{"id":"9e7b2d52-100d-44d7-972a-449db9abec5b","arxiv_id":"2607.26242","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A boundary-integral solver computes nanoscale-interface participation ratios in 2D superconducting circuits roughly 170x faster than finite-element methods, revealing that metal-air sidewall participation violates the standard linear-scaling assumption.","lead":"This paper presents a fast 2D electrostatic solver based on boundary integral equations for computing electric field participation ratios in thin dielectric layers of superconducting devices. The solver claims about two orders of magnitude speedup over commercial FEM tools, with the key application being the breakdown of dielectric-constant linearity assumptions in coplanar waveguide geometries.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (5)'s corner quadrature is the load-bearing link between the claimed 1e-7 accuracy and CPW participation ratios; no convergence or perturbative cross-check is reported, and Table V's 8% p_TJ discrepancy (trenched) contradicts the '<1% except p_MA,corner' claim.","rationale":"The reader's verdict is CONDITIONAL, and the identified weakest assumption—numerical capture of corner singularities in Eq. (5)—is exactly where the central claim is least secure. The solver has genuine supporting evidence: exact capacitance checks to 13 digits, square-coaxial corner convergence to 2.4e-10, and <0.5% agreement with Wenner et al.'s COMSOL results. These give credibility to the underlying BIE capacitance solver. However, the paper's advertised '10^-7 relative errors' is not demonstrated for participation ratios, and the 8% discrepancy for the trenched triple junction is a concrete red flag that the text itself misreports. The load-bearing step is not the existence of the Green's identity—that is mathematically sound given the edge condition—but whether the discretized quadrature actually captures the sharp corner/triple-junction contribution at the ppm level. The Appendix A perturbative method is the natural arbiter because it computes participation via capacitance derivatives rather than the boundary integral of φ ∂φ/∂n. The absence of any reported values from that check is a significant omission. The reader's conditional verdict is appropriate: the method is promising and mostly validated, but the headline accuracy for the specific regions of interest is not yet established. Our proposed test would either validate Eq. (5) against the perturbative route or expose a systematic corner-bias that would require a REJECT or major revision.","tokens_in":16822,"tokens_out":10713,"duration_ms":115772,"concrete_test":"Run the complex-step perturbative check described in Appendix A on the isotropically trenched d=100 nm, f=114 µm geometry: set ε_TJ = 10 + i h with h = 1e-12, recompute the total capacitance C, and evaluate p_TJ = (ε_TJ/W) ∂W/∂ε_TJ from the imaginary part. Compare this to the Green's-identity value reported in Table V (5.6 ppm). If the two agree to <1%, the Eq. (5) boundary quadrature is not the source of the 8% Maxwell discrepancy; if they disagree by more than 1%, the corner/triple-junction boundary integral is biased and the claimed 1e-7 participation accuracy fails for the highlighted regions.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The headline accuracy claim—relative errors around 10^-7 for a ten-minute runtime—is not actually connected to the participation ratios in the regions the paper highlights (MA sidewall, triple junction). The solver's capacitance validation is strong: two-wire exact to 13 digits and square coaxial capacitance to 2.4e-10, but participation ratios are a different functional. Eq. (5) computes p_i as a boundary integral of φ ∂φ/∂n. The physical edge condition (refs. 17-19) guarantees the energy density is integrable, and therefore the boundary product is integrable, but it does not guarantee that the dyadic/adaptive quadrature resolves the corner/triple-junction contribution to ppm accuracy. No convergence study of p_TJ or p_MA,side versus chunk refinement is reported. The only external check is Table V, which for the isotropically trenched case shows p_TJ = 6.1 ppm (Maxwell) vs 5.6 ppm (this work), an 8% difference, and p_MA,side and p_MS at 1% differences—while the main text states all participation ratios agree within 1% except p_MA,corner. The appendix describes a complex-step perturbative validation via ∂W/∂ε_i, but no numerical results are given. Without that internal cross-check, the 8% discrepancy remains unresolved: it could be Maxwell's FEM error, or it could be a systematic bias in Eq. (5). If the latter, the central physics conclusions—nonlinear MA-sidewall/TJ participation and the trenching comparisons—could be numerical artifacts.