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Beyond sensitivity: mechanism-resolved error budgets for designing quantum sensors

Nima Leclerc, Marco Capelli, Kevin James Rietwyk, Mark Dong, Dmitry Lyakh, Geoffrey Iwata, Brandon Rodenburg, Sean Oliver, Benedikt Kloss, Jin-Sung Kim, Stefan Bogdanovic, Yunheng Chen, Meysam Sharifzadeh Mirshekarloo, Cedric Weber, Marcus Doherty, Ethan Pratt, Joseph Hagmann

arXiv:2608.28519v1quant-pheess.SYphysics.app-ph

TL;DR

Quantum sensors need accuracy and reliability alongside sensitivity, but existing methods do not resolve how interacting mechanisms form per-metric error budgets. This paper introduces a single open-system modeling framework that computes and attributes sensitivity, accuracy, and robustness, showing distinct limiters across metrics and supporting metric-targeted design.

  • Problem

    Quantum sensors require multiple performance metrics, yet no existing tool resolves interacting mechanisms into a per-mechanism budget for each metric from a common device model.

  • Method

    The framework uses one open-system solve to compute sensitivity, accuracy, and robustness and attributes each metric to interacting physical mechanisms.

  • Results

    For the NV ensemble, spin dephasing governs sensitivity, the thermal ground-state shift governs accuracy, and optical leakage governs robustness; accuracy bias spans 8 to 1500 nT.

  • Takeaways & Limitations

    The per-mechanism map identifies the lever for each metric and predicts the gain from addressing its limiter, enabling designs targeted to application requirements.

  • Takeaways & Limitations

    The paper does not carry out the redesign implied by its identified mechanism and metric levers.

Abstract

from arXiv · show

Quantum sensors are specified by a headline sensitivity, yet applications also demand accuracy and reliability. The dominant limiter of one metric is often known, but no method resolves how interacting mechanisms combine into a signed, per-mechanism budget for each metric. We introduce a framework that computes a sensor's sensitivity, accuracy, and robustness from one open-system simulation and attributes each to its limiting mechanism. For a nitrogen-vacancy diamond ensemble the attribution inverts across metrics: dephasing limits sensitivity, the thermal ground-state shift limits accuracy, and optical leakage limits robustness. At identical sensitivity the recovered-field bias spans $8$ to $1500$\,nT, so tuning to sensitivity alone can miss the accuracy target by two orders of magnitude. The same modeling transfers to a cesium optically pumped magnetometer recording a human magnetocardiogram. As a digital twin, it predicts the gain from addressing each limiter, so sensors can be designed to the required metrics.

1 Introduction

Quantum-sensor applications require simultaneous sensitivity, accuracy, and robustness, but existing approaches rarely attribute these metrics to interacting mechanisms from one device model. The framework provides a single open-system, per-mechanism accounting that supports quantitative, application-specific design.

  • Motivation: Sensitivity, accuracy, and robustness are functionals of the same open-system physics rather than independent design knobs.The sensor state evolves under a Lindblad master equation, with metrics determined by responses to the sensed field and device imperfections.
  • Motivation: Different mechanisms can limit different metrics: dephasing degrades sensitivity while leaving the recovered field unbiased, so it does not affect accuracy.This motivates identifying the mechanisms setting each metric rather than optimizing a single figure such as coherence time.
  • Gap: Existing tools typically optimize or bound one performance axis and rarely attribute accuracy or robustness to specific mechanisms from a common forward model.Current practice often tunes sensitivity empirically while assuming other metrics follow.
  • Framework: The framework evaluates sensitivity, accuracy, and robustness from one open-system solve and assigns each metric a signed budget over physical mechanisms.Robustness is defined as stability of sensitivity under operating-parameter drift, and the construction can extend to dynamic range.
  • Framework: Shapley values attribute each metric to interacting mechanisms, while a tangent master-equation solve jointly propagates the state and field derivative.The resulting budgets are validated against measured NV diamond and cesium optically pumped magnetometer devices.
  • Results: For the NV ensemble, spin dephasing limits sensitivity, the thermal ground-state shift limits accuracy, and optical leakage limits robustness.Equal sensitivity can therefore coexist with markedly different accuracy and calibration stability.
  • Implications: The model identifies the dominant mechanism for each metric and predicts the gain from acting on it, making application-specific sensor design quantitative.The framework is presented as transferable beyond magnetometry to open quantum systems with optical readout.

