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REVIEW 3 major objections 5 minor 29 references

Statistics of Strongly Coupled Defects in Superconducting Qubits

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper argues that low-T1 tails in superconducting qubits are caused by strongly coupled defects at the edges of liftoff-defined junction leads within 500 nm of the junction, and that eliminating liftoff residues would tighten T1…

desk verdict Solid swap-spectroscopy study with a genuinely useful long-vs-short liftoff comparison; the near-junction defect conclusion survives, but the 500 nm edge-specific localization is underdetermined by the paper's own Appendix C.2. read the letter →

arxiv 2506.00193 v1 pith:EO57EOQS submitted 2025-05-30 quant-ph cond-mat.mes-hall

S. Weeden , D. C. Harrison , S. Patel , M. Snyder , E. J. Blackwell , G. Spahn , S. Abdullah , Y. Takeda
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B. L. T. Plourde J. M. Martinis R. McDermott
This is my paper
classification quant-phcond-mat.mes-hall
keywords superconductingqubitstransmontwo-levelsystemdefectsenergyrelaxationtimeswapspectroscopyTLSspectraldiffusionJosephsonjunctionliftoffnongaussianT1tails
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 reports that the low-T1 tails seen in superconducting transmon qubits are caused by a small population of strongly coupled two-level-system defects concentrated at the edges of the liftoff-defined junction leads, within about 500 nm of the junction. The authors reach this conclusion by measuring energy relaxation time T1 as a function of qubit operating frequency over 24 hours for twelve qubits spanning six geometries, and by matching cumulative distributions of qubit-TLS coupling with Monte Carlo simulations. If correct, the result matters because those nongaussian T1 tails, not the average relaxation time, are what limit the yield and calibration stability of large multiqubit processors. It also gives fabrication a concrete target: avoid or shorten additive liftoff structures near the junction, since liftoff residues appear to be the source of the strongly coupled defects.

What carries the argument

The argument is carried by swap-spectroscopy maps of relaxation rate versus frequency, turned into cumulative histograms of the inverse square of qubit-TLS coupling. Because Eq. 4 gives a linear cumulative distribution for defects at the coplanar gap edges and the lead-edge field profile of Eq. 7 gives a different, shallower slope at strong coupling, the two distinct slopes in the measured histograms separate gap defects from lead-edge defects. The lead defects are modeled in Monte Carlo as a uniform linear density along the lead edges, and the model attributes the nongaussian low-T1 tails to defects within 500 nm of the junction. An analytical expression for the lead-defect cumulative distribution produces the dotted curve that anchors the comparison.

What would settle it

Fabricate qubits with liftoff lead length varied from 0.5 um to 100 um while keeping the island-to-ground gap fixed, and measure the cumulative (2pi/g)^2 histogram: the edge-defect model predicts the shallow-slope tail grows with lead length and the strongest defects disappear once the liftoff lead is shorter than roughly 1 um. A device whose junction leads are defined without any liftoff step should show no such tail; observing a persistent tail in that device would falsify the localization claim.

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Extended reading notes

Core claim

The paper's central claim is that the dominant relaxation dropouts in these transmons come from discrete defects at the edges of the Josephson-junction leads, not from the tunnel barrier or from the general substrate-air interface of the qubit gap. For long-liftoff devices, where the entire lead is formed in the double-angle evaporation and liftoff step, the T1 distributions develop pronounced low-T1 tails; Monte Carlo simulations with a linear defect density along the lead edges reproduce the measured cumulative coupling distributions, and the strongest-coupled defects sit within 500 nm of the junction. Devices whose leads are mostly defined by the initial etch, leaving only a 2 um liftoff portion, show tighter, near-gaussian T1 distributions. The paper also finds that larger gaps from qubit island to ground raise T1 as expected for interface loss, and extracts a TLS spectral diffusivity consistent with previous reports.

Load-bearing premise

The load-bearing premise is that the electric field along the lead edges falls off as E(x) = (1/2) V / (r-bar ln(4x/r-bar)) and that defects are distributed uniformly along those edges; if that field profile or defect placement is wrong, the strong-coupling population could be located elsewhere or spread over a different distance, though the near-junction concentration would likely survive.

