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REVIEW 4 major objections 4 minor 122 references

Fast-tracking and disentangling of qubit noise fluctuations using minimal-data averaging and hierarchical discrete fluctuation auto-segmentation

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A measurement-plus-segmentation framework tracks qubit frequency fluctuations at tens-of-millisecond resolution over hours and attributes them to overlapping charge-parity switching and two-level-system defects.

desk verdict A genuinely new segmentation method for qubit frequency noise with a credible but incompletely validated experimental demonstration; the CP/TLS attributions are plausible, not proven. read the letter →

arxiv 2505.23622 v1 pith:YHN53PW3 submitted 2025-05-29 quant-ph

Abhishek Agarwal , Lachlan P. Lindoy , Deep Lall , Sebastian E. de Graaf , Tobias Lindström , Ivan Rungger This is my paper
classification quant-ph
keywords qubitnoisecharacterisationtransmonqubitschargeparityswitchingtwo-levelsystemsrandomtelegraphhierarchicaldiscretefluctuationauto-segmentationGaussianmovingaveragefastfrequencytracking
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper builds a two-stage method for following the fast, overlapping frequency fluctuations that limit superconducting qubits. The measurement stage runs idle-qubit tomography circuits with very few repetitions and averages the binary outcomes with a Gaussian window, so the qubit frequency can be estimated at intervals of a few tens of milliseconds. The analysis stage, called hierarchical discrete fluctuation auto-segmentation (HDFA), automatically decomposes the resulting frequency time series into nested two-state jump processes ordered by timescale. Applied to three transmon qubits over hours, the method resolves fast jumps with switching rates of about 3–5 per second plus slower jumps on timescales of seconds to minutes, and disentangles them from each other. The paper concludes that the fast fluctuations are charge-parity switching and the slower ones are an off-resonant charge-dipole two-level system, based on matching predicted charge dispersions and observed charge-offset jumps.

What carries the argument

The load-bearing object is the hierarchical discrete fluctuation auto-segmentation (HDFA) algorithm, built on hidden Markov models and time-series segmentation. It models each fluctuation level as a random telegraph $f^{(n)}(t) = f_c^{(n)}(t) + s^{(n)}(t) f_\Delta^{(n)}(t)/2$ and then recursively strips off the fastest level: after fitting an HMM with Baum-Welch and decoding states with Viterbi, it segments the series by growing each segment until a mean-log-likelihood threshold flags a change in the centre or magnitude, then feeds the centre $f_c^{(n)}$ into the next level. The measurement side is the few-repetition Gaussian averaging protocol, which weights binary measurement outcomes by $w(i,r) = \exp[-(i-r)^2/(2 W_G^2)]$ with $W_G = 2$ to $4$, giving tens-of-millisecond resolution while still allowing a Markovian single-frequency noise model to be fitted at each time step. Together these parts turn raw single-shot outcomes into a time-ordered stack of disentangled fluctuation processes with rates, magnitudes, and uncertainties.

What would settle it

A supervised emulation with known fast and slow random-telegraph ground truth, run at jump durations near the detection limit, would falsify the disentanglement claim if HDFA fails to recover the known rates and magnitudes within the quoted uncertainties.

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Extended reading notes

Core claim

The paper claims that qubit frequency noise, which usually appears as a messy mixture of overlapping stochastic processes, can be resolved into a clean hierarchy of independent random-telegraph fluctuations if one combines few-repetition Gaussian averaging with recursive auto-segmentation. At each hierarchy level the frequency obeys $f^{(n)}(t) = f_c^{(n)}(t) + s^{(n)}(t) f_\Delta^{(n)}(t)/2$, with the centre of the fast random telegraph becoming the input to the next slower level, $f^{(n+1)} = f_c^{(n)}$. On the transmon data, the fastest level switches at a few times per second with roughly symmetric rates and a fluctuation magnitude whose maximum matches the device's predicted charge dispersion, identifying it as charge-parity switching; the next level switches much more slowly and asymmetrically, and each switch is accompanied by a small measurable jump in the qubit charge offset, matching an off-resonant charge-dipole two-level-system model. The paper presents this as a demonstration that concurrent fluctuations can be disentangled automatically and attributed to physical origins without assuming that one source dominates.