2 Results

The validated open-system framework produces all three metrics from one solve and attributes their limits to physical mechanisms. Across interrogation time, operating conditions, and measured optical intensity, the limiting mechanism depends on the metric rather than sensitivity alone.

  • Framework: A single validated forward model computes sensitivity, accuracy, and robustness and assigns each metric a per-mechanism budget.The accounting uses mechanism toggles in the open-system solve, including interactions that leave-one-out accounting would leave unassigned.
  • Sensitivity: The sensitivity curve is U-shaped because phase gain initially improves with interrogation time, then contrast decay overtakes it.At high nitrogen concentration, conversion-efficiency roll-off and coherence penalties eventually make additional nitrogen cost sensitivity.
  • Metric-dependent attribution: Dephasing contributes about 89% of sensitivity across short and intermediate interrogation times, declining to 83% at the longest times as optical leakage grows.Thermal and T1 channels each remain below 2% because they do not reshape the fringe contrast setting sensitivity.
  • Metric-dependent attribution: A 0.1 K temperature offset produces an apparent field of approximately 282 nT through the thermal ground-state splitting shift.The thermal bias is interrogation-time independent before calibration cancellation effects alter the net RMSE.
  • Metric-dependent attribution: At the operating point, coherence limits sensitivity, temperature limits accuracy, and leakage drift limits robustness, with the ordering stable across 500 shot-noise realizations.Robustness is best at the shortest interrogation time, where sensitivity is worst, so no single interrogation time optimizes all three metrics.
  • Design implications: Along a 100 pT sensitivity locus, recovered-field bias ranges from 8 to 1500 nT, showing that equal sensitivity does not ensure equal accuracy.Across the design plane, sensitivity is dephasing-limited over 57%, accuracy changes limiter near ε ≈3 × 10−5, and robustness is leakage-drift-limited over 78%.
  • Measured operating knob: Accuracy remains nearly flat across almost three decades of measured intensity because the thermal bias stays above the shot-noise floor.The thermal bias is about 282 nT for a 0.1 K stability specification.

3 Discussion

The framework resolves each quantum-sensor metric into the mechanism that sets it, revealing that identical headline sensitivity can conceal large accuracy differences. Grounded in measured device data, the workflow supports metric-specific design and transfers across sensor platforms.

  • A headline sensitivity alone can miss the accuracy or robustness required by an application.No single figure of merit certifies a design because the dominant mechanism depends on the requested metric.
  • The per-mechanism map ties each metric to its limiting mechanism and predicts where real data are scarce.It provides an interaction-aware alternative to budgets that assume contributions simply add.
  • For the studied NV-diamond ensemble, spin dephasing governs sensitivity, thermal ground-state shift governs accuracy, and optical leakage governs robustness.Each metric carries a signed share of its budget.
  • 8 to 1500 nT: along a locus of identical nominal sensitivity, the accuracy bias spans this range at ΔT = 0.1 K.The factor of approximately 200 scales with the drift, so devices indistinguishable by headline sensitivity can differ greatly in accuracy.
  • Measured device data update the model, making it a digital twin that maps each fabricated device to an attributed budget and predicts gains from removing limiters.Because the figures of merit are differentiable, design can proceed by specification instead of iteration.
  • The framework stops at attribution: it identifies the limiter and target lever but does not perform the redesign or demonstrate the resulting metric improvement.Forecast validation on a device remains an immediate next step.
  • The attribution is conditional on modeled noise and identifiability, with richer readout channels needed to sharpen partitions when mechanism signatures are nearly degenerate.The studied noise environment is modeled as Gaussian; strongly non-Gaussian processes remain an extension.
  • The workflow transfers from an NV-diamond ensemble to a cesium optically pumped magnetometer array and applies to open quantum systems read out by photon counting.Examples include optical clocks, atom interferometers, and Rydberg electrometers.

4 Methods

The methods instantiate an NV-center open-system digital twin with a ten-level Hamiltonian, dissipative channels, and tangent dynamics. It computes sensitivity, accuracy, and robustness budgets while accounting for calibration, optical readout, noise, and mechanism interactions.