Editorial extensions

If this is right

  • If the edge-defect localization is right, shortening the liftoff portion of the leads removes the shallow-slope population of strong couplers and restores near-gaussian T1 distributions.
  • Processor yield for fixed-frequency qubits and calibration stability for tunable qubits should improve once liftoff residues near the junction are eliminated, because the worst-case dropouts rather than the median T1 set system performance.
  • The measured scaling of T1 with island-to-ground gap means qubit design can trade gap against coherence, pushing strongly coupled defects to weaker coupling.
  • The extracted TLS spectral diffusivity implies that T1 maps must be reacquired on timescales of tens of minutes to maintain calibration.
  • Tracking the cumulative coupling-distribution slope provides a statistical fingerprint for process-induced defects, so the same measurement can serve as a fabrication-quality metric.

Reading between the lines

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

  • I would infer a concrete fabrication threshold from these results: keeping any liftoff-residue-affected lead length below about 1 um should eliminate the strongest coupling tail, because the defects that matter sit within 500 nm of the junction.
  • The appendix's equivalence between a linear edge-defect model and a 2D model with enhanced areal density near the junction means the data establish a near-junction concentration of lossy residues, but not whether the defects literally sit on the lead edges; any residue-removing step could be tested by the same histogram.
  • A testable extension would be to apply the same two-slope analysis to fixed-frequency qubit yield data, predicting that measured processor yield should correlate with the length of liftoff lead and not just junction area.
  • The extracted upper coupling range of about g/2pi = 0.3 MHz implies fields of order tens of V/m at the defect sites; independent field simulations of realistic lead geometries could be compared with this bound to localize the defects further.
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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

3 major / 5 minor

Summary. The paper reports 24-hour swap-spectroscopy measurements of energy relaxation in twelve flux-tunable transmon qubits with three island-to-ground gap sizes (5, 20, and 100 µm) and two junction-lead geometries (long-liftoff and short-liftoff). The authors find that larger gaps give longer T1, that short-liftoff devices have higher median T1 than long-liftoff devices at fixed gap, and that long-liftoff devices show pronounced low-T1 tails. They extract qubit-TLS coupling strengths g and defect relaxation rates from fits to T1 dropouts, model the data with Monte Carlo simulations using gap defects and lead-edge defects, and argue that the dominant strongly coupled defects are located at the edges of the liftoff-processed junction leads within 500 nm of the junction. They also track the spectral diffusion of eight TLS and report a diffusivity consistent with Klimov et al.

Significance. If the central localization claim is correct, the paper provides a concrete, fabrication-relevant conclusion: strongly coupled TLS defects that produce non-Gaussian low-T1 tails are concentrated in liftoff-processed regions near the Josephson junction, motivating liftoff-free or residue-free junction fabrication. The experimental effort is substantial, including repeated swap scans over 24 hours, active flux-drift correction, two independent geometric variations (gap and lead length), and a Monte Carlo extraction check showing that fitted coupling strengths recover generated values to within a few percent. The long-versus-short liftoff comparison is a genuinely external, unfitted experimental variable and is the strongest evidence for an enhanced defect population in the liftoff region. The principal weakness is that the specific attribution to lead edges within 500 nm is not uniquely determined by the data; the paper itself shows in Appendix C.2 that a two-dimensional areal defect model reproduces the same coupling statistics as the one-dimensional edge model.