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript presents a boundary integral equation solver for 2D electrostatic capacitance and participation-ratio calculations in superconducting coplanar-waveguide (CPW) cross-sections. The solver uses a single-layer potential representation, Legendre-chunk discretization, FMM acceleration, and GMRES iteration. Participation ratios are computed from Green's first identity, avoiding explicit squaring of the singular electric field. The paper validates the solver on two circular wires and a square coaxial line, compares it against Ansys Maxwell and COMSOL, and then applies it to test dielectric-constant linearity assumptions for the MA sidewall and triple junction, and to study isotropic versus anisotropic trenching. The advertised central claims are relative errors around 1e-7 for a ten-minute runtime and a speedup of about two orders of magnitude over conventional solvers.","tokens_in":17191,"tokens_out":5136,"duration_ms":45134,"significance":"If the stated accuracy carries over to participation ratios, this would be a valuable tool for superconducting-device surface-loss engineering, enabling fine geometric subdivisions and parameter sweeps that are impractical with FEM. The Green's-identity formulation is an elegant treatment of corner singularities, and the exact capacitance validations are excellent. The reproduction of Wenner et al.'s COMSOL values and the described complex-step perturbative check are also strengths in principle. However, the paper does not demonstrate that the headline accuracy extends to the participation ratios in the regions most relevant to its physics conclusions, and one external comparison shows an 8% discrepancy in the triple-junction participation for the trenched geometry. These gaps are load-bearing and must be addressed before the main claims can be accepted.","major_comments":[{"comment":"The load-bearing claim is that Eq. (5) gives participation ratios with errors well below 1 ppm, but no convergence study of p_TJ or p_MA,side is shown. The 1e-7 and 1e-10 accuracies in Appendix C are capacitance values for geometries without thin dielectric layers or triple junctions; they do not validate the boundary integral of phi * dphi/dn near corners and multi-material junctions. The physical edge condition only guarantees integrability, not that the dyadic/adaptive quadrature resolves the singular integrand at ppm level. Please provide a refinement study for p_TJ, p_MA,side, and p_MA,corner in the untrenched and trenched CPW geometries, and report the sum_i p_i deviation.","section":"Sec. III, Eq. (5)"},{"comment":"The text states that the complex-step perturbative formula p_i = (epsilon_i/W) dW/depsilon_i is used as an independent validation of the Green's-identity results, but no numerical comparison is reported. This is precisely the cross-check that would detect a systematic quadrature bias in Eq. (5). Please include a table of p_i from both methods for at least the untrenched and isotropically trenched geometries of Table V, including the complex-step step size h and convergence behavior.","section":"Appendix A, perturbation method"},{"comment":"The main text says all participation ratios agree within 1% except p_MA,corner, but Table V's isotropically trenched row shows p_TJ = 6.1 ppm (Maxwell) versus 5.6 ppm (this work), an 8% difference, plus 1% differences in p_MA,side and p_MS. This contradiction concerns the same TJ region highlighted in the paper. The discrepancy must be resolved: either the statement is inaccurate, the Maxwell value is unreliable, or Eq. (5) has a systematic bias. Without this resolution, the trenching conclusions in Fig. 4 are not fully supported.","section":"Sec. III and Table V"},{"comment":"The advertised 'relative errors around 10^-7 for a ten-minute solution runtime' is not connected to participation ratios. The 13-digit two-wire and 2.4e-10 square-coaxial results are capacitance only; the square-coaxial test used 1.3M points, and no runtime is reported there. The CPW/Maxwell comparison reports about 170x speedup and below-1% participation agreement, not 1e-7. Please qualify the accuracy claim so that it is not read as applying to the participation ratios themselves.","section":"Abstract; Sec. III"}],"minor_comments":[{"comment":"Table IV appears malformed: after the capacitance row there is an unexplained row 'log10(energy density [J/m^3]) Potential (V)' with no values. Please remove it or complete the table.","section":"Appendix C, Table IV"},{"comment":"The formulas for p_i,parallel and p_i,perp are typeset ambiguously. Parenthesize the thickness and permittivity ratios so that the linear and inverse-linear scalings are unambiguous.","section":"Eq. (8)"},{"comment":"The text mentions that results for MS, SA, MA top, and MA corner appear in the supplemental, but these are described only briefly in Appendix E and Fig. 8. Please make the main-text/supplement distinction consistent.","section":"Sec. IV, Fig. 3"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is likely to be acceptable after the validation gap is closed. The main concern is not the solver's capacitance accuracy but the unverified participation-ratio accuracy in exactly the regions where the physics claims are made. I would ask for the complex-step perturbative comparison and convergence studies before publication. I see no concerns about novelty or citation practice; the work builds on standard integral-equation methods and properly credits prior surface-loss simulation literature."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Zydrunas — quick take on 2607.26242. The real contribution is the Green's first identity formula for participation ratios inside a boundary-integral capacitance solver: instead of squaring a singular E-field and integrating it over a thin region, you integrate φ ∂φ/∂n over the region boundary, which is mathematically equivalent and numerically better behaved. That is a legitimate new trick for this application, and the paper is honest about the edge-condition integrability that makes it work.