{"id":"a056fbbc-4e09-4c36-8149-60c02c690c02","arxiv_id":"2411.12611","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Granular aluminum lumped-element inductors with a few nH of inductance reach internal quality factors above 3 million while staying linear and compact.","lead":"Granular aluminum films can be made into compact, low-loss microwave inductors for superconducting quantum circuits, with internal quality factors above three million. The work shows a systematic trade-off between compactness and loss, and demonstrates a simple way to attach these inductors to aluminum or tantalum electrodes.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Bulk-loss subtraction makes the best-device residual loss consistent with zero, so the grAl-surface-loss conclusion is an upper bound.","rationale":"The reader's weakest-assumption analysis correctly identifies the most load-bearing uncertainty in the paper's argument: the loss budget of Sec. VI depends on subtracting a literature bulk-loss value from measured Qint values, and for the best devices the residual is within the uncertainty of the bulk term. This means the specific claim that low-resistivity grAl surface loss is 'similar to pure Al' is not firmly established by the data; it is an upper bound. The reader's CONDITIONAL verdict already reflects this by accepting the measured device performance while treating the loss-budget interpretation as needing further support. I agree with that assessment. I found no additional concern that would change the verdict: the headline Qint and self-Kerr values are direct measurements, the kinetic-inductance extraction is checked by high participation ratios, and the paper honestly notes the unmeasured contact loss and the lack of a microscopic mechanism for the resistivity trend. The proposed concrete test—a reference resonator on the same substrate batch—would directly resolve whether the bulk loss assumption is the limiting factor. The paper's own language in the abstract ('suggests', 'could be explained') is appropriately hedged, though the conclusion section's 'our analysis indicates... comparable' is slightly stronger than the data support. Overall, the central claim of demonstrating compact, linear, low-loss grAl inductors is robust; the conditional verdict is appropriate.","tokens_in":31078,"tokens_out":10510,"duration_ms":105783,"concrete_test":"Fabricate an Al (or Ta) reference resonator with identical geometry on the same unannealed EFG sapphire batch used for the all-grAl devices and measure its Qint to determine the batch's actual bulk loss tangent. Compare the extracted Gamma_bulk to (26.6 +/- 6.9) x 10^-8 (Refs. [10,76]). If Gamma_bulk differs by more than the combined uncertainty, recompute the residual losses in Fig. 6c for all devices. If the low-resistivity all-grAl residual becomes negative or falls well below the Al-transmon reference line, the statement 'Gamma_grAl_surf similar to pure Al' should be weakened to an upper bound, and the abstract's last sentence should be revised to avoid implying a firm equality. A complementary test is to perform a multimode analysis on a single all-grAl device (as in Refs. [10,74]) to separate bulk, surface, and inductive loss without relying on the literature value.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The measured Qint values (up to 3.5e6 all-grAl, 4.7e6 hybrid) directly support the headline claims of compact, linear, low-loss inductors. The load-bearing uncertainty is in the loss attribution of Sec. VI, Eq. (2). The residual loss Qres^-1 = Qint^-1 - Qbulk^-1 is obtained by subtracting the literature bulk-loss tangent of unannealed EFG sapphire, Gamma_bulk = (26.6 +/- 6.9) x 10^-8 [10,76], which corresponds to Qbulk ~ 4.5e6 for these geometries. For the best all-grAl device (GH23, rho_n = 555 uOhm cm, Qint = 3.66e6), 1/Qint = 2.73e-7 and 1/Qbulk = 2.22e-7, giving a residual of 5.1e-8. The uncertainty in 1/Qbulk from the quoted Gamma_bulk error alone is p_bulk * 6.9e-8 ~ 5.8e-8, so the residual is within one sigma of zero. Thus the data cannot distinguish between Gamma_grAl_surf ~ Gamma_Al_surf and Gamma_grAl_surf < Gamma_Al_surf with the device limited by bulk loss; the conclusion in Sec. VI that low-resistivity grAl surface loss is 'similar to pure Al' is really an upper bound. The increasing loss with resistivity (factor ~6 from rho_n ~ 830 to ~4000 uOhm cm) is robust because high-resistivity residuals are much larger than the bulk uncertainty, but attributing that trend specifically to conductor loss in the grAl strip (rather than, e.g., loss in the AlOx grain-boundary dielectrics, whose participation is not simulated) is an inference. For the hybrid grAl/Ta devices, the authors explicitly state they do not independently measure contact (bandage) loss, so the claim of integration 'without increasing total internal losses' rests on the observed Qint values, not on a direct measurement of the contact contribution.