Load-bearing premise

The method assumes that at most time points the qubit's noise parameters are constant inside the short Gaussian averaging window, so each fitted frequency value is the true instantaneous frequency; a frequency jump inside the window breaks this assumption and shows up as a pure-dephasing spike that the analysis excludes rather than models.

Editorial extensions

If this is right

  • Qubit frequency noise can be tracked at tens-of-millisecond resolution for hours, revealing concurrent random-telegraph fluctuations whose rates span more than three orders of magnitude.
  • The fastest fluctuations were attributed to charge-parity switching because their symmetric rates (about 3–5 s$^{-1}$) and maximum magnitudes match the device charge dispersion; if this attribution is right, charge-parity noise is present and dominant at sub-second timescales on these qubits.
  • The slower fluctuations were attributed to an off-resonant charge-dipole two-level system because each slow frequency jump coincides with a charge-offset jump, and the extracted two-level-system parameters fall in ranges reported for such defects.
  • The disentangled fluctuation information can be used to update qubit calibration on the fly, mitigate errors, and inform error-correction scheduling, since the discrete noise state at the time of an algorithm run becomes knowable.
  • The framework generalizes to other qubit platforms and to fluctuations in parameters other than frequency, provided the noise can be approximated as piecewise-constant within the averaging window.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A direct hardware test of the charge-parity assignment would be simultaneous parity-sensitive readout on the same qubit: the fastest HDFA state switches should coincide with independently observed parity flips, which would also reveal how often the assignment misses very short parity dwells.
  • Because the averaging window is optimized for frequency, the same protocol could be re-optimized for relaxation or pure-dephasing fluctuations; the paper's emulations suggest fast relaxation fluctuations are mostly statistical, but a window optimized for that parameter would settle whether true fast relaxation fluctuations exist.
  • The HDFA hierarchy treats each level as a two-state random telegraph, so continuous drifts are approximated by nesting many small segments; a testable extension is to compare HDFA output against a multi-state or continuous-state model on simulated drifts to quantify the residual approximation error.
  • The observed correlation between two-level-system frequency shifts and charge-offset jumps suggests that monitoring the charge offset alone could act as a cheap early-warning signal for impending TLS switching, potentially enabling pre-emptive recalibration.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. This manuscript develops and demonstrates a two-stage framework for characterizing time-dependent qubit frequency fluctuations. Stage one uses repeated idle-circuit tomography with Gaussian-weighted few-repetition averaging to estimate time-dependent parameters δf(t), Γ1(t), Γϕ(t) by fitting a Markovian Lindblad model (Eq. (3)). Stage two, HDFA, recursively segments the δf(t) series into a hierarchy of random-telegraph-noise components, each described by a state, center, and magnitude, with the hierarchy relation f^{(n+1)} = f_c^{(n)}; switching rates and magnitudes are then extracted. On three transmon qubits of the IBM Lima device, the authors report fast RTN fluctuations at rates of 3–5 s^{-1} whose maximum amplitudes roughly match independently computed charge dispersion, and slower asymmetric RTN fluctuations attributed to charge-dipole TLSs, with correlated charge-offset jumps |δng| of order 0.001–0.011. The paper claims temporal resolution of tens of milliseconds over hours and positions the framework as a tool for calibration, error mitigation, and physical diagnostics.