  • NV-center model: The NV sensor is modeled as a ten-level open quantum system containing ground and excited triplet manifolds plus a metastable singlet.The model includes spin-dependent optical processes and phonon-mediated dynamics.
  • NV-center model: The coherent dynamics address the |0⟩↔|−1⟩ transition, with the sensed field entering through an effective detuning and γe ≈28.03 GHz/T.Excited-state coherences are treated in the secular, fast-orbital-averaging limit.
  • Digital-twin computation: Tangent master-equation propagation co-evolves the state and field derivative, allowing exact readout derivatives and Fisher-information-based sensitivity from one solve.The spin projection is converted to an optical signal through the readout contrast.
  • Validation and budgets: Across parameter draws, each metric retains its dominant mechanism, while the calculated sensitivity budget separates the spin-projection floor from photon-readout shot noise.The thermal channel and T1 remain below 2% for sensitivity because they do not reshape the fringe contrast.

Ethics declarations

The human magnetocardiogram was a single, non-invasive, non-clinical technical recording from an author-participant. It was not used for diagnosis, treatment, or clinical decision-making.

  • Recording scope: The human recording was a single non-invasive, non-clinical technical measurement obtained from an author-participant.The participant provided written consent for recording and publication.
  • Use and data governance: The recording was not collected or used for diagnosis, treatment, or clinical decision-making.Raw identifiable data will not be shared; processed data may be available subject to privacy and governance requirements.

Supplementary Information

The Supplementary Information supplies derivations, numerical methods, parameter tables, and validation for the main text. It also develops time-dependent noise, GPU-scale spatial structure, and a second sensor platform in supplementary results.

  • Overview: Supplementary Notes 1–10 cover the open-system model, validation, first-principles inputs, metrics, attribution, noise, GPU implementation, and experimental charge-state extraction.The overview identifies the scope of each supplementary note.
  • Experimental inputs: The supplementary material includes charge-state-fraction extraction from photoluminescence spectra.This extraction supports the experimental modeling inputs.
  • Supplementary extensions: Time-dependent noise, per-pixel spatial structure at GPU scale, and a second sensor platform are developed and exercised only in the Supplementary results.The main text reports deterministic single-point and real-device results.

Extended Theoretical Derivations

The theoretical derivations formulate the sensor Hamiltonian, control, sensed field, noise, and dissipative channels for open-system simulation. Tangent dynamics and photon-counting readout then support metric evaluation and attribution.

  • Hamiltonian construction: The total Hamiltonian combines intrinsic sensor structure, control, sensed field, and time-dependent noise: Htotal = H0 + Hcontrol + Hsense + Hnoise.The formulation supports spatial and temporal dependencies in the sensor and control fields.
  • Dissipative channels: Dissipation includes optical pumping, radiative decay, intersystem crossing, singlet decay, phonon-driven orbital hopping, and longitudinal relaxation.Temperature-dependent lifetimes and detailed-balance rate terms are included.
  • Hamiltonian construction: The NV implementation uses a 10 × 10 Hamiltonian assembled from ground, excited, and shelving-state blocks.The shelving state represents the singlet levels through a scalar energy.
  • Reduced dynamics: The rotating-wave treatment retains microwave control, bias, temperature, and noise contributions in an effective detuning while neglecting small counter-rotating shifts.Temperature enters through the ground-state splitting Dg(T).
  • Metric evaluation: The tangent master equation supplies analytic parameter derivatives for Fisher information, while photon-counting models evaluate sensitivity and related error budgets.The framework is designed to propagate impacts of shot noise and time-dependent noise through quantum dynamics.

Validation and benchmarks

The framework is validated against known optical-pumping behavior, end-to-end field recovery, Fisher-information limits, and derivative benchmarks. Tangent propagation avoids the step-size limitations of finite differences while maintaining documented agreement with independent references.

  • Optical-pumping validation: All initial spin states converge to approximately 0.69 population in ms=0 within approximately 2 µs under optical pumping.Spin-selective intersystem crossing through the shelving singlet reproduces the NV− initialization mechanism that sets readout contrast.
  • End-to-end recovery: The empirical field uncertainty is approximately 4.0 times the ideal projection Cramér–Rao bound because of finite contrast and the 1/f background.Contrast dilution, 1/f dephasing, and shot noise account for the separation between the realistic device and the quantum limit.
  • End-to-end recovery: A digital-twin Ramsey chain recovers a true 2.0 µT field as 1.91 ± 0.21 µT from 100 photon shots under 1/f and photon shot noise.The chain propagates the readout, samples the noisy probability, and inverts the calibration fringe.
  • Fisher-information validation: The tangent Fisher pipeline reproduces the closed-system quantum Fisher information to approximately 5 × 10^-5 and tracks the Markovian-dephasing limit.The propagated derivative also supports the classical Fisher calculation and remains independent of the integration time-grid when accumulated correctly.
  • Derivative validation: The central finite-difference derivative has a U-shaped error with a minimum near 1 × 10^-12 at Δb⋆ ≈ 5 × 10^-11 T, three to four orders above machine precision.The optimum balances truncation error against floating-point cancellation and is problem-dependent, whereas the tangent solve reaches the roundoff floor without tuning.
  • Benchmark traceability: Each validation benchmark compares a digital-twin output with an independent analytic or numerical reference and is documented at the stated tolerance.The checks cover headline quantities including thermal apparent-field bias, readout contrast, sensitivity, and GPU/CPU parity.

