{"id":"a45a47bb-c56e-430c-806c-dc7df22a16a2","arxiv_id":"2411.16974","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":9,"one_line_summary":"A Geant4/PARMA simulation study compresses natural radiation backgrounds in superconducting qubit substrates into three rates with analytic scaling formulas, validated against an earlier TKID measurement.","lead":"This paper uses particle-transport simulations to estimate how natural radiation from the ground and the sky deposits energy in the silicon chips used for superconducting qubits and sensors. It reduces the results to three simple rates with scaling formulas that depend on elevation, substrate material, thickness, and shielding.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Equation (1) defines the elevation factor as exp(H/λ) but never gives λ; Table II omits it, so the central formula cannot predict rates at any nonzero elevation, including the 1640 m validation.","rationale":"The reader's weakest_assumption emphasizes validation against a single measurement and the sparse high-energy Mγ extrapolation. Those are real concerns, but the most load-bearing problem is more direct: Eq. (1) claims to summarize elevation dependence through exp(H/λ), yet λ is never given. Table II, presented as the complete parameter set, has no λ entry, and Section V gives only species-dependent scale heights with no single value for the combined rates. Without λ, no user can evaluate Eq. (1) at any nonzero elevation, including the 1640 m TKID comparison that is the paper's only validation point. Section V also implies that a single λ may be inappropriate, because R, P, and M are dominated by different particle species whose fluxes grow at different rates with altitude. At 1640 m, plausible λ values from 1 km to 3 km change the cosmic-ray factor by a factor of three, far exceeding the ±25% accuracy claim. This is a concrete, citable omission rather than a judgment about the Monte Carlo inputs. It is fixable by supplying the missing value or fitting separate elevation exponents for R, P, and M, so the appropriate disposition is CONDITIONAL pending that correction, rather than REJECT.","tokens_in":27,"tokens_out":8398,"duration_ms":211678,"concrete_test":"Ask the authors for the λ value used in the TKID comparison at 1640 m, or rerun the cosmic-ray Geant4/PARMA simulations at elevations 0, 500, 1000, 1500, 2000, and 3000 m and separately fit exp(H/λ) to R, P, and M. If a single λ does not reproduce all three rates within the claimed ±25%, or if no λ is recoverable from the published inputs, the elevation factor in Eq. (1) is not well specified and the central claim is not testable.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The paper's central deliverable is Eq. (1), which is supposed to summarize R, M, and P as functions of elevation, substrate, and shielding. In Section VI, the cosmic-ray contribution is defined as a multiplicative factor ãCR ≡ exp(H/λ) 'for an appropriate scale height λ.' But no value of λ is given anywhere: Table II has no λ entry, Section V reports only species-dependent scale heights (about 5 km for muons, 1 km for nuclear particles, and intermediate values for e±, γ, and the overall rate), and no caption or equation supplies the single number needed. This is not a cosmetic omission. First, without λ an experimenter cannot evaluate Eq. (1) at any nonzero elevation, so the formula is incomplete in one of its headline variables. Second, Section V's own observation that different particle species have different scale heights undermines the form of Eq. (1), which applies one exponential factor to all three rates; the composition of the cosmic-ray flux changes with elevation, so R, P, and M should in principle have different λ values. At H = 1640 m, exp(1.64/1) ≈ 5.1 while exp(1.64/3) ≈ 1.7, a factor-of-three swing that dwarfs the claimed ±25% accuracy. The low-statistics Mγ ∝ τ^5 extrapolation noted in Section IV is a second fragility, but the missing λ is a direct blocker: the model as published cannot be applied to the paper's own validation measurement, and the accuracy claim cannot be checked without an additional unstated parameter.