major comments (3)
  1. [Abstract, Sec. IV, Appendix C.2, Fig. 11(b)] The claim that the dominant defects reside at the edges of the leads within 500 nm of the junction is stronger than the evidence supports. Appendix C.2 and Fig. 11(b) explicitly show that a 2D model with an areal defect density of 3.2/GHz/µm² reproduces the cumulative (2π/g)² distribution of the 1D lead-edge model with λ = 0.4/GHz/µm. The measured histograms therefore do not distinguish defects localized at the lead edges from defects distributed over the nearby lead surface. The long- versus short-liftoff comparison is an external variable and does support an enhanced population of strongly coupled defects in the liftoff-processed region, but the wording 'edges of the leads within 500 nm' should be softened to 'near the liftoff-processed junction region' unless a discriminating measurement is added.
  2. [Sec. III, Eq. (7), Eqs. (E2)-(E3)] The quantitative 'within 500 nm' distance scale is not directly measured; it is derived from the assumed 1D logarithmic field profile of Eq. (7), the assumed uniform linear edge density λ, and the assumed value pmax = 5 Debye. Because Appendix C.2 demonstrates a degenerate model with a different spatial distribution, the extracted distance scale is model-dependent. The authors should either present this scale explicitly as an inference under a particular model or test it with an additional geometric variation (for example, varying lead width or liftoff length independently).
  3. [Sec. III, Appendix C.2, Fig. 14] The lead-defect density λ is not a single predictive value but is adjusted per geometry: the text quotes a range 0.4-0.7/GHz/µm, and Fig. 14 uses 0.4/GHz/µm for the 2-µm short-liftoff lead, 0.25/GHz/µm for the tapered optically-defined portion, and 0.6/GHz/µm for the long-liftoff lead. The agreement between simulated and measured T1 tails is therefore a consistency check with fitted parameters, not an independent prediction. To make the central claim load-bearing, the authors should report whether a single λ (or a physically motivated scaling of λ) can describe all six geometries simultaneously, and quantify the sensitivity of the long-versus-short-liftoff difference to λ.
minor comments (5)
  1. [Introduction] There is a typo in the fourth paragraph: 'mutiqubit arrays' should be 'multiqubit arrays'.
  2. [Appendix D] The definition of α is missing parentheses as printed: it should read α = log[(r_o² - r_i²)/(δ√(2 r_i r_o))] (or an equivalent explicit expression).
  3. [Appendix E, Eq. (E2)] The notation h is used for the Planck constant while Sec. III uses ħ for the reduced Planck constant; please state the convention explicitly near Eq. (E2) to avoid confusion in the prefactor 12h².
  4. [Fig. 3] The caption lists panels (a)-(f) with mean T1 values, but the main text refers to them only as 'upper panels' and 'lower panels'; please reference the explicit panel labels for clarity.
  5. [Fig. 4] The dashed black line for the short-liftoff 100 µm-gap distribution is described as a Gaussian model; please report the fitted mean and standard deviation or state that the line is a guide to the eye.

Circularity Check

2 steps flagged · score 4.0 of 10

Monte Carlo parameters are fitted to the same histograms and T1 tails that the model then 'localizes', but the long-versus-short liftoff comparison gives independent support; score 4.

  1. fitted input called prediction [Section III (Modeling), paragraph after Fig. 5(b); Appendix C.2]
    "We find that λ in the range 0.4-0.7/GHz/ µm to yield distributions that match the measured data. Our modeling shows that the dominant lead defects corresponding to (2π/g)² < 3 × 10^8 GHz−2 are located within 500 nm of the junction."

    The linear edge density λ is tuned so that the Monte Carlo reproduces the measured cumulative (2π/g)^2 histograms and T1 tails; σ and pmax are likewise set by matching the measured T1 distribution width in Appendix C.4. The 500 nm localization and the attribution of the nongaussian tails to lead-edge defects are then read out of this same fitted model, so the 'prediction' is partly constrained by the data it is used to explain. Appendix C.2 shows the degeneracy: a 2D areal defect model with σ = 3.2/GHz/µm² reproduces the same coupling distribution as the 1D edge model with λ = 0.4/GHz/µm, so the edge-specific and 500 nm conclusions are interpretive outputs of the assumed field model rather than independent measurements.

  2. fitted input called prediction [Appendix C.4 and Fig. 1(d) caption]
    "The simulated and measured data match well for pmax = 5 Debye, σ = 2/GHz/µm2. ... assuming defect density σ = 2/GHz/µm2 at the SA interface and maximum TLS dipole moment pmax = 5 Debye."