\n\nThe solver itself is well validated for capacitance: 13 digits on two circular wires, sub-1e-10 on square coaxial at high refinement, and dyadic refinement gets there with far fewer points than uniform. The COMSOL comparison against Wenner et al. reproduces participation ratios to fractions of a percent for an untrenched CPW. That is real evidence the method captures the physics in at least one practical geometry. The 170x speedup over Ansys Maxwell is believable and practically important.\n\nNow the soft spots, in order of how much they matter. First, the abstract's 'relative errors around 1e-7' is not connected to the participation ratios. The 1e-7 is convergence of capacitance for exact-solution test cases. No convergence study is reported for p_TJ or p_MA,side versus mesh refinement. The paper says the perturbative complex-step method (Appendix A) is used as an independent validation, but gives no numerical results from it. That's the natural check for whether the corner quadrature is biased, and it's missing.\n\nSecond, there is an internal contradiction. The main text says all participation ratios agree with Ansys Maxwell within 1% except p_MA,corner; Table V shows p_TJ differs by 8% in the isotropically trenched case, with p_MA,side and p_MS at 1%. That discrepancy is not discussed. It could be FEM error, but it could also be a sign the corner quadrature misses a divergent contribution in exactly the regions the paper highlights. The untrenched comparisons look healthy, so I'm not ready to call the central physics wrong, but the paper needs to address it directly.\n\nThird, no code or data is shipped. The implementation is described in enough detail to reimplement, but reproducibility would be much better with the solver or at least the geometry definitions for the tables.\n\nWho is this for? Anyone doing surface-loss participation simulations in superconducting circuits. The method could genuinely replace hours of COMSOL/Ansys runs with minutes, and the linearity findings give a useful caution about extrapolating with Eq. 9. It deserves a serious referee, but the current version overstates its accuracy claim and has an unresolved internal inconsistency. Send it to review, and ask for the perturbative cross-check, a participation-ratio convergence study, and a fix to the 1% claim.","headline":"Useful solver paper with a genuine methodological trick, but the advertised 1e-7 accuracy is for capacitance, not participation ratios, and the trenched-geometry Table V contradicts the 'within 1%' claim.","tokens_in":17745,"tokens_out":2394,"would_cite":true,"duration_ms":23747,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A fast boundary integral solver computes participation ratios for thin device interfaces roughly 170x faster and to 1e-7 relative error in ten minutes, revealing where linear dielectric-loss scaling holds.","keywords":["participation ratio","superconducting qubits","dielectric loss","two-level systems","boundary integral equation","coplanar waveguide","electric field simulation","trenching"],"falsifier":"Take the trenched geometry on which the solver and a conventional finite-element solver disagree by 8% for the triple-junction participation and compute that participation at a sequence of increasingly fine corner discretizations, comparing the boundary-integral result against a direct volume integration of ε|E|² over a small excluded corner patch. If the boundary-integral value drifts or does not converge to the volume-integrated value, the Green's-first-identity corner quadrature is losing energy.","tokens_in":16665,"feed_emoji":"⚡","tokens_out":7109,"duration_ms":64257,"temperature":0.7,"pith_summary":"The paper aims to make precise simulation of electric-field energy in the nanometer-thick, micrometer-wide interfaces of superconducting devices practical. It presents a boundary integral equation solver for 2D electrostatic cross-sections that computes participation ratios — the fraction of field energy stored in each lossy region — using Green's first identity, turning a singular area integral into a better-behaved boundary integral. The central claim is that this approach is roughly two orders of magnitude faster than conventional finite-element solvers, with relative errors around 10^-7 for a ten-minute run, which the paper supports with convergence tests and comparisons against commercial solvers. Using that speed, the paper re-examines the common assumption that each interface's participation ratio scales linearly (or inversely linearly) with its dielectric constant, and finds the assumption holds for some interfaces but fails for the metal-air sidewall and the metal-air-substrate triple junction. Trenching studies then identify the sidewall and triple junction as the regions most strongly affected by etch profile.","feed_headline":"New solver simulates qubit surface loss in minutes, not hours","feed_subtitle":"Boundary-integral method hits 1e-7 relative error and exposes where linear loss scaling breaks down.","key_machinery":"The solver represents the scalar potential as a single-layer potential from an unknown charge density distributed on conductor and dielectric interfaces, reducing the electrostatic boundary value problem to a second-kind integral equation. Boundaries are split into chunks with Legendre polynomial expansions, quadratures are specialized for logarithmic and corner singularities, and a fast multipole method accelerates matrix-vector products. The