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper uses Geant4/TOPAS with PARMA cosmic-ray spectra to simulate energy deposition from natural radiation (terrestrial gamma rays and cosmic rays) in silicon and other substrates typical of superconducting qubits and detectors. It distills the simulation output into three rates—R (any energy event), M (events >1 MeV), and P (total deposited power)—and packages them in Eq. (1) with parameters in Table II, intended to let experimenters estimate background rates as functions of substrate area, thickness, material, elevation, and ceiling thickness. The authors report consistency with their earlier TKID measurement at 1640 m altitude and claim roughly ±25% accuracy over realistic conditions.","tokens_in":8383,"tokens_out":2333,"duration_ms":25473,"significance":"If Eq. (1) and Table II are reliable, the paper provides a genuinely useful practical tool: experimenters could obtain approximate background rates for superconducting qubit and sensor substrates without running dedicated Monte Carlo simulations. The two-step re-aiming Monte Carlo scheme and the explicit three-rate parametrization are sensible and clearly described. However, the central formula as printed is incomplete because the cosmic-ray elevation scale height λ is never given, and the claimed accuracy is not backed by quantitative uncertainties or a quantitative validation. The paper's practical value therefore depends on addressing these gaps.","major_comments":[{"comment":"The cosmic-ray elevation factor is defined as ãCR ≡ exp(H/λ) with \"an appropriate scale height λ,\" but no value of λ is given anywhere in the paper: Table II has no λ entry, and Section V reports only species-dependent scale heights (about 5 km for muons, 1 km for nuclear particles, and intermediate values for e±, γ, and the overall rate). This is a load-bearing omission because Eq. (1) cannot be evaluated at any nonzero elevation without λ, including the 1640 m altitude of the paper's own validation measurement. Moreover, the Section V observation that scale heights differ by particle species directly undermines the single-exponential form for all three rates; at 1640 m, exp(1.64/1) ≈ 5.1 versus exp(1.64/3) ≈ 1.7, a factor-of-three spread that dwarfs the claimed ±25% accuracy. The authors must either supply the λ value used for each rate or reformulate the elevation dependence to reflect the species-dependent composition changes.","section":"Section VI, Eq. (1), Table II"},{"comment":"Table II lists fitted parameters cs, gs, ps, βs, ms, αs, and ρGa,s without any statistical or systematic uncertainties, yet Section VII claims the absolute rates are accurate to about ±25%. The uncertainty claim is therefore unsupported: the reader cannot tell whether 25% reflects Monte Carlo statistical errors, PARMA model uncertainty, concrete activity variation, or the re-aiming approximation. I ask the authors to provide uncertainties for the fitted parameters (at least for the dominant terms) or to weaken the accuracy claim to a qualitative estimate until such uncertainties are quantified.","section":"Table II and Section VII"},{"comment":"The >1 MeV terrestrial gamma rate Mγ is stated to scale approximately as t^5 (Section IV), but the paper acknowledges that this is \"difficult to estimate from the few simulated events above that energy.\" No event counts, confidence intervals, or goodness-of-fit measures are given, and Section VI similarly states that too few MeV-scale events were generated to characterize any shape correction to M. A power-law exponent of 5 inferred from a handful of events is not a reliable interpolation or extrapolation basis, and it directly affects Eq. (1)'s M row. The authors should provide the number of simulated events above 1 MeV for the relevant thicknesses and a quantitative measure of the fit quality, or explicitly mark the Mγ scaling as preliminary.","section":"Section IV, Mγ scaling"},{"comment":"The only validation is a qualitative consistency statement against the authors' own TKID measurement at 1640 m altitude: \"A TKID-based spectroscopic measurement [8] is consistent with the models' results under nominal conditions.\" No quantitative comparison (e.g., fitted normalization, chi-square, ratio of modeled to measured rates) is shown, and the validation measurement is at an altitude where the model cannot currently be evaluated because λ is missing. Without a quantitative validation, the ±25% accuracy claim in Section VII cannot be checked. I recommend adding a direct comparison plot or table with the measured and modeled R, P, and energy spectra, including the elevation scaling with a specified λ.","section":"Section VI, validation against Ref. [8]"}],"minor_comments":[{"comment":"The table's header row and last row (Cosmic rays) are hard to parse because the columns ns, cs, gs, ps, βs, ms, αs, ρGa,s are not all applicable to cosmic rays; consider using separate sub-tables or explicit placeholders (e.g., em dashes) with a footnote explaining which coefficients are used for the cosmic-ray term in Eq. (1).","section":"Table II"},{"comment":"The sentence \"Each term in the event rate R depends linearly on τ, with both constants depending on the source\" is confusing because Eq. (1) shows R depending on τ through gs τ only, with cs independent of τ; consider rewording to \"the gamma-ray contribution to R scales linearly with τ, while the charged-particle contribution cs is thickness-independent.