Significance. If the physical attributions hold, the framework is a useful addition to qubit-noise characterisation: the minimal-data Gaussian averaging is tested on simulated data (Appendices B and D), the bootstrap uncertainty propagation in Appendix C is carefully specified, and the comparison of fΔmax with independent charge-dispersion calculations in Table I is a falsifiable check rather than a circular fit. The authors also acknowledge several limitations in the text, including HDFA misclassification when fΔ is small and Γϕ artifacts near jumps. However, the central novelty is the hierarchical auto-segmentation, and the manuscript does not yet provide a synthetic benchmark with known multi-level fluctuation structure; the physical attributions are consistency arguments rather than unique identifications. The value of the paper therefore depends on closing that validation gap.

major comments (4)
  1. [Secs. II.D and III.D; Appendices B and F] The HDFA disentanglement is not tested on synthetic data with known hierarchical fluctuation structure. Appendix B validates only a single-level RTN with constant f_c and f_Δ, and Appendix D tests the noise-model fitting chain rather than the multi-level segmentation. The hyperparameters λll and Lmin are chosen by elbow and RMSE heuristics on the experimental data (Figs. 10 and 11), and because any noisy time series can be segmented into piecewise-constant RTN pieces, the visual agreement in Fig. 4 does not by itself demonstrate that recovered f_c^{(n)}, f_Δ^{(n)}, s^{(n)}, and rates are the true generators. Please add emulations with known two-level (and, if possible, continuously drifting f_c or f_Δ) hierarchies, and report state-assignment error, rate bias, and bias in the f_Δ distribution as functions of λll and Lmin. This is load-bearing because Table I and Appendix G2 derive physical attributions directly from HDFA outputs.
  2. [Sec. II.C and Fig. 2(c)] The Markovian-constant-within-window assumption used to fit Eq. (3) is violated whenever a frequency jump falls inside the Gaussian averaging window, and the resulting artifact is explicitly visible as sharp Γϕ peaks in Fig. 2(c). These jump-adjacent δf(t) estimates are fed into HDFA without exclusion or refitting with the two-frequency model of Ref. [25]. The statement in Sec. II.C that 'for the majority of times' a Markovian model is adequate is not quantified on the experimental data. Please estimate the fraction of time steps whose windows contain a jump (from the fitted s^{(1)}(t) and WG), and show that removing or refitting those points does not materially alter f_c^{(1)}, f_Δ^{(1)}, the level-1 rates, or the level-2 outputs. Without such a check, the bias near jumps is an uncontrolled systematic in the input to the central algorithm.
  3. [Table I and Eq. (G2)] Using the maximum observed HDFA amplitude fΔmax as the estimate of the charge dispersion ΔCP is subject to unquantified sampling and noise biases: maximization over noisy segment estimates tends to be upward-biased, while finite observation time may also under-sample ng values near the dispersion maximum. The quoted uncertainties reflect segmentation and fitting noise only, not the bias of the maximum statistic, so the agreement in Table I is not yet a quantitative consistency test. The same fΔmax enters Eq. (G2) to convert fΔ(t) into ng(t), so any bias propagates directly into the charge-offset jumps |δng| of Table II. Please calibrate this using synthetic data with known ΔCP and finite observation length, or replace fΔmax by a robust estimator with known sampling distribution, and propagate that uncertainty through the |δng| extraction.
  4. [Sec. III.E and Appendix G2, Fig. 12] The charge-dipole TLS attribution rests on the claim that the distribution of |δng| across level-2 switching events is peaked away from zero. The statistical significance of this peak is not quantified, and for qubit 0 the counts in Fig. 12 are very small. In addition, the calculation uses ng values obtained from HDFA-segmented fΔ(t) via Eq. (G2), so segmentation errors near fΔ minima or near f_c^{(2)} jumps could produce an apparent δng correlation. Please provide a null distribution from randomized jump positions (or from emulations with known TLS-free noise), state the number of events and significance for both qubits, and either add a direct experimental check of the TLS (e.g., avoided crossings or frequency-tuned spectroscopy) or soften the abstract and Sec. III.E from 'identify the origins' to 'consistent with' a charge-dipole TLS origin.
minor comments (4)
  1. [Sec. III.A] The statement that crosstalk across the three parallel qubits was verified to be negligible is asserted without data, a metric, or a description of the verification; please add this evidence or an explicit caveat.
  2. [General] The manuscript does not provide raw data or code; given the algorithmic nature of HDFA and the hyperparameter choices, a data/code availability statement or repository would materially aid reproducibility.
  3. [Fig. 12 caption and Appendix G3] There are several typographical errors that should be corrected: 'shaded greed region' should be 'shaded green region' in the Fig. 12 caption, Appendix G3 contains an unfinished sentence beginning 'The TLS is Since', and Sec. III.D contains 'is applied to to the results'.
  4. [Eq. (F4)] The missed-jump correction in Eq. (F4) assumes that jumps shorter than τmin are completely missed while all longer jumps are detected, but Appendix B shows partial detection and temporal smearing for finite WG; please test this rate correction on simulated hierarchical data or state its assumptions more carefully.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the extracted fluctuation parameters are compared against independent theoretical predictions, and the attribution tests have falsifiable content.

