Analysis of RF Surface Loss in a Planar 2D Qubit

Akshay Murthy (1); Alexander Romanenko (1) ((1) Fermi National Accelerator Laboratory); Andrei Lunin (1); Anna Grassellino (1); Mustafa Bal (1); Shaojiang Zhu (1)

REVIEW 3 major objections 5 minor 5 references

Analysis of RF Surface Loss in a Planar 2D Qubit

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read This paper claims that RF surface losses in planar transmon qubits can be accurately predicted by simulating oxide layers tens of nanometers thick and linearly extrapolating the energy participation ratio down to the real few-nanometer…

desk verdict Practical extrapolation scheme for transmon oxide-loss EPR, with one load-bearing gap: the linear-in-thickness assumption is never checked at the real 3–5 nm target. read the letter →

arxiv 2507.18672 v2 pith:HX3TFI64 submitted 2025-07-24 quant-ph physics.acc-ph

Andrei Lunin (1) , Mustafa Bal (1) , Akshay Murthy (1) , Shaojiang Zhu (1) , Anna Grassellino (1) , Alexander Romanenko (1) ((1) Fermi National Accelerator Laboratory) This is my paper · ORCID

classification quant-phphysics.acc-ph

keywords transmonqubitRFsurfacelossenergyparticipationratiooxidethicknessextrapolationfiniteelementmethodsubstrateetchingT1coherencetime

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 tries to establish that a practical numerical method can estimate the dominant dielectric surface loss in planar transmon qubits, without directly meshing the true 3-5 nm oxide layer. The proposed asymptotic method simulates oxide layers of order 20-30 nm and linearly extrapolates the energy participation ratio (EPR) down to nanometer thicknesses, claiming good accuracy above a threshold thickness. Applying this method to three transmon antenna designs, the paper finds that larger pad spacing and substrate etching reduce surface losses, with EPR values listed in Table 1. These results matter because surface oxide loss is widely considered the main limit on transmon coherence time, so reliable EPR estimates translate into concrete design guidance.

What carries the argument

The central object is the energy participation ratio, EPR_i, defined as the fraction of total stored electromagnetic energy that resides in the i-th lossy dielectric layer, computed from the electric field distribution of the qubit eigenmode. In practice, the fields come from a finite-element eigenmode solver with fields normalized to 1 J of stored energy, with an explicit correction for energy stored in lumped inductors. The method that carries the argument is asymptotic thickness extrapolation: a moving-mesh scheme reuses one fixed mesh to simulate oxide thicknesses from tens to one hundred nanometers, and a linear extrapolation maps those EPR values down to the physical 3-5 nm range. Second-order mesh elements are identified as necessary for a converged field solution near sidewalls and corners.

What would settle it

Fabricate two or more of the studied transmon designs with the same measured oxide thickness and permittivity, measure their surface-loss-limited T1, and check whether the ratio of measured losses matches the ratio of extrapolated EPR values in Table 1; alternatively, run a solver capable of directly meshing a 3-5 nm oxide on the same geometry and compare its EPR to the extrapolated numbers for the same corner radii.

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Extended reading notes

Core claim

The central claim is that the energy participation ratio of a natural surface oxide, the quantity that controls dielectric loss, can be obtained by a two-step asymptotic procedure when direct simulation of the true oxide thickness is numerically impossible. First, simulate a thicker oxide layer, tens of nanometers, with a converged second-order finite-element mesh; second, linearly extrapolate the EPR to the real few-nanometer thickness. The paper demonstrates that for flat surfaces the EPR is exactly linear in thickness, and that for geometries with sharp corners the linear regime is reached above roughly 20-30 nm, the thickness range used for the simulations. Using this method on three transmon layouts with pad spacings of 20, 70, and 150 micrometers, the paper finds that the design with the largest pad spacing and rounded pads has the lowest oxide EPR, and that etching a trench into the substrate suppresses the field enhancement at the lower sidewall corner.