\"","section":"Section VI"},{"comment":"The y-axis of Figure 3 is labeled \"Event rate (s−1)\" but the axis values appear to span 10−3 to 10−1; please clarify the units (per substrate? per cm2?) and ensure the axis label matches the text's description of rates in the nominal substrate.","section":"Section V, Figure 3"},{"comment":"Panel (b) is labeled \"P/t (keV s−1 µm−1)\", but the text discusses P growing as t^1.12; please define whether P is the total deposited power or power per unit thickness, and keep the notation consistent with Eq. (1).","section":"Section IV, Figure 2"}],"recommendation":"major_revision","confidential_remarks":"The missing λ is the most straightforward blocker: it is a single omitted number, but without it the paper's central formula is not usable at nonzero elevation and the validation cannot be reproduced. The low-statistics Mγ ∝ t^5 and the unsupported ±25% uncertainty claim are more serious if the authors intend Table II to be a quantitative reference table for the community. The paper is within scope for IEEE TAS and the overall modeling approach is sound; I would be willing to reconsider after the above points are addressed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This paper gives the community something it genuinely lacks: simple, compact formulas for radiation background rates in superconducting qubit substrates. The three-rate summary (any-energy events R, >1 MeV events M, total power P) with scaling in area, thickness, material, elevation, and ceiling is a legitimate extension of prior modeling work, and Table II is a useful starting point for rough estimates. The re-aiming trick in Section III is also a sensible variance-reduction tactic, and the paper is honest about the one-parameter-at-a-time exploration and the qualitative nature of the TKID consistency check.\n\nThe soft spots are real, and one is load-bearing. The stress-test concern is correct: Eq. (1) defines the cosmic-ray elevation factor as exp(H/λ) and never gives λ. Table II has no λ entry, and Section V reports only species-dependent scale heights (about 5 km for muons, 1 km for nuclear particles, intermediate for e±/γ). Without a value for λ, an experimenter cannot evaluate Eq. (1) at any nonzero elevation, including the 1640 m validation site. And the species-dependent scale heights themselves undermine the single-λ form: at 1640 m, using 5 km versus 1 km changes the rate by a factor of roughly three, far outside the claimed ±25% accuracy. The authors should either give λ for each rate or replace the exponential with a more composition-aware elevation correction. This is fixable, but it is a blocker as published.\n\nOther issues are less severe but worth naming. Table II parameters have no uncertainties. The Mγ ∝ t^5 scaling is inferred from very few simulated events. The claimed ±25% accuracy is asserted, not demonstrated, and no code or data are shipped. Validation rests on a single measurement by the same group. None of these are fatal for a modeling paper, but they should be addressed in a revision.\n\nOverall: the central scaling behavior for R and P is probably robust, and the paper fills a practical gap. As published, though, the headline formula is incomplete for its headline variable (elevation), and the high-energy rates are shaky. It should go to peer review, because a careful referee will force the missing definitions and uncertainties out into the open. I would not cite it until the elevation factor is actually specified.","headline":"Useful compact background-rate formulas, but the elevation scale height λ is never given, so Eq. 1 cannot be evaluated at nonzero altitude as published.","tokens_in":8917,"tokens_out":1448,"would_cite":false,"duration_ms":16149,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Natural radiation backgrounds in superconducting qubit substrates are summarized by a single scaling law that gives three event rates to roughly ±25 percent accuracy.","keywords":["superconducting qubits","natural radiation backgrounds","cosmic rays","terrestrial gamma rays","energy deposition in substrates","scaling laws","kinetic inductance detector","Monte Carlo particle transport"],"falsifier":"Measure the three rates $R$, $M$, and $P$ in a 10 mm by 10 mm, 500 µm silicon substrate at sea level under roughly 20 cm of concrete, using a detector that records the full deposited-energy spectrum; if the measured values differ from Eq. (1) with Table II by more than the claimed ±25 percent, or if the thickness dependence of $M$ departs from the quoted power laws, the central claim would be undercut.","tokens_in":7741,"feed_emoji":"☢️","tokens_out":14016,"duration_ms":119091,"temperature":0.7,"pith_summary":"Natural radioactivity in concrete and cosmic rays from the atmosphere deposit energy in the silicon and compound-semiconductor substrates that hold superconducting qubits, producing the correlated decoherence events that currently