full rationale

The paper's central derivation chain is not circular. The noise model in Eq. (3) is stated explicitly as a Markovian single-qubit model with parameters δf, Γ1, and Γϕ; these parameters are extracted by fitting the same equation to averaged data, and are then used as inputs to HDFA. HDFA's segmentation is validated on emulated data with known ground truth in Appendix B (single-level RTN recovery) and Appendix D (noise-model parameter recovery), even though multi-level disentanglement is not benchmarked against synthetic multi-level ground truth—that is a correctness/validation gap, not a definitional circularity. The CP attribution compares the HDFA-extracted maximum fΔmax against independent theoretical charge-dispersions ΔCP computed from device calibration parameters via analytic and numerical transmon Hamiltonians in Appendix G1; fΔmax is not defined to equal ΔCP, and the measured values differ from both predictions (e.g., 50.6 kHz vs 39.8/48.7 kHz for qubit 0), so the comparison is not forced. The TLS attribution in Appendix G2 uses Eq. (G2) to convert the measured fΔ(t) into a charge-offset ng and then tests whether S(2) frequency jumps coincide with nonzero |δng|; this is a consistency test with falsifiable content, since fΔ(t) being constant across S(2) jumps would give δng=0. The self-citation to Ref. [25] for the noise model is not load-bearing in a circular sense: the relevant model is reproduced explicitly and is a standard Lindblad-plus-detuning model, not an unexamined uniqueness theorem. The main limitations—unvalidated multi-level HDFA on synthetic data, upward bias in using a maximum as an estimate, and the Markovian-assumption violations at jump times—are external-validity or statistical concerns, not cases where a prediction reduces by construction to its own input.

Assumptions & free parameters 3 free parameters · 7 assumptions · 1 invented entities

The central method rests on a small number of modeling choices: a Markovian Lindblad noise model valid within short windows, an assumed two-state hierarchical structure for fluctuations, a Poissonian correction for missed short jumps, and a specific charge-dipole TLS model with assumed junction thickness and TLS temperature ranges. None of these are derived from first principles or directly verified, but they are standard or clearly stated. The hyperparameters WG, λll, and Lmin are tuned on the same data, which introduces a mild risk of overfitting, partly mitigated by the hyperparameter uncertainty propagation in Appendix F2a.

