{"id":"be2d4141-9cd8-4b7c-ab9a-604a92db7a82","arxiv_id":"2507.03642","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A transmon molecule with nonlinear cosφ coupling achieves 99.21% readout fidelity at 89 photons and remains QND with less than 4% errors up to 300 photons, with a theoretical critical photon number of 377.","lead":"A superconducting transmon qubit, coupled to its readout cavity through a purely nonlinear 'cosφ' interaction, was read out with 99.21% fidelity using 89 photons in the cavity. The readout stayed quantum non-demolition (QND) even at hundreds of photons, and the authors derive a critical photon number of 377 that explains the robustness.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Photon-number calibration extrapolation is the main quantitative risk; the 300-photon plateau and the match to 377 photons may shift if the AC-Stark calibration saturates above 200 photons.","rationale":"I read the paper as an experimental demonstration plus a parameter-free theoretical account of why the cosφ-coupling readout remains QND at high photon numbers. The core physics claims—the nonlinear coupling produces a large cross-Kerr shift, the readout is robust at high drive power, and the derived critical photon number is of order hundreds for this sample—are plausible and supported by detailed appendices. The most load-bearing quantitative assumption is the photon-number calibration of Appendix F. Both the abstract and the QNDness analysis reference specific photon numbers (89, 300, 377), and the claim of agreement between the onset of QNDness degradation and the derived nbar_crit = 377 depends directly on this scale. The manuscript itself states that the linear calibration was verified only up to 200 photons and extrapolated beyond. The QNDness model is not fit to the data (no free parameters), which is a genuine strength, and the qualitative result—that errors stay at a few percent over a wide high-power plateau—does not collapse even if the calibration is slightly off. Still, since the central quantitative headline attaches numbers to the plateau and to the theoretical match, the calibration extrapolation is the weakest link. A straightforward extension of the Stark-shift measurement (or an independent calibration) would settle it. I agree with the Reader's identification of this same assumption, and the CONDITIONAL verdict is appropriate: the claims should be either backed by an extended calibration or stated with softened quantitative language.","tokens_in":23975,"tokens_out":1924,"duration_ms":20302,"concrete_test":"Repeat the AC-Stark calibration of Appendix F beyond 200 photons (ideally beyond 400 photons) by measuring Δωq(P) at higher drive powers and comparing with the linear extrapolation, and replot the Fig. 3(b) QNDness-error map and the extracted onset of non-QND errors using the corrected nbar(P) curve. If the corrected QNDness onset stays within, say, 20% of 377 photons and the errors remain below 4% up to a corrected 300-photon point, the quantitative claims hold; if the corrected onset shifts substantially (e.g., below ~250 photons), the 377-photon match and the 300-photon plateau claim should be softened accordingly.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The paper's headline numbers—99.21% fidelity at 89 photons, 96.7% QNDness at that power, and the 'errors < 4% up to 300 photons' plateau—all rely on the photon-number scale nbar = Δωq(P)/(2χqr) calibrated in Appendix F. The supplemental text states explicitly that linearity of the AC-Stark shift was experimentally verified only up to 200 photons and extrapolated to higher powers. Figure 7 shows the frequency vs power data and its linear fit; if the Stark shift saturates above 200 photons, as physical mechanisms such as dressing with higher transmon levels or onset of nonlinear readout-mode response would produce, then nbar for the points above 200 photons is overestimated. The QNDness map in Fig. 3(b), including the onset of non-QND errors near 400 photons (claimed to coincide with nbar_crit = 377), is plotted on that extrapolated scale. This concern is explicitly acknowledged in the manuscript (last sentence of Appendix F), so it is not an artifact of my reading. It does not invalidate the central qualitative claim that the cosφ-coupling supports high-power QND-resilient readout, because the plateau and the robust behavior extend well below the extrapolated region and are corroborated by direct power sweeps. It does, however, weaken the quantitative matching between the measured high-power QNDness onset and the derived critical photon