Load-bearing premise

The load-bearing premise is that linearly extrapolating the energy participation ratio from simulated oxide thicknesses of 20-30 nm down to the real 3-5 nm thickness remains accurate near sidewall corners, where the paper itself acknowledges that local field enhancements make the linear assumption not always accurate.

Editorial extensions

If this is right

If the extrapolation method is accurate, the EPR values in Table 1 directly translate a measured oxide loss tangent into a surface-loss-limited T1 for each transmon design.
Larger pad spacing reduces oxide EPR by roughly a factor of two between the 20 and 150 micrometer pad designs, giving a quantitative rationale for wide-pad transmon layouts.
Substrate etching to a depth of about 10 nm substantially reduces EPR, with diminishing returns once the trench depth approaches the film thickness, so shallow etches capture most of the benefit.
The same asymptotic procedure can be applied to the aluminum conductor oxide and to other planar superconducting circuit geometries without re-meshing the true nanoscale film.
The observation that EPR does not simply scale inversely with permittivity means that material-parameter uncertainty in thin oxide films must be propagated through EPR calculations, not assumed away.

Reading between the lines

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

A natural testable extension is to run the same two-step extrapolation on a geometry with deliberately varying corner roundness, to map where the 20-30 nm linear threshold shifts and whether the method needs a higher simulation thickness for sharper corners.
The paper's method could be applied to other ultra-thin lossy interfaces, such as the tunnel barrier of the Josephson junction itself, where similar mesh-size obstacles prevent direct simulation.
If the extrapolated EPR ranking were combined with independent TLS-loss measurements on identically fabricated devices, the predicted order of T1 across the three designs could be checked without needing a solver that resolves the true oxide thickness.
The etching benefit is shown for one transmon variant; the expectation that it transfers to other pad spacings is plausible but remains an extrapolation from a single geometry.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Worth a serious referee, but the referee should make them close one obvious gap before publication.

What is actually new: they propose an asymptotic workaround for a real nuisance—HFSS cannot mesh a 3–5 nm oxide conformally on a 200 nm film—so they simulate at 25–100 nm and extrapolate EPR linearly downward. The three pad-layout comparisons (V1/V2/V3, spacings 20/70/150 µm) and the substrate-etching curves are new numerical results, and the moving-mesh idea (reassigning virtual objects rather than regenerating geometry) is a sensible practical trick. The field-map comparisons to the electrostatic ρ^{-1/3} corner singularity give a useful sanity check on the FEM.

The paper does not oversell the physics. It does not claim a new decoherence mechanism or a new analytic formula. The EPR values are direct simulation outputs, not fitted to conclusions. The authors correctly note that the linear extrapolation is not guaranteed near sharp corners; Fig. 11 even shows the sidewall-plus-corner EPR deviating from the dotted linear line at small thicknesses, which is exactly where they want to use it.

The soft spots, in proportion: (1) The central extrapolation is empirical. The manuscript concedes that for side walls with sharp corners 'this assumption is not always accurate.' The stress-test note's fractional-power argument (corner contribution scaling like t^{5/3} rather than t^1) is not in the paper, but the paper's own Fig. 11 shows a kink at low thickness. That makes the Table 1 numbers at 3–5 nm uncertain, and Table 1 drives the V1 vs V3 design conclusion. (2) The claimed agreement with experiment cites [6], but reference [6] is missing from the list. The text says 'good agreement with the experiment [6]' but no experiment is actually shown. That is an incomplete citation, not necessarily a fatal flaw, but it must be fixed. (3) No error bars on the EPR values, and no convergence data at the extrapolated thickness. (4) Minor: the paper treats the oxide and substrate permittivity both as 10 in Table 1, so the numbers are conditional on that choice; that is disclosed, so it is fine.

On the citation pattern: self-citations are reasonable here—their own group's experimental work on transmon performance is directly relevant, and citing it is not a problem when the cited results are externally verifiable. The missing [6] is the only actual citation issue.