limit large processors. This paper tries to turn that problem into a small set of numbers: it claims that, for any substrate area, thickness, material, ceiling thickness, and laboratory elevation, three rates---the rate of any energy-depositing event $R$, the rate of events above 1 MeV $M$, and the total deposited power $P$---are captured by one analytic formula, Eq. (1), with the parameters listed in Table II. If the formula is right, a researcher can estimate background levels to roughly $\\pm25\\%$ over realistic conditions without running Monte Carlo simulations. The modeled rates and energy-deposited spectrum are consistent with the authors' earlier measurement with a silicon thermal kinetic-inductance detector at 1640 m elevation.","feed_headline":"Qubit chip radiation rates reduce to one equation","feed_subtitle":"Inputs are substrate area, thickness, material, elevation, and shielding; output includes event rate to ±25 percent.","key_machinery":"The load-bearing object is the three-rate summary and the closed-form scaling law of Eq. (1). The rates are: $R$, the rate of any event depositing energy $E>0$; $M$, the rate of events depositing $E>1$ MeV, chosen because it marks the transition from terrestrial-gamma and charged-particle events to proton and neutron events and corresponds to roughly one event per hour in the nominal substrate; and $P$, the total power deposited. Equation (1) is separable: an area factor $A/(100\\,\\mathrm{mm}^2)$, a sum over six background sources of terms $c_s+g_s\\tau$, $p_s\\tau^{\\beta_s}$, and $m_s\\tau^{\\alpha_s}$, and corrections $\\kappa_c\\kappa_{sh}\\kappa_\\rho$ for ceiling, shape, and density. This factorization is what carries the argument, because it reduces a six-dimensional simulation space to a table of constants that any user can evaluate directly.","core_discovery":"On the paper's own terms, the central claim is that all simulated background behavior in superconducting-circuit substrates can be summarized by Eq. (1), which expresses the three summary rates as products of the wafer area, a sum over six source terms (the $^{40}$K, $^{232}$Th, and $^{238}$U decay chains, with the uranium and thorium chains each split into two halves around radon, plus cosmic rays), and three multiplicative corrections for ceiling, shape, and density. Each source term is proportional to its relative activity $\\tilde a_s$; the gamma contributions scale with thickness $\\tau \\equiv t/500\\,\\mu\\text{m}$ as $c_s + g_s\\tau$ for $R$ and as power laws $\\tau^{\\beta_s}$ and $\\tau^{\\alpha_s}$ for $P$ and $M$, while the cosmic-ray contribution grows with elevation as $\\exp(H/\\lambda)$ with different scale heights for different particle species. The paper states that the absolute rates are accurate to about $\\pm25\\%$ over a range of realistic conditions, and that the model reproduces the measured event-rate spectrum of the authors' thermal kinetic-inductance detector.","pith_inferences":["Extension: if Eq. (1) generalizes as claimed, a lab can identify its dominant background term without simulation---at sea level terrestrial gamma rays set the low-energy rate, while the once-per-hour MeV events are mostly cosmic-ray protons and neutrons---so the relative benefit of underground siting versus additional local shielding follows directly from the two scale heights.","Extension: the gamma-ray $M_\\gamma \\propto \\tau^5$ exponent is estimated from very few simulated events; a testable consequence is that measuring MeV events in substrates of thickness 30, 100, and 500 µm should reveal this steep dependence, and if it does not, the exponent needs revision.","Extension: because the nominal concrete activities are European averages, labs using unusual aggregates or with elevated radon should expect systematic offsets; assaying local concrete and rescaling via $\\tilde a_s$ is a natural extension of the formula."],"forward_implications":["Any lab can compute approximate background rates for its own substrate geometry, material, shielding, and elevation by evaluating Eq. (1) with Table II, without specialized simulation expertise.","Thinning the substrate is an effective lever: the high-energy event rate scales as $M_\\gamma \\propto \\tau^5$ for gamma rays and as $\\tau^{1.8}$ for cosmic rays, so a thinner wafer suppresses the rare damaging events far more than it suppresses the total rate.","Adding concrete ceiling reduces cosmic-ray $R$ and $P$ by only about 2% per 10 cm, so overhead shielding is not a strong mitigation against cosmic-ray backgrounds.","The $M$ rate in the nominal 500 µm silicon substrate is about once per hour, the level flagged as a concern for quantum error correction.","Denser and gallium-containing substrates have higher rates; for gallium the gamma-ray rates scale as if the density were increased by a source-dependent amount, and