participation ratios are then extracted from a single unperturbed solution using Green's first identity, which replaces the area integral of the singular ε|E|² with the boundary integral of ε/2 φ ∂φ/∂n. The same quantities are checked independently by","core_discovery":"The paper's central claim is that a boundary integral equation capacitance solver can compute participation ratios for coplanar waveguide cross-sections with accuracy and speed that make systematic parameter studies possible. Rather than integrating ε|E|² over each thin region — which is hard because the field diverges at conductor corners — the solver uses Green's first identity to write each participation ratio as a boundary integral of ε/2 φ ∂φ/∂n. Since φ stays bounded while ∂φ/∂n is only integrably singular, the numerical quadrature handles corners far better than squaring the field would. The paper reports relative errors around 10^-7 for a ten-minute solution, a speed-up of about 170","pith_inferences":["A testable extension: measure loss in a set of resonators with varying trench depth and compare the measured loss tangent to the solver's prediction; the predicted order-of-magnitude drop in sidewall participation between 0 and 100 nm trench depth gives a sharp experimental signature.","Since the perturbative route p_i = (ε_i/W) ∂W/∂ε_i is validated here, one could invert the relationship: from measured capacitance shifts as thin layers are modified, one might extract interface participation ratios without knowing layer thickness or permittivity in advance.","The failure of linearity in the sidewall and triple-junction regions implies that 'effective' interface loss tangents extracted from experiment are geometry-dependent; comparisons across devices with different etch profiles should not be made with a single effective value.","The 2D boundary-integral approach could be combined with a 3D eigenmode solver by slicing the qubit into cross-sections whose mode potentials are matched, but that requires validating the quasi-TEM slice approximation for each 3D mode — a natural next check."],"forward_implications":["The common practice of re-scaling a simulated participation ratio by thickness and dielectric-constant ratios is safe for the metal-air top, metal-air corner, metal-substrate, and substrate-air interfaces, but unsafe for the metal-air sidewall and triple junction; experimental analyses that use this scaling for those regions need a different procedure.","In untrenched coplanar waveguides, the metal-air sidewall holds about an order of magnitude more field energy than the metal-air top; this asymmetry matters for capping studies, since coating only the top leaves the dominant sidewall loss source untouched.","Trenching the substrate by about 100 nm sharply reduces the sidewall and triple-junction participation, after which the sidewall participation is comparable to the top and further trenching has little additional effect.","Other components placed within roughly 20–40 µm of a coplanar waveguide can shift its participation ratios by more than 1%, so device-level proximity must be included when interpreting loss measurements.","Because a ten-minute run replaces solver runs of hundreds of minutes, the method opens the way to sweeping dielectric constants, etch profiles, and layer thicknesses over many cases, and to subdividing interfaces into many more loss regions."],"fun_headline_variants":["Qubit loss solver hits 1e-7 precision, 170x speedup","Boundary method cuts qubit loss simulation 100x","Fast solver maps qubit dielectric loss in minutes","New solver exposes nonlinear loss scaling in qubit interfaces","Precise qubit loss simulation via Green's identity"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The solver's corner accuracy rests on the physical edge condition that ε|E|² is integrable near conductor corners and triple junctions, plus the numerical quadrature's ability to capture that integrable but singular boundary contribution; if the corner quadrature misses part of it, the emphasized metal-air sidewall and triple-junction participation ratios are biased.","fun_headline_variants_meta":{"raw":{"variants":["Qubit loss solver hits 1e-7 precision, 170x speedup","Boundary method cuts qubit loss simulation 100x","Fast solver maps qubit dielectric loss in minutes","New solver exposes nonlinear loss scaling in qubit interfaces","Precise qubit loss simulation via Green's identity"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000168,"raw_usage":{"total_tokens":1129,"prompt_tokens":804,"completion_tokens":325,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":548,"completion_tokens_details":{"reasoning_tokens":240}},"tokens_in":548,"tokens_out":325,"duration_ms":3340,"temperature":1.0,"reasoning_tokens":240,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T00:22:54.567784+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take the trenched geometry on which the solver and a conventional finite-element solver disagree by 8% for the triple-junction participation and compute that participation at a sequence of increasingly fine corner discretizations, comparing the boundary-integral result against a direct volume integration of ε|E|² over a small excluded corner patch. If the boundary-integral value drifts or does not converge to the volume-integrated value, the Green's-first-identity corner quadrature is losing energy.","supporting_citations":[],"review_version":1}