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports the design, fabrication, and microwave characterization of lumped-element resonators whose inductance is dominated by the kinetic inductance of granular aluminum (grAl) films. The authors measure sheet inductances of 30–320 pH/sq, self-Kerr coefficients of 0.2–20 Hz/photon, and single-photon internal quality factors up to 3.5×10^6 for all-grAl devices and 4.7×10^6 for hybrid grAl/Ta devices. They also demonstrate ex-situ integration with Al and Ta capacitor electrodes using an Al bandage layer, study quasiparticle dynamics after high-energy impacts, and propose a loss budget separating bulk, surface, conductor, and contact losses. The central claim is that grAl inductors can be simultaneously compact, linear, low-loss, and compatible with standard Al/Ta circuit fabrication.","tokens_in":31462,"tokens_out":6788,"duration_ms":64517,"significance":"If the results hold, the paper delivers a practical solution to a recognized problem: a compact, linear, low-loss inductor for circuit QED that is lithographically simple and integrable with Al and Ta. The direct measurements are of high quality: Qint is extracted from transmission fits at single-photon powers, the self-Kerr from power-dependent frequency shifts, and Lk from frequency combined with FEM simulations of the geometry. The improvement over previous grAl resonators (best reported Q ~ 3×10^5) is substantial, and the large sample set with clear fabrication details in the appendices is a strength. The main weakness is the loss attribution: several conclusions rest on subtracting a literature bulk-loss value and on unmeasured contact losses. Nevertheless, the demonstrated Qint values themselves support the primary claim of low-loss inductors and should be of considerable interest to the circuit QED community.","major_comments":[{"comment":"The conclusion that low-resistivity grAl has a surface loss factor similar to pure Al is not supported by the data as stated. For the best all-grAl device (GH23, rho_n = 555 uOhm cm, Qint = 3.66e6), subtracting the literature bulk loss of unannealed EFG sapphire (Gamma_bulk = (26.6 +/- 6.9)e-8, Qbulk ~ 4.5e6) gives a residual loss of about 5.1e-8, whereas the uncertainty in 1/Qbulk alone is about 5.8e-8. The residual is therefore consistent with zero, and the data can only place an upper bound on the grAl surface loss at this resistivity. Please propagate the bulk-loss uncertainty through Eq. (2) and rephrase the related claims in Sec. VI and the abstract (e.g., 'comparable to or lower than' instead of 'similar to').","section":"Sec. VI, Eq. (2), Fig. 6(c)"},{"comment":"The attribution of the resistivity-dependent loss to conductor loss in the grAl strip is an inference rather than a unique conclusion. The residual loss shows a saturable power dependence (App. F), which is more typical of two-level-system or quasiparticle loss than of the classical conductor loss described by Q_ind in Eq. (2). In addition, the FEM participation calculation does not include dielectric loss in the AlOx grain-boundary network, whose volume fraction and disorder increase with oxygen content (i.e., with rho_n). The authors are appropriately cautious in the abstract ('could be explained'), but Sec. VI states 'we attribute their increasing losses with resistivity to an increase in conductor loss' without ruling out these alternatives. Please soften this claim and discuss how a multimodal analysis or an explicit grain-boundary loss model could distinguish the mechanisms.","section":"Sec. VI, App. F, Fig. 10"},{"comment":"The claim that ex-situ hybrid integration does not increase total internal losses is not backed by an independent measurement of the bandage contact loss. As the authors state in Sec. I, contact losses are not measured separately, and Sec. VI acknowledges that Q_contact may have a resistivity dependence. While the comparable Qint of hybrid and all-grAl devices from the same wafers supports the practical utility of the bandage process, the loss budget in Eq. (2) is underdetermined for the hybrids: Q_contact is degenerate with Q_ind and Q_surf. An upper-bound estimate of contact loss (e.g., from devices with different numbers of contacts or contact areas) would strengthen the integration claim.","section":"Sec. V, Sec. VI"}],"minor_comments":[{"comment":"The oxygen