Numerical Implementations and Benchmarks

The implementation converts Fisher information from a single sensing cycle into sensitivity while modeling temperature-dependent phonon hopping and optical readout quantities from the open-system dynamics. Lookup tables accelerate contrast evaluation without replacing the underlying model.

  • Sensitivity benchmark: The reported sensitivity ηB combines single-cycle Fisher information with sensing time, readout duration, and additional dead time through the Cramér–Rao bound.The total Fisher information is the number of repetitions multiplied by the single-cycle value.
  • Phonon processes: The retained Raman rate scales as T^5 at low reduced temperature, while same-direction two-phonon channels contribute below 1% in the stated regime.The neglected-channel condition applies for strains below 100 GHz and temperatures above 10 K.
  • Phonon processes: The digital twin retains one-phonon and two-phonon Raman hopping terms across the modeled strain and temperature range rather than using a fitted polynomial or limiting approximation.The rates are inserted into Lindblad collapse operators coupling Ex and Ey.
  • Optical readout: Effective contrast and detected-photon budget are computed from the open-system model, with contrast reduced by temperature, transverse strain, and the NV− charge-state fraction.The optical-cycle contrast is obtained from a full ten-level initialization-and-readout propagation.
  • Optical readout: A tabulated contrast surface replaces expensive per-point optical-cycle solves while maintaining relative interpolation error below 2% over the operating region.The table lookup provides an approximately 10^6× speed-up over 10^4 direct solves.

Supplementary Note 4: Multi-metric definitions and per-mechanism

Sensitivity, accuracy, and robustness are distinct functionals of one open-system density-matrix solve and its field tangent. Mechanism attribution therefore changes across metrics, with interactions requiring an order-independent Shapley partition for accuracy.

  • Metric definitions: The framework evaluates sensitivity ηB, accuracy, and robustness from the same field-dependent density matrix and tangent while treating nominal performance and parameter drift differently.Sensitivity and accuracy use fixed nominal parameters; robustness measures stability around that point.
  • Metric definitions: Pure dephasing lowers fringe visibility, the thermal shift displaces fringe phase, and optical leakage lowers visibility while adding a readout-baseline offset.These mechanisms act on different factors of the same Ramsey fringe.
  • Accuracy versus sensitivity: Sensitivity is governed by Fisher information, whereas accuracy includes an independent deterministic bias functional in addition to the shot-noise floor.This distinction permits sensitivity and accuracy to disagree even for the same device.
  • Per-mechanism attribution: Shapley attribution is required for accuracy because leave-one-out ordering leaves 89% of the bias as a non-additive residual, while sensitivity interactions are small.The order-averaged partition provides a unique, order-independent share.
  • Per-mechanism attribution: The dephasing–thermal interaction is −91 nT, representing 83% of total accuracy degradation; leakage–thermal interaction contributes a further 10%.Thermal-only bias is 282 nT, decreases to 189 nT with dephasing, and reaches 110 nT for the full device.
  • Design-space generality: Across every explored design plane, dephasing limits sensitivity, the thermal ground-state shift limits accuracy, and optical leakage limits robustness.The inversion persists across the design space, with leakage taking over accuracy only in high-leakage, low-thermal-drift corners.

Noise Models

The noise model represents control, field, and optical fluctuations through power spectral densities and inserts them into Hamiltonian or dissipative channels. Band-limited Hermitian-symmetric synthesis preserves target spectra and variance, enabling time-resolved sensitivity studies.