high-energy events scale roughly as $\\tilde\\rho^{2.7}$."],"supporting_citations":[{"why":"provides the standalone thermal kinetic-inductance detector measurement of radiation-induced energy deposition that the modeled rates and spectrum are checked against.","marker":"[8]"},{"why":"supplies the particle-transport Monte Carlo engine used for every shielding and substrate simulation.","marker":"[14]"},{"why":"provides the simulation configuration tool used to set up the particle-transport runs and phase-space inputs.","marker":"[17]"},{"why":"provides the parameterized cosmic-ray spectra by particle species that drive the cosmic-ray source sampling.","marker":"[21]"},{"why":"supplies the elevation and zenith-angle dependence of terrestrial cosmic-ray fluxes behind the scale-height trends.","marker":"[22]"},{"why":"supplies the nominal specific activities of potassium-40, thorium-232, and uranium-238 in typical building materials that set the benchmark gamma-ray source.","marker":"[12]"},{"why":"gives photon cross sections and attenuation lengths justifying the 50 cm concrete slab approximation.","marker":"[20]"}],"fun_headline_variants":["One equation predicts qubit radiation backgrounds","Radiation rates for qubits summarized by single formula","Natural radiation effects on qubits reduced to one equation","Model predicts qubit decoherence from cosmic rays and gamma","Simple formula captures radiation backgrounds in superconductor chips"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The fragile premise is that the simulated backgrounds, built from standard cosmic-ray spectra and typical European concrete, match real labs closely enough that the scaling formulas hold to the claimed 25 percent for any substrate and elevation, even though only one measurement is used for comparison.","fun_headline_variants_meta":{"raw":{"variants":["One equation predicts qubit radiation backgrounds","Radiation rates for qubits summarized by single formula","Natural radiation effects on qubits reduced to one equation","Model predicts qubit decoherence from cosmic rays and gamma","Simple formula captures radiation backgrounds in superconductor chips"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000143,"raw_usage":{"total_tokens":1150,"prompt_tokens":901,"completion_tokens":249,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":517,"completion_tokens_details":{"reasoning_tokens":174}},"tokens_in":517,"tokens_out":249,"duration_ms":2457,"temperature":1.0,"reasoning_tokens":174,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T12:40:43.936083+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the three rates $R$, $M$, and $P$ in a 10 mm by 10 mm, 500 µm silicon substrate at sea level under roughly 20 cm of concrete, using a detector that records the full deposited-energy spectrum; if the measured values differ from Eq. (1) with Table II by more than the claimed ±25 percent, or if the thickness dependence of $M$ departs from the quoted power laws, the central claim would be undercut.","supporting_citations":[{"cited_title":"Spectroscopic measurements and models of energy deposition in the substrate of quantum circuits by natural ionizing radiation,","cited_arxiv_id":null,"evidence_quote":"provides the standalone thermal kinetic-inductance detector measurement of radiation-induced energy deposition that the modeled rates and spectrum are checked against."},{"cited_title":"Geant4—a simulation toolkit,","cited_arxiv_id":null,"evidence_quote":"supplies the particle-transport Monte Carlo engine used for every shielding and substrate simulation."},{"cited_title":"TOPAS: An innovative proton Monte Carlo platform for research and clinical applications,","cited_arxiv_id":null,"evidence_quote":"provides the simulation configuration tool used to set up the particle-transport runs and phase-space inputs."},{"cited_title":"Particle and heavy ion transport code system, PHITS, version 2.52,","cited_arxiv_id":null,"evidence_quote":"provides the parameterized cosmic-ray spectra by particle species that drive the cosmic-ray source sampling."},{"cited_title":"Analytical model for estimating the zenith angle dependence of terrestrial cosmic ray fluxes,","cited_arxiv_id":null,"evidence_quote":"supplies the elevation and zenith-angle dependence of terrestrial cosmic-ray fluxes behind the scale-height trends."},{"cited_title":"Kovler, Radioactive materials","cited_arxiv_id":null,"evidence_quote":"supplies the nominal specific activities of potassium-40, thorium-232, and uranium-238 in typical building materials that set the benchmark gamma-ray source."},{"cited_title":"Xcom: Photon cross section database (version 1.5), nist standard reference database 8,","cited_arxiv_id":null,"evidence_quote":"gives photon cross sections and attenuation lengths justifying the 50 cm concrete slab approximation."}],"review_version":1}