This paper is for people doing transmon or CPW loss engineering, especially in the SRF community. It gives concrete design guidance (large pad spacing, substrate etching) and a repeatable workflow. It deserves peer review. I would send it out, with a request that the authors report corner/sidewall/top EPR fractions and provide at least one direct check at a true few-nm thickness, or a quantitative statement of extrapolation uncertainty. Those are addressable revisions, not core-argument killers.

Recommendation: accept for peer review with requested major revision; the method is plausible, the results are new, and the missing validation is fixable.

Referee Report

3 major / 5 minor

Summary. The manuscript presents finite-element eigenmode simulations (ANSYS HFSS) of three planar transmon antenna designs, with the goal of estimating microwave surface losses arising from the natural oxide layers on the superconductor. Because HFSS meshing is difficult at the physical 3–5 nm oxide thickness, the authors propose an asymptotic method: simulate oxide thicknesses in the 25–100 nm range, verify that the energy participation ratio (EPR) becomes linear above roughly 20–30 nm, and linearly extrapolate to the few-nanometer scale. They report EPR values for three transmon variants (V1, V2, V3) with different pad spacings and aspect ratios, study the dependence of the EPR on oxide permittivity and substrate trench depth, and conclude that larger pad spacing and substrate etching reduce RF surface loss.

Significance. If the linear extrapolation is valid, the paper offers a practical methodology for estimating surface-loss-limited coherence in planar transmons without meshing sub-nanometer dielectric layers. The paper has several genuine strengths: a convergence study favoring 2nd-order mesh elements; a moving-mesh approach that keeps the geometry consistent across oxide thicknesses; an electrostatic benchmark for the field singularity at sharp corners; and EPR values that are direct simulation outputs rather than parameters fit to the conclusions. The design trends (lower EPR for larger pad spacing and for substrate trenching) are plausible and actionable. However, the central extrapolation from 20–30 nm to 3–5 nm is not validated at the target thickness, and the claimed agreement with experiment is unverifiable because reference [6] is missing. These gaps affect the quantitative design guidance in Table 1 and therefore need to be addressed before the central claim can be accepted.

major comments (3)

[Study of EPR Variation in Transmons with Different Antenna Geometries (first Fig. 8, Fig. 11, Table 1)] The extrapolation from 20–30 nm to 3–5 nm oxide thickness is the load-bearing step of the proposed method, but it is not validated at the target thickness. The manuscript itself acknowledges that for a side wall with sharp corners 'this assumption is not always accurate due to local field enhancements' (discussion of Fig. 11). The electrostatic comparison in Fig. 8 shows |E| ~ ρ^{-1/3} near a right-angle corner, and for such a singular field the corner contribution to the EPR is not guaranteed to be affine in thickness; it can scale as a fractional power. No simulation is run at 3–5 nm, no error bars are given on the extrapolated values, and no estimate is provided of the fraction of EPR coming from corner regions. Because Table 1 and the design ranking (V1 vs V2 vs V3, trench etching) rest on these extrapolated numbers, this is a load-bearing gap. A direct simulation at the physical thickness for at least one geometry, or an analytic corner correction with a quantified error bound, would resolve the concern.
[Conclusion and Fig. 14] The claim of agreement with experiment cannot be checked because reference [6], cited in both Fig. 14 and the Conclusion, does not appear in the reference list. Please add the reference or remove the claim. In addition, the Conclusion states that the advantage of large pad spacings and substrate etching is 'confirmed in experiments,' but the only cited experiment concerns the etching effect; no experimental comparison is shown for the pad-spacing trend.
[Table 1] The EPR values in Table 1 are extrapolated estimates, but no uncertainty or confidence interval is reported. Since these values drive the quantitative comparison among V1, V2, and V3, even a rough uncertainty estimate (for example, from the scatter in Fig. 11 or from the difference between linear and alternative fits) should be included so that the reader can judge whether the ranking is statistically meaningful.

minor comments (5)