partial pressure during grAl deposition is given as ~5e-5 mbar in Sec. II and ~5e-5 Torr in App. B; these differ by a factor of 1.333. Please harmonize the units.","section":"Sec. II vs App. B"},{"comment":"The equation for the self-Kerr coefficient appears as '|K| = p2Eca2/l2 strip' due to a typesetting error; it should read K = p^2 E_c a^2 / l_strip^2.","section":"Sec. III.B"},{"comment":"The term 'psurf tan δTLSp' should be 'psurf tan δ_TLS' (missing underscore and space).","section":"App. E, Eq. (E1)"},{"comment":"The header 'W afer' should be 'Wafer'.","section":"Table II"},{"comment":"The caption uses Q_i for internal quality factor while the text uses Qint; please unify the notation.","section":"Fig. 3(a)"},{"comment":"'under coupled' should be 'undercoupled'.","section":"Sec. II"}],"recommendation":"major_revision","confidential_remarks":"The manuscript reports direct, credible measurements of high Qint and low self-Kerr in grAl lumped-element resonators, which are the core experimental findings. The loss attribution sections, however, need reworking because the key 'surface loss similar to pure Al' claim is currently an upper bound given the bulk-loss uncertainty, and the conductor-loss interpretation is degenerate with other mechanisms. These are load-bearing issues for the paper's interpretive claims, but they are fixable by softening language and adding uncertainty propagation. The paper is otherwise a strong experimental contribution well matched to a quantum-device journal."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The headline measurements are solid. The paper reports the first grAl lumped-element resonators with single-photon Q above 3e6 (up to 3.7e6 all-grAl, 4.7e6 hybrid grAl/Ta), self-Kerr nonlinearities of 0.2–20 Hz/photon, and a systematic factor-of-six degradation in Qint as film resistivity increases from ~830 to ~4000 µΩ·cm. That last trend is new and, for the high-resistivity devices, robust. The ex-situ bandage integration with Al and Ta is also a practical step forward, and the measurements are careful: transmission fits, power-dependent TLS saturation, FEM participation ratios, package-loss budget, and a control Al tripole in App. H. The quasiparticle dynamics section adds a useful datapoint—millisecond relaxation, much faster than earlier grAl stripline resonators.\n\nThe soft spot is the loss attribution, and the stress-test note is right. For the best low-resistivity devices, the residual loss after subtracting the literature bulk-loss tangent of unannealed EFG sapphire is within about one sigma of zero. So the claim that low-resistivity grAl surface loss is “similar to pure Al” is really an upper bound: the device could be bulk-limited. The paper's own wording (“suggests”, “could be explained”) is appropriately cautious, but the conclusion in Sec. VI should be stated as an upper bound unless supported by additional data. The resistivity-dependent increase in loss at higher ρn is a measured fact, but attributing it specifically to conductor loss in the grAl strip is an inference—grain-boundary dielectric loss with resistivity-dependent participation is not simulated, and for hybrid devices the contact loss is explicitly unmeasured. These are real limitations, but they do not undermine the directly measured Qint, Lk, and K values, which are the core of the paper.\n\nWho is this for: people building compact superinductors, fluxonium-like circuits, or high-impedance resonators for spin qubits. It advances the practical toolkit for grAl and gives a clear design trade-off. The paper deserves a serious referee: the experimental demonstration is valuable and the loss analysis needs tightening (state the upper-bound nature, or add a multimodal measurement), not rejection. I would send it to review.","headline":"Solid experimental advance: grAl lumped-element inductors with Q above 3e6 and a clean resistivity-loss trend, but the surface-loss claim is an upper bound, not a measured equality.","tokens_in":727,"tokens_out":1105,"would_cite":true,"duration_ms":32550,"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":"Granular aluminum can form compact, linear, low-loss inductors for superconducting quantum circuits, with internal quality factors exceeding three million.","keywords":["granular aluminum","kinetic inductance","lumped-element resonators","superconducting quantum circuits","internal quality factor","self-Kerr nonlinearity","quasiparticle dynamics","hybrid superconductor integration"],"falsifier":"Fabricate the same resonator layouts on sapphire substrates whose bulk dielectric loss is independently varied or measured, for example annealed versus