuned window.Source: §VI · p. 14
  • With a linewidth search range set from an independent resonator measurement, Q2 model-based template estimation required 89.8% fewer labeled shots than direct averaging; sequential replay’s primary split mean time was 1.80 µs.Across three overlapping splits, mean decision times ranged from 1.69 to 1.80 µs; equivalence was not established on every split.Source: §VI · pp. 14–15
  • The deployed instrument tested the frozen-filter result on fabric and linked measured behavior to implemented arithmetic using coefficient readback and a bit-true model.Telemetry may support drift detection, but its value for triggering recalibration remains untested.Source: §VI · p. 15
  • The next architectural step is direct control of decision weights and assignment time, with in-situ state assignment, active-reset feedback, and drift-triggered recalibration left for future testing.Fig. 12 presents fixed-window curves without a stopping rule and distinguishes acquisitions across Q1, Q2, and Q3.Source: Figure 12 · p. 14, §VI · p. 15
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