    The parameters used to compute the T1-versus-gap curve in Fig. 1(d) are fixed by matching the width of the measured T1 distribution of the 100 µm-gap short-liftoff device (simulated standard deviation 37 µs versus experimental 34 µs). Agreement for that device is therefore by construction. The geometric scaling T1 ∝ Δr^0.6 is a separate, unfitted prediction and survives, but the absolute calculated T1 values inherit the fitted parameters. This is a mild fitted-input issue rather than a collapse of the central geometry comparison.

full rationale

The paper is transparent about fitting its model parameters: λ is chosen to match the measured cumulative coupling histograms, and σ and pmax are fixed by the width of the measured T1 distribution in Appendix C.4. As a result, the Monte Carlo reproductions of the T1 tails and (2π/g)^2 slopes for the fitted geometries are not independent confirmations; they are outputs of parameters set by the same data. This is the main circularity-adjacent element. However, the central causal comparison between long-liftoff and short-liftoff leads is an external, unfitted experimental variable: the observed increase in low-T1 tails with liftoff lead length was not used to fit λ or pmax, and it supports the existence of liftoff-related strongly coupled defects independent of the Monte Carlo. The 500 nm and lead-edge localization is weaker: Appendix C.2 shows that a 2D areal defect model reproduces the same coupling statistics as the 1D edge model, and the distance scale derives from the assumed field profile Eq. 7 (cited to co-author Martinis's earlier work) together with the fitted pmax. That is an underdetermination of the spatial model, not an equation-level identity. Eq. 7 is internally cross-checked by the Ansys Maxwell 2D calculation in Appendix C.2, so the self-citation is not load-bearing on its own. Treating the model output as a measured localization overstates the evidence, but the paper's main qualitative conclusion—that liftoff residues near the junction produce strongly coupled defects that cause the low-T1 tails—survives the degeneracy. Score 4 reflects the partial fit-to-prediction overlap while crediting the independent geometry comparison.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the standard TLS tunneling model (density of states ∝ 1/Δ0), on Fermi's Golden Rule, and on two approximate electric field distributions (coplanar gap field Eq. 3 and lead-edge field Eq. 7). The model parameters σ, p_max, and λ are not independently measured; they are chosen so the simulations match the measured histograms and T1 widths, which adds to the circularity burden. No new physical entities are proposed. The attribution of the near-junction defect population to liftoff residues is an inference from geometry, not a direct measurement.

free parameters (7)
  • TLS surface density σ = 2/GHz/µm²
    Set by matching the slope of the cumulative (2π/g)² histograms and the width of the T1 distribution; see Eq. 4 and App C.4.
  • Maximum TLS dipole moment p_max = 5 Debye
    Set together with σ by matching the simulated T1 distribution width to the measured 34 µs standard deviation for the 100 µm short-liftoff device (App C.4).
  • Linear lead-edge defect density λ = 0.4-0.7/GHz/µm
    Chosen so the Monte Carlo cumulative histograms match the experimental data (App C.2); the range reflects device-to-device variation.
  • Qubit self-capacitance C = 70 fF
    Used to compute Vzp and set the absolute field scale; App C.1 states C = 70 fF.
  • Field cutoff δ at metal edges = not given explicitly
    Introduced in App D to regularize the logarithmic divergence in Γ1; enters α and thus the absolute Γ1 prediction.
  • Geometric factor α = order 10
    A logarithmic geometric factor from the field integral in App D; depends on the cutoff δ.
  • Mean defect relaxation rate in Monte Carlo = Γd mean = 5 µs⁻¹
    Drawn from a Gaussian centered at 5 µs⁻¹ to match the experimental data (App C.3); used only for the extraction check.
assumptions (6)
  • domain assumption Standard tunneling model: TLS density of states independent of Δ and proportional to 1/Δ0.
    Invoked in Sec III to derive the dipole moment distribution Eq. 2; standard for amorphous TLS (Phillips, ref 17).
  • standard math Electric dipole coupling g = E·p/ħ and Fermi's Golden Rule for relaxation.
    Used in Eq. 1 and App D; foundational quantum mechanics.
  • domain assumption Coplanar transmission line field approximation E(r) from Eq. 3.
    Agrees with numerical fields to within about 20% integrated participation (App C.1), but is an approximation.
  • domain assumption Lead-edge field profile E(x) from Eq. 7 for junction leads.
    Approximate analytic expression from ref 23; assumed for all lead-edge modeling and underlies the 500 nm localization.
  • ad hoc to paper Defects distributed uniformly in energy and space (gap area with σ, leads with λ).
    The spatial distribution of TLS is assumed, not measured; the value of λ is fitted to data.
  • domain assumption T1 is limited solely by interfacial TLS loss.
    The analysis attributes all observed Γ1(f) structure to TLS; other loss channels (quasiparticles, radiation) are not explicitly separated.