number nbar_r_crit = 377, and it softens the 300-photon plateau claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports an experimental study of a transmon-molecule readout scheme in which the qubit is coupled to a readout mode through a purely nonlinear cos(φ) coupling rather than through the usual transverse linear coupling. The authors report a post-selected readout fidelity of 99.21 ± 0.01% at an average readout photon number of 89, a two-pulse QNDness of 96.7 ± 0.2% at the same power, and QNDness errors below 4% for powers corresponding to up to 300 photons. They also derive a critical photon number associated with the low phase-drop approximation, obtaining nbar_r^crit = 377 photons for their sample parameters, and they argue that this value explains the observed onset of non-QND errors at high power. The manuscript includes detailed appendices on the circuit Hamiltonian, hybridization, fabrication, setup, and calibration, as well as a comparison with an equivalent standard dispersive readout scheme.","tokens_in":24195,"tokens_out":5502,"duration_ms":68098,"significance":"If the results hold, this is a significant experimental advance for superconducting qubit readout: it demonstrates that a purely nonlinear coupling can provide high-fidelity, high-QND readout at photon numbers where standard dispersive readout degrades, and it does so without Purcell filtering. The measurement protocols are standard and the headline numbers come with error bars. A notable strength is that the theoretical critical photon number is not fitted to the QNDness curve but is evaluated from independently characterized circuit parameters, and the manuscript provides extensive supporting details on fabrication, setup, and calibration. The work should be of interest to the circuit-QED and quantum-computing communities, both for the specific transmon-molecule platform and for the general lesson that nonlinear couplings can extend the high-power readout regime.","major_comments":[{"comment":"The photon-number axis used for the high-power QNDness map in Fig. 3(b) is calibrated via the AC-Stark shift using nbar_r(P) = Delta-omega_q(P)/(2 chi_qr). The last sentence of Appendix F states that this linear calibration was experimentally verified only up to 200 photons and then extrapolated to higher powers. Because the quantitative claims 'errors below 4% up to 300 photons' and 'the onset near 400 photons coincides with nbar_r^crit = 377' are read off this extrapolated axis, the linearity assumption is load-bearing. If the AC-Stark shift saturates or deviates from linearity above 200 photons, the photon-number scale is overestimated and the apparent coincidence with the theoretical ncrit would shift. I recommend extending the calibration into the 300-400 photon range, or, if that is not possible, explicitly marking the extrapolated region in Fig. 3 and softening the quantitative wording of the plateau and onset claims.","section":"Appendix F and Fig. 3(b)"},{"comment":"The theoretical critical photon number nbar_r^crit = nbar_r^lowphi = 377 is presented as a quantitative prediction that coincides with the measured onset of QNDness errors. Equation (A14) is evaluated using EJ, La, ECa, and sin^2(theta), but Table II does not specify whether these are measured values, design targets, or extracted fit parameters, nor does it give their uncertainties. To make the claimed agreement convincing, the manuscript should state the provenance of each input and propagate its uncertainty to nbar_r^crit, or at least give a sensitivity estimate. As written, the good agreement between 377 and the observed onset could be fortuitous, especially given the calibration caveat in Appendix F.","section":"Section VI, Eq. (A14)"}],"minor_comments":[{"comment":"When the readout power is first quoted as '89 photons', the text refers the reader to Appendix F for the calibration; it would be helpful to state already at that point that the calibration is linear only up to 200 photons and that higher-power data are extrapolated.","section":"Section IV.A"},{"comment":"The caption says 'ovelayed black line' and the main text says 'shifts quite linearly as a function of power until it reaches about 1.7 GHz'; this wording is ambiguous because it is not clear whether 1.7 GHz refers to the shifted qubit frequency or to the total shift. Please clarify the sentence and correct the typo.","section":"Fig. 7 caption"},{"comment":"The derivation of nbar_r^RWA states that the perturbative term 'reaches the same probability amplitude as the non-perturbative term,' but the threshold criterion is not