unannealed wafers with known different loss tangents, and check whether the extracted residual loss of the granular-aluminum strip stays constant. If the residual-loss-versus-resistivity trend persists unchanged under a different substrate loss, the conductor-loss attribution is supported; if the trend tracks the substrate instead, the central loss conclusion is wrong.","tokens_in":30864,"feed_emoji":"⚛️","tokens_out":8132,"duration_ms":79571,"temperature":0.7,"pith_summary":"Granular aluminum is a superconductor whose microstructure gives it a large kinetic inductance, and this paper argues that this property can be turned into a practical lumped-element inductor for quantum circuits. The authors build microwave resonators in which a narrow strip of granular aluminum provides almost all of the inductance, and they show that these strips are simultaneously compact, highly linear, and low-loss. Their best all-granular-aluminum devices reach single-photon internal quality factors around $3.5 \\times 10^6$, and hybrid devices with tantalum capacitors exceed $4.5 \\times 10^6$, comparable to the best superconducting circuits. They also find a systematic trade-off: higher room-temperature resistivity gives more compact inductors but lower quality factors, and their analysis attributes the low-resistivity surface loss to a level similar to pure aluminum.","feed_headline":"Granular aluminum inductors hit million-scale quality factors","feed_subtitle":"Thick granular-aluminum films make compact linear inductors; hybrid tantalum devices stay above 4.5 million Q","key_machinery":"The argument runs through the kinetic inductance of granular aluminum and its description as a one-dimensional array of effective Josephson junctions. In the device, a narrow granular-aluminum strip carries more than 90 percent of the total inductance, so the resonator frequency is set by the sheet inductance times the number of squares; the self-Kerr coefficient is diluted roughly as $E_c/N_{\\text{JJ}}^2$, which lets the authors infer an effective junction size of 10 to 30 nm from measured nonlinearities. For loss, the paper uses an energy-participation-ratio budget, $1/Q_{\\text{int}} = 1/Q_{\\text{bulk}} + 1/Q_{\\text{surf}} + 1/Q_{\\text{ind}} + 1/Q_{\\text{contact}}$, with the substrate bulk term and surface participation computed by finite-element simulation, and the contact term relevant only for the hybrid devices.","core_discovery":"The central claim is that granular aluminum, in films about 90 nm thick, can serve as a linear inductive element whose performance is no longer the limiting factor in high-coherence circuits. The measured sheet inductance ranges from 30 to 320 pH/sq, so a few-nH inductor can be made in a strip only tens of micrometers long, up to 100 times more compact than a pure-aluminum geometric inductor; the self-Kerr nonlinearity stays at 0.2 to 20 Hz per photon, far below the linewidth. Internal quality factors at single-photon power reach $3.5 \\times 10^6$ for all-granular-aluminum resonators and exceed $4.5 \\times 10^6$ for hybrid granular-aluminum/tantalum devices. After subtracting the known bulk dielectric loss of the substrate, the remaining loss in the lowest-resistivity films is comparable to that of standard aluminum transmon circuits, and the increase of loss with film resistivity is attributed to conductor loss in the granular aluminum rather than to a worse surface dielectric. The paper also reports that quasiparticle relaxation after a high-energy impact occurs on millisecond timescales, matching aluminum transmons and contradicting earlier thin-film granular-aluminum results.","pith_inferences":["If the resistivity-loss trend is a general property of granular aluminum, coherence-critical qubit designs should favor low-resistivity strips even at the cost of area, while high-resistivity strips remain attractive for high-impedance applications such as spin-qubit readout.","The ex-situ bandage contact is demonstrated only with aluminum and tantalum electrodes, but the same method may extend to other high-gap superconductors; that extension is not established by this paper.","Because the inferred effective junction size is 10 to 30 nm, pushing strip dimensions toward that scale should eventually reveal single-junction nonlinear behavior, a regime the paper's model does not address.","The fast millisecond quasiparticle relaxation, if reproduced in full qubit devices, would shorten the duration of radiation-induced frequency excursions compared with earlier thin-film granular-aluminum results."],"forward_implications":["Granular-aluminum lumped-element inductors can serve as linear shunts