  • Noise channels: Four stochastic channels model microwave phase noise, microwave amplitude noise, background magnetic-field noise, and laser/AOM rate fluctuations.Phase, amplitude, and field noise are synthesized as time traces, while optical-rate noise enters collapse-operator rates.
  • PSD synthesis: Band-limited Hermitian-symmetric synthesis preserves a target 1/f slope of −1.00 across the sensing band and keeps delivered variance independent of oversampling.Naive decimation aliases the slope toward −0.64 near Nyquist and inflates variance as oversampling grows.
  • Hamiltonian and rate insertion: Synthesized traces enter phase and amplitude control terms, the field channel enters the Zeeman term, and laser/AOM fluctuations enter dissipative rates.The phase trace additionally contributes through a discrete derivative to the effective detuning.
  • Study scope: The main-text figures use deterministic dynamics with a parametric drift budget, while synthesized stochastic channels are exercised only in the time-dependent-noise study.This is identified as a scope choice for the paper rather than a model limitation.
  • Time-dependent sensitivity: For each noise flavor, the study averages 4096 independent realizations and forms Poisson-photon Fisher information at the measured contrast and photon budget.The resulting field sensitivity ηB(τ) reflects the spectral content of the environment because the synthesized trace is the sole decoherence source.

Simulation Methods

The framework propagates open-system states and field tangents across noise, pulse-sequence, and spatial dimensions, then derives sensitivity, accuracy, and robustness maps. Batched multi-GPU execution enables per-pixel mechanism attribution at scale.

  • Time integration: Fixed-step RK4 advances the batched states, while the scalar-OPM cross-check uses Strang splitting and optionally adaptive dopri5 integration.At each stage, experimental pulses and noise traces determine the effective Hamiltonian coefficients.
  • Open-system propagation: The simulation propagates density matrices and their field tangents under a time-dependent Liouvillian containing Hamiltonian commutators and dissipators.The tangent master equation reuses the operator action and adds the source term ∂θL ρ.
  • Distributed observables: Observable probabilities, field tangents, and Fisher increments are reduced over local noise and pulse-sequence axes before global spatial maps are assembled.This produces noise-averaged statistics and mechanism-resolved outputs across distributed ranks.
  • GPU-scale spatial simulation: A 64 × 64 grid with 64 noise realizations per pixel and Nt=1500 steps generated 2.6 × 10^5 tangent trajectories across eight GPUs in one run.Each pixel has its own coherence, relaxation, control, and stress inputs, so spatially varying devices require independent open-system solves.
  • Metric-dependent attribution: Per-pixel attribution is local: the limiting mechanism depends on each pixel’s material rather than being uniform across the sensor.The batched GPU formulation replaces tens of thousands of serial solves with a single propagation.
  • Metric-dependent attribution: Sensitivity follows coherence, whereas accuracy is limited almost entirely by irreducible strain, producing different spatial patterns for the metrics.Control bias vanishes where the drive amplitude matches its calibration, further separating its map from the coherence-set sensitivity.

Supplementary Note 7: Optically pumped magnetometer: cesium

The study transfers its open-system, Fisher-based sensitivity, and system-level design-margin framework to a cesium-133 scalar optically pumped magnetometer. Applied to a human magnetocardiogram, the model separates quantum sensitivity from heading, environmental, and array-level constraints.

  • Platform transfer: The cesium OPM uses the same open-system solve, Fisher-based sensitivity, and system-level design margin as the NV platform.The model is applied to a real magnetocardiography recording to test transfer across sensing platforms.
  • Cesium model: The cesium ground manifold has nuclear spin I = 7/2, hyperfine manifolds F = 3 and F = 4, and low-field gyromagnetic ratio γ ≈ 3.50 Hz/nT.The Breit–Rabi formula gives the exact eigenvalues, while the quadratic Zeeman term sets the scalar heading dependence.
  • Open-system dynamics: The density matrix includes spin-destruction, spin-exchange, and optical-pumping dissipators, with nonlinear mean-field feedback through the ensemble spin.Strang splitting advances coherent Larmor precession and spin exchange while preserving second-order accuracy.
  • Tangent solve: The field tangent is propagated alongside the density matrix, and its readout tangent is ∂B⟨Fy(t)⟩ = Tr(FyGB) without finite differences.The tangent equation includes a source term from the field derivative of the Hamiltonian and a Fréchet derivative for nonlinear spin exchange.
  • Accuracy and localization: At 1% gain match, the localization error is 0.37 mm, about 14× below the 5 mm clinical specification, making array-level field noise the binding constraint.The limiting floor rises to ∼60 mm at raw single-channel ambient noise.
  • Sensitivity and noise: 4.0 fT/√Hz sensitivity is reached at T ≈ 4.9 ms, while the quantum layer remains far below the unshielded ambient noise.The result is readout-noise-limited under the assumed σn, rather than projection-limited.
  • Array processing: ∼13× common-mode rejection reduces integrated 1–10 Hz ambient noise from 58.7 to 4.4 pT/√Hz while preserving the cardiac signal.The leading spatial mode carries 99.9% of array variance and is nearly orthogonal to the cardiac dipole pattern.