precisely defined. Please state the exact condition used to obtain Eq. (A10).","section":"Section VI, Eq. (A10)"},{"comment":"The equivalent standard readout scheme uses a transverse coupling g_eq/(2pi) = 515 MHz, which is a very large coupling that would also produce strong dressing beyond the dispersive approximation; the comparison is illustrative, but it should be labelled as such so that the derived nbar_std^crit = 26 is not overinterpreted.","section":"Appendix A.4"},{"comment":"The sentence introducing Eq. (G2) says 'the dephasing induced by both of the readout mode and the unused lower polariton, which is noted with the index l'; this is grammatically awkward and should be rephrased for clarity.","section":"Appendix G"}],"recommendation":"major_revision","confidential_remarks":"The paper is a solid experimental contribution with a clearly identified calibration caveat. The main revision needed is to address the extrapolated photon-number scale, which affects several headline quantitative claims, and to document the uncertainty budget for the theoretical ncrit. With those changes the paper would be suitable for publication in a strong journal. I do not see a circularity problem in the central results, but the quantitative match between theory and experiment should not be oversold until the calibration issue is resolved."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a credible experimental advance, not a revolution. The transmon molecule with cosφ coupling was introduced by the same group, but this paper adds a new optimized device, a clean high-power readout demonstration at 89–300 photons, and a specific theoretical critical photon number ncrit=377 that is evaluated from independently characterized parameters rather than fitted to the QNDness data. If the photon-number calibration holds, the claim that high-fidelity QND readout survives at an order of magnitude above standard dispersive readout is supported.\n\nWhat's genuinely good: the fabrication and characterization are thorough. The circular design and reduced qubit dipole are sensible, and the T1 improvement from 3.3 to 124.5 µs is evidence the Purcell mitigation works. The QNDness map over pulse duration and power is the right kind of data, and the plateau below 4% errors up to 300 photons is a strong qualitative result. The theoretical breakdown into three separate high-power limits (RWA, readout-mode nonlinearity, low phase-drop) is useful; the low phase-drop limit at 377 photons is specific to this coupling and is not just borrowed from the transverse-coupling literature.\n\nSoft spots: the photon-number axis uses AC-Stark calibration nbar = Δωq/(2χqr), and linearity is explicitly verified only up to 200 photons. The 300-photon plateau and the claimed match to ncrit=377 both sit in the extrapolated region. If the Stark shift saturates above 200 photons, those numbers shift, though the qualitative behavior does not because the plateau is broad and the direct sweeps show robustness. The paper acknowledges this in Appendix F, so it is not a hidden flaw, but it does mean the quantitative boundary at 400 photons should be read with caution. Also, the device is a single sample; no repeatability claim is made. The QNDness protocol is correlation-based rather than full tomography, but the cited protocol from Ref. [12] is adequate for the claim being made.\n\nBottom line: the central result—high-power QND persistence with cosφ coupling—is likely correct and useful for the field. The exact photon numbers at the high end are less certain. The paper deserves a serious referee; I would recommend conditional acceptance with the authors either extending the Stark calibration or softening the 300-photon/377-photon quantitative language.","headline":"Solid experimental demonstration of high-power QND readout with nonlinear cosφ coupling; the 300-photon plateau is credible qualitatively, but the photon-number axis is calibrated only to 200 photons, so the highest-power numbers should be taken with a grain of salt.","tokens_in":24876,"tokens_out":1852,"would_cite":true,"duration_ms":21698,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["85.25.Cp","03.67.Lx"],"model":"deepseek-v4-flash","headline":"A purely nonlinear coupling keeps transmon readout faithful and QND at hundreds of photons.","keywords":["transmon molecule","cosφ-coupling","QND readout","high-power readout","cross-Kerr coupling","superconducting qubits","critical photon number","Purcell protection"],"falsifier":"Compare an independent photon-number calibration, such as transmitted-power measurement or sideband