in inductively shunted qubit designs without the footprint of geometric inductors.","Compactness reduces the number of low-frequency parasitic modes compared with millimeter-long geometric inductors.","Ex-situ bandage integration means granular-aluminum strips can be added to circuits whose capacitors are made from aluminum or tantalum with no measured increase in loss.","Resistivity becomes a design knob with a known trade-off: lower resistivity gives higher internal quality factor and lower sheet inductance.","At low resistivity, granular-aluminum surface loss is comparable to pure aluminum, so replacing aluminum with granular aluminum need not introduce extra surface dielectric losses."],"supporting_citations":[{"why":"Supplies the independently measured bulk dielectric loss tangent of unannealed sapphire, the aluminum and tantalum transmon surface-loss reference lines, and the package-loss characterization used in the loss budget.","marker":"[10]"},{"why":"Provides the precision measurement of sapphire bulk dielectric loss that fixes the bulk quality factor for the unannealed substrates.","marker":"[76]"},{"why":"Supplies the energy-participation-ratio method used to compute surface and bulk loss contributions from the finite-element field simulations.","marker":"[73]"},{"why":"Prior granular-aluminum resonator study whose loss levels and quasiparticle relaxation times are the baseline this work exceeds and reinterprets.","marker":"[57]"},{"why":"Introduces the effective Josephson-junction-array description of granular aluminum that the authors use to extract the number of junctions from the self-Kerr coefficient.","marker":"[64]"},{"why":"Standard theory relating normal-state resistivity to kinetic inductance and surface impedance, used to connect film resistivity to sheet inductance and conductor loss.","marker":"[75]"},{"why":"Provides the quasiparticle recombination and trapping model, and the aluminum-transmon relaxation comparison, used to interpret the measured time traces.","marker":"[70]"}],"fun_headline_variants":["Granular aluminum inductors hit Q of 4.5 million","Compact, linear inductors from granular aluminum reach Q 4.5M","Granular aluminum shrinks inductors 100x while keeping Q high","Hybrid tantalum-grAl resonators exceed 4.5 million Q"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the unannealed sapphire substrates have the bulk dielectric loss tangent measured previously, $(26.6 \\pm 6.9) \\times 10^{-8}$; because the best measured quality factors sit near the resulting bulk limit, a different substrate loss would change the attribution of the remaining loss and weaken the conclusion that low-resistivity granular-aluminum surface loss matches pure aluminum.","fun_headline_variants_meta":{"raw":{"variants":["Granular aluminum inductors hit Q of 4.5 million","Compact, linear inductors from granular aluminum reach Q 4.5M","Granular aluminum shrinks inductors 100x while keeping Q high","Hybrid tantalum-grAl resonators exceed 4.5 million Q"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000764,"raw_usage":{"total_tokens":3476,"prompt_tokens":1116,"completion_tokens":2360,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":732,"completion_tokens_details":{"reasoning_tokens":2279}},"tokens_in":732,"tokens_out":2360,"duration_ms":17721,"temperature":1.0,"reasoning_tokens":2279,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T17:22:09.817012+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Fabricate the same resonator layouts on sapphire substrates whose bulk dielectric loss is independently varied or measured, for example annealed versus unannealed wafers with known different loss tangents, and check whether the extracted residual loss of the granular-aluminum strip stays constant. If the residual-loss-versus-resistivity trend persists unchanged under a different substrate loss, the conductor-loss attribution is supported; if the trend tracks the substrate instead, the central loss conclusion is wrong.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the precision measurement of sapphire bulk dielectric loss that fixes the bulk quality factor for the unannealed substrates."},{"cited_title":"Gr¨ unhaupt, N","cited_arxiv_id":null,"evidence_quote":"Prior granular-aluminum resonator study whose loss levels and quasiparticle relaxation times are the baseline this work exceeds and reinterprets."},{"cited_title":"Maleeva, L","cited_arxiv_id":null,"evidence_quote":"Introduces the effective Josephson-junction-array description of granular aluminum that the authors use to extract the number of junctions from the self-Kerr coefficient."}],"review_version":1}