[Throughout] The figure numbering is inconsistent: two different figures are labeled Fig. 8 (the electrostatic comparison and the mesh-convergence study).
[Eq. (1)] Equation (1) is garbled in the typesetting; the intended relation appears to be Qi = 1/(epri · tan δ), but the expression should be rewritten clearly.
[Table 1] The header of Table 1 is ambiguous: the G-factor columns are labeled with '(ε = 10, 5 nm)' and '(ε = 10, 4 nm)', although the G-factor defined in Eq. (4) does not depend on permittivity or oxide thickness. Please clarify what these headers mean.
[Abstract/Conclusion] The text alternates between 'interpolation' and 'extrapolation' for the step from 25–100 nm to a few nanometers; this should be made consistent, since the procedure is an extrapolation outside the simulated thickness range.
[Conclusion] The Conclusion says the method reduces oxide thickness 'from hundreds to tens of nanometers,' but the simulations in Fig. 11 run up to 100 nm; please align the wording with the actual simulated range.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the EPR values are direct simulation outputs checked against an external electrostatic benchmark, and the linear thickness extrapolation is an approximation rather than a fitted input.

full rationale

The paper's central quantity, the energy participation ratio (EPR), is defined by Eq. (3) as a ratio of stored electric energy in a dielectric layer to the total stored energy, and every reported EPR is a direct output of the HFSS eigenmode simulation. No parameter is fitted to the design conclusions; in particular, the EPR values in Table 1 are not used as inputs to infer the design ranking. The only extrapolation in the paper is the linear extension of EPR from oxide thicknesses of 20-30 nm down to the real 3-5 nm range, described and tested in the discussion of Fig. 11. This is an approximation, not a circular reduction, because the target few-nanometer EPR is not an input to the simulation or to the linear fit; the fit is performed on simulated values at larger thicknesses and then used to estimate a distinct quantity. The electrostatic benchmark in Fig. 8 provides an independent check of the HFSS field behavior against the analytic rho^{-1/3} singularity, and the mesh convergence study in the following figure validates numerical accuracy. The paper does cite its own group's experimental and material work (e.g., references [3] and [5], and the reference [6] invoked in the Fig. 14 caption, which is missing from the bibliography), but these citations support context and qualitative agreement rather than the derivation of the EPR values. The missing reference and the unquantified extrapolation error are correctness and support concerns, not circularity, because the numerical derivation remains self-contained and does not assume its own conclusion.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The calculations rest on five stated modeling assumptions; the most consequential is the empirical linear extrapolation of EPR from tens of nanometers down to the real 3-5 nm oxide thickness, which is not directly validated. No new physical entities are introduced; the 'moving mesh' is a numerical technique, not an entity.

free parameters (1)

Extrapolation threshold oxide thickness = 20-30 nm
The paper observes that EPR becomes linear with thickness only above roughly 20-30 nm for sidewall/corner regions; below this, linear extrapolation is assumed. This threshold is chosen empirically from HFSS results in Fig. 11, not derived.

assumptions (5)

domain assumption The natural oxide layer is an amorphous dielectric of uniform thickness with constant permittivity and loss tangent.
Idealized model based on SEM images, Section 'Transmon Electromagnetic Modeling', Fig. 3.
standard math The HFSS eigenmode solution at about 5 GHz is close to the electrostatic regime, so field singularities at sharp edges follow the power-law rho^{-1/3} for a right external corner.
Based on Jackson Classical Electrodynamics [2], compared in Fig. 8.
standard math In a lossless resonant system, the maximum stored electric and magnetic energies are equal (W_E = W_H + W_Q).
Used in Eq. (2) to compute total stored energy and normalize fields.
domain assumption The Josephson junction can be modeled as a lumped rectangular inductor with given surface inductance and aspect ratio.
Section 'Transmon Electromagnetic Modeling', Fig. 4.
ad hoc to paper The EPR scales linearly with oxide thickness down to 3-5 nm from the 20-30 nm range, including sidewall and corner regions.
Central enabling assumption for the asymptotic method; supported only by empirical observation of a threshold in Fig. 11, not by a derivation or direct simulation at target thickness.