Supplementary Note 8: Charge-state characterization from photo-

Charge-state characterization extracts the NV− fraction from photoluminescence spectra for use in effective contrast and photon-budget modeling. The method separates charge-state line shapes and corrects their integrated intensities for differing detection efficiencies.

  • Role of charge state: Only NV− centers contribute spin contrast, so the effective readout contrast is Ceff = Coptical fNV−.The measured NV−/NVT fraction versus optical power is an input to the sensitivity analysis.
  • Caveat: The 532 nm Raman line at 572.6 nm overlaps the NV0 scaling window and can slightly bias fNV− by being absorbed into the NV0 amplitude.The residual is below 1% of peak, and a Raman-free window or explicit Raman basis would remove the effect.
  • Spectral decomposition: The two charge-state spectra are decomposed with non-negative least squares, and area-normalized coefficients give integrated NV0 and NV− photoluminescence intensities.A representative decomposition is shown in Fig. S13, with RMS residual below 1% of peak intensity across the data set.
  • Population extraction: The corrected ratio of NV− to total charge-state intensity yields fNV− for the effective contrast model.Correction is required because the two charge states have different emission and collection efficiencies within the detection window.

Data and code availability

The work combines charge-state and saturation measurements, per-pixel material maps, imaged field maps, and a human magnetocardiogram. Supporting code and data are available from the corresponding authors on reasonable request.

  • Datasets: Charge-state and saturation measurements from two diamond growths set the power-dependent contrast and photon budget used in Fig. 4.The measurements cover 0.3 and 4.5 ppm nitrogen, with three confocal positions per growth.
  • Datasets: Per-pixel maps include coherence, relaxation, diagonal stress, Ramsey validity, and magnetic-field distributions sampled on a 64 × 64 grid.These maps support the spatially resolved accuracy and sensitivity analysis for four NV orientations.
  • Data provenance: The per-pixel material maps were digitized from published characterization figures, with a quantization caveat documented in the dataset README.This bounds the provenance of the spatial inputs used for the real-device analysis.
  • Datasets: The magnetocardiogram dataset is a single unshielded scalar OPM recording of a human heartbeat used in Fig. 5.The code and data supporting the findings are available from the corresponding authors on reasonable request.

adaptive, meta-learned control

The framework combines a mechanism-resolved twin with meta-learned and runtime adaptation to diagnose device variation and target controllable error sources. It separates online calibration from design-time changes and requires readouts that distinguish mechanisms.

  • Twin-based attribution: A mechanism-resolved twin supplies objective, gradients, sensitivities, and Shapley shares from a single tangent solve.The control vector is agnostic to physical parameterization when its coupling to model parameters is characterized.
  • Twin-based attribution: The twin generates synthetic training data with ground-truth per-mechanism labels for meta-training a control policy across device configurations.A batched multi-GPU campaign sweeps experimental parameters, positions, and noise realizations to define the task distribution.
  • Runtime adaptation: Runtime adaptation uses measured heterogeneity and local tangent geometry to set a finite step budget, with expected gain increasing with variance and saturating as K grows.The reproduced scaling form has an achievable ceiling A∞ and adaptation-rate constant β; its derivation and validity conditions are attributed to prior work.
  • Runtime adaptation: Mechanism-targeted calibration applies masked gradient descent only to the parameter block coupled to the diagnosed mechanism, holding inactive parameters fixed.The update is budgeted per device and tracked online rather than repeatedly optimizing the full parameter space.
  • Readout design: Per-mechanism targeting is well-posed only when the readout separates mechanisms; richer time-resolved, spectral, or multi-axis measurements improve identifiability.The NV sequence separates coherence loss from temperature shifts, while the cesium spectrum separates heading bias from true field through their different line-shape effects.
  • Design-time versus runtime: Attribution allocates intervention across the development cycle: adjustable channels suggest runtime correction, whereas fabrication-fixed parameters require design-time changes.This distinguishes whether a metric is best recovered through operation or fabrication.
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