thermometry, against the Stark-shift scale between 200 and 400 photons; a disagreement would rescale $\\bar{n}_r^{\\mathrm{crit}}$ and the QNDness-versus-power map, while a match would confirm the 377-photon limit.","tokens_in":23731,"feed_emoji":"⚛️","tokens_out":4890,"duration_ms":53708,"temperature":0.7,"pith_summary":"The paper claims that qubit readout through a purely nonlinear $\\cos\\varphi$ coupling, implemented by a transmon molecule, keeps high fidelity and quantum non-demolition (QND) behavior at readout powers where the standard dispersive scheme degrades. In this sample, single-shot fidelity reaches 99.21% at roughly 89 photons in the readout mode, and the QNDness stays at 96.7% at that power and above 96% up to about 300 photons. The authors explain the stability by deriving a new critical photon number, $\\bar{n}_r^\\mathrm{crit} = 377$, set by the low phase-drop approximation used to reduce the $\\cos\\varphi$ coupling to a cross-Kerr term, rather than by the perturbative detuning criterion of transverse coupling. If correct, the scheme lifts the standard power ceiling on readout signal-to-noise ratio and does so without Purcell filtering, since the qubit is decoupled from the cavity by symmetry.","feed_headline":"Nonlinear transmon readout hits 99.21% fidelity at 89 photons","feed_subtitle":"The cosφ-coupled transmon molecule stays QND up to 300 photons, where dispersive readout degrades.","key_machinery":"The load-bearing element is the purely nonlinear coupling term $-2E_J[\\cos(\\hat{\\varphi}_q)-1][\\cos(\\hat{\\varphi}_a)-1]$, which comes from galvanic coupling between two transmon modes and contains no linear term. After the low phase-drop approximation and rotating-wave approximation it yields the nonperturbative cross-Kerr coupling, and every transition it induces conserves parity in both transmon excitations and readout photons. A third resonator, transversely coupled to the ancilla and decoupled from the qubit by symmetry, hybridizes into polariton readout modes; choosing the more linear polariton gives the reduced dispersive Hamiltonian and protects the qubit from Purcell decay. The paper's new high-power scale is the critical photon number $\\bar{n}_r^{\\mathrm{crit}} = \\frac{1}{2\\sin^2\\theta}\\sqrt{\\frac{E_J(1+2L_J/L_a)}{E_{Ca}}} = 377$ photons, marking where the fourth-order Taylor expansion of $\\cos(\\hat{\\varphi}_a)$ stops being valid.","core_discovery":"The central claim is that the transmon molecule's $\\cos\\varphi$-coupling produces a nonperturbative cross-Kerr interaction of the form $2\\chi_{qr}\\,\\hat{q}^\\dagger\\hat{q}\\hat{c}_r^\\dagger\\hat{c}_r$, so the readout Hamiltonian looks like dispersive readout but without any large-detuning approximation. Consequently, the standard critical photon number $\\bar{n}_\\mathrm{std}^\\mathrm{crit} = \\Delta^2/(2g)^2$ does not limit this scheme; the limiting assumptions are instead the rotating-wave approximation, linearization of the readout mode, and the low phase-drop Taylor expansion. For this sample the last gives $\\bar{n}_r^{\\mathrm{crit}} = 377$ photons, which coincides with the abrupt rise in QNDness errors visible in the measured power map. The device achieves $T_1 = 124.5\\,\\mu\\mathrm{s}$ without any Purcell filter, whereas the equivalent transverse-coupling readout would have $T_1 \\approx 800\\,\\mathrm{ns}$ and a critical photon number of only 26.","pith_inferences":["If the AC-Stark photon-number calibration is independently verified above 200 photons, the 377-photon critical number becomes a quantitative design rule; if that calibration drifts, the quoted power scale shifts but the qualitative robustness of the readout likely remains.","The parity-conservation property of the $\\cos\\varphi$ coupling suggests that measurement-induced state transitions are strongly suppressed compared with transverse readout; a systematic census of transitions above 300 photons would test this directly.","Because the qubit is Purcell-protected by symmetry, the scheme could plausibly be extended to multiplexed multi-qubit readout where several high-power measurements coexist on one chip, though this would require a dedicated architecture study."],"forward_implications":["Readout power can be pushed to roughly 100 photons while keeping fidelity above 99% and QNDness near 97%, so signal-to-noise ratio is no longer limited by dispersive-shift collapse.","A transmon molecule can deliver high-fidelity readout without a Purcell filter, with $T_1 = 124.5\\,\\mu\\mathrm{s}$ compared with about $800\\,\\mathrm{ns}$ for an equivalent transverse-coupling readout