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Cite this review

Pith. "Pith review of Statistics of Strongly Coupled Defects in Superconducting Qubits." pith.science (2026). https://pith.science/paper/EO57EOQS

@misc{pith2026250600193,
  author       = {Pith},
  title        = {Pith review of: Statistics of Strongly Coupled Defects in Superconducting Qubits},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EO57EOQS}},
  note         = {Machine review of arXiv:2506.00193}
}
abstract

Decoherence in superconducting qubits is dominated by defects that reside at amorphous interfaces. Interaction with discrete defects results in dropouts that complicate qubit operation and lead to nongaussian tails in the distribution of qubit energy relaxation time $T_1$ that degrade system performance. Spectral diffusion of defects over time leads to fluctuations in $T_1$, posing a challenge for calibration. In this work, we measure the energy relaxation of flux-tunable transmons over a range of operating frequencies. We vary qubit geometry to change the interface participation ratio by more than an order of magnitude. Our results are consistent with loss dominated by discrete interfacial defects. Moreover, we are able to localize the dominant defects to within 500 nm of the qubit junctions, where residues from liftoff are present. These results motivate new approaches to qubit junction fabrication that avoid the residues intrinsic to the liftoff process.

Figures

Figures reproduced from arXiv: 2506.00193 by the authors.

Figure 1
Figure 1. FIG. 1. Optical micrograph of single-ended long-liftoff transmon [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. (a). Here, we bias the qubit to the flux-insensitive up￾per sweet spot and apply a π-pulse to prepare the qubit |1⟩ state. We then apply a flux pulse to rapidly tune the qubit to a different operating point where it idles for a variable time before returning to the upper sweet spot for measurement. To account for slow drifts in qubit frequency due to changes in the local magnetic flux environment, we perform qubit s… view at source ↗
Figure 3
Figure 3. FIG. 3. Repeated swap spectroscopy scans for the six device geometries. Qubit gap [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Integrated [PITH_FULL_IMAGE:figures/full_fig_p003_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Cumulative histograms of [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Optical images of short-liftoff qubits. (a) 100 [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Cumulative histograms of [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Extracted defect lifetime [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 10
Figure 10. Figure 10: FIG. 10. (a) Electric field magnitude in the gap as a function of [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]
Figure 13
Figure 13. Figure 13: FIG. 13. Simulated cumulative [PITH_FULL_IMAGE:figures/full_fig_p010_13.png]
Figure 12
Figure 12. Figure 12: FIG. 12. (a) Simulated qubit relaxation rate [PITH_FULL_IMAGE:figures/full_fig_p010_12.png]
Figure 14
Figure 14. Figure 14: FIG. 14. Monte Carlo simulations of [PITH_FULL_IMAGE:figures/full_fig_p011_14.png]
Figure 15
Figure 15. Figure 15: FIG. 15. Repeated swap spectroscopy scans for qubits with [PITH_FULL_IMAGE:figures/full_fig_p012_15.png]

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    Contribution of Lead Defects to T1 Tails In Figure 14, we plot simulated Γ1 versus operating fre- quency for (a) the 100 µm-gap long-liftoff geometry and (b) the 100 µm-gap short-liftoff geometry. Both lead and gap de- fects are considered. For both devices, we take gap defect...

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