free parameters (3)
  • Gaussian averaging window width WG = 2, 2, 4 for qubits 0, 2, 4
    Chosen as the smallest value that still gives sufficient accuracy in δf estimates; affects temporal resolution and statistical precision (Sec. III A/B).
  • HDFA log-likelihood threshold λll = not tabulated; chosen from elbow plots per qubit and level
    Controls segmentation sensitivity; selected using the same data (Appendix F1).
  • HDFA minimum segment length Lmin = not tabulated; chosen from RMSE curves per qubit and level
    Controls the shortest fluctuation timescale that can be detected; selected using the same data (Appendix F1).
assumptions (7)
  • domain assumption Lindblad noise model with relaxation, pure dephasing and detuning describes idle transmon dynamics
    Used in Eq. (3) for fitting p(τ,b,t_r); standard but an approximation.
  • ad hoc to paper Noise parameters are constant within each Gaussian averaging window
    Assumed in Sec. II.C so that Eq. (3) can be fit at each t_r; acknowledged to fail when a jump falls inside the window.
  • ad hoc to paper Frequency fluctuations are a hierarchy of two-state random telegraph processes, with slower processes acting only on the center f_c and f_Δ piecewise constant
    Core structural assumption of HDFA, Eqs. (5)-(6); not derived from microscopic physics.
  • domain assumption Switching jumps are Poissonian and jumps shorter than τ_min are wholly undetected
    Used in Appendix F2b, Eq. (F4), to correct raw switching rates.
  • domain assumption The qubit-TLS interaction is via an off-resonant charge dipole in the junction barrier with the standard tunnelling model Hamiltonian
    Used in Appendix G3 to derive Eqs. (G9) and (G14) for |δng| and fΔ^(2).
  • domain assumption The TLS is in thermal equilibrium with an environment at 10-100 mK
    Used with Eq. (G15) to estimate fTLS ranges; TTLS is not measured.
  • domain assumption Junction thickness x lies between 1 and 2 nm
    Assumed in Appendix G3 to solve for d∥ and energies, based on prior literature [115].
invented entities (1)
  • Specific off-resonant charge-dipole TLS defects assigned to qubits 0 and 2
    purpose: To explain the observed second-level frequency fluctuations and correlated offset charge jumps
    No direct spectroscopy or avoided-crossing measurement; parameters inferred from a model with assumed junction thickness and TLS temperature ranges. The paper itself calls it a minimal model.

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Cite this review

Pith. "Pith review of Fast-tracking and disentangling of qubit noise fluctuations using minimal-data averaging and hierarchical discrete fluctuation auto-segmentation." pith.science (2026). https://pith.science/paper/YHN53PW3

@misc{pith2026250523622,
  author       = {Pith},
  title        = {Pith review of: Fast-tracking and disentangling of qubit noise fluctuations using minimal-data averaging and hierarchical discrete fluctuation auto-segmentation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YHN53PW3}},
  note         = {Machine review of arXiv:2505.23622}
}
read the original abstract

Qubit noise and fluctuations of the noise over time are key factors limiting the performance of quantum computers. Characterising them with high temporal resolution is challenging due to multiple overlapping stochastic processes such as discrete jumps and continuous drifts. Hence, experiments typically probe individual sources of fluctuations rather than concurrent fluctuations caused by multiple sources. To overcome this limitation we develop a framework comprising a noise characterisation method with minimal measurements allowing high temporal resolution, combined with a hierarchical discrete fluctuation auto-segmentation tool to disentangle the overlapping fluctuations without human intervention, enabling their characterisation and tracking over long times. We show that on transmon qubits the method can track and disentangle qubit frequency fluctuations with temporal resolution of a few tens of milliseconds over hours. This enables us to identify the origins of the fluctuations as overlapping charge parity and two-level-systems switching. Beyond insights into the fluctuation origins, our method also provides information that can be used to improve qubit calibration, error mitigation and error correction.

Figures

Figures reproduced from arXiv: 2505.23622 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic representing the framework for characterising and disentangling noise fluctuations. (a) The single-qubit [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Example of the noise model evaluation results ob [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Results of the qubit frequency estimation procedure illustrating fluctuations at different timescales (shown in different [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Results of the HDFA algorithm for the three qubits, where the columns of plots represent the increasing levels of HDFA [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 6
Figure 6. Figure 6: FIG. 6. (a): Example of the results of [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Qubit layout of the [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Simulated results for a fluctuation lasting for different [PITH_FULL_IMAGE:figures/full_fig_p017_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. (a): Example of three sets of noise model evaluation results with simulated data. The green lines denote the true noise [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Power spectral density (PSD) of Γ [PITH_FULL_IMAGE:figures/full_fig_p018_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Elbow plots for determining the hyperparameter [PITH_FULL_IMAGE:figures/full_fig_p019_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. The accuracy of the results of the auto-segmentation as a function of the minimum segment length hyperparameter, [PITH_FULL_IMAGE:figures/full_fig_p019_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12. Distribution of the jump in the charge offsets, [PITH_FULL_IMAGE:figures/full_fig_p021_12.png]

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.