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Cite this review

Pith. "Pith review of Analysis of RF Surface Loss in a Planar 2D Qubit." pith.science (2026). https://pith.science/paper/HX3TFI64

@misc{pith2026250718672,
  author       = {Pith},
  title        = {Pith review of: Analysis of RF Surface Loss in a Planar 2D Qubit},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HX3TFI64}},
  note         = {Machine review of arXiv:2507.18672}
}

read the original abstract

The Josephson junction and shunt capacitor form a transmon qubit, which is the cornerstone of modern quantum computing platforms. For reliable quantum computing, it is important how long a qubit can remain in a superposition of quantum states, which is determined by the coherence time (T1). The coherence time of a qubit effectively sets the "lifetime" of usable quantum information, determining how long quantum computations can be performed before errors occur and information is lost. There are several sources of decoherence in transmon qubits, but the predominant one is generally considered to be dielectric losses in the natural oxide layer formed on the surface of the superconductor. In this paper, we present a numerical study of microwave surface losses in planar superconducting antennas of different transmon qubit designs. An asymptotic method for estimating the energy participation ratio in ultrathin films of nanometer scales is proposed, and estimates are given for the limits of achievable minimum RF losses depending on the electrical properties of the surface oxide and the interface of the qubit with the substrate material.

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Works this paper leans on

5 extracted references · 4 canonical work pages

[1]

https://www.ansys.com/Products/Electronics/ANSYS-HFSS

work page
[2]

Jackson JD, Classical Electrodynamics, 3rd ed, Wiley, 1999

work page 1999
[3]

Disentangling the Impact of Quasiparticles and Two-Level Systems on the Statistics of Superconducting Qubit Lifetime

S. Zhu,1, X. You, et.al., “Disentangling the Impact of Quasiparticles and Two-Level Systems on the Statistics of Superconducting Qubit Lifetime”, FERMILAB-PUB-24-0577-SQMS (2025)

work page 2025
[4]

Electronic, dielectric, and optical properties of the b phase of niobium pentoxide and tantalum pentoxide by first-principles calculations

S. Pérez-Walton, C. Valencia-Balvín, et.al., “Electronic, dielectric, and optical properties of the b phase of niobium pentoxide and tantalum pentoxide by first-principles calculations”, Phys. Status Solidi B 250 (8) (2013)

work page 2013
[5]

Identifying Materials -Level Sources of Performance Variation in Superconducting Transmon Qubits

A. Murthy M. Bal, et.al., “Identifying Materials -Level Sources of Performance Variation in Superconducting Transmon Qubits”, arXiv.2503.14424 (2025)

arXiv 2025

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

https://www.ansys.com/Products/Electronics/ANSYS-HFSS

work page

[2] [2]

Jackson JD, Classical Electrodynamics, 3rd ed, Wiley, 1999

work page 1999

[3] [3]

Disentangling the Impact of Quasiparticles and Two-Level Systems on the Statistics of Superconducting Qubit Lifetime

S. Zhu,1, X. You, et.al., “Disentangling the Impact of Quasiparticles and Two-Level Systems on the Statistics of Superconducting Qubit Lifetime”, FERMILAB-PUB-24-0577-SQMS (2025)

work page 2025

[4] [4]

Electronic, dielectric, and optical properties of the b phase of niobium pentoxide and tantalum pentoxide by first-principles calculations

S. Pérez-Walton, C. Valencia-Balvín, et.al., “Electronic, dielectric, and optical properties of the b phase of niobium pentoxide and tantalum pentoxide by first-principles calculations”, Phys. Status Solidi B 250 (8) (2013)

work page 2013

[5] [5]

Identifying Materials -Level Sources of Performance Variation in Superconducting Transmon Qubits

A. Murthy M. Bal, et.al., “Identifying Materials -Level Sources of Performance Variation in Superconducting Transmon Qubits”, arXiv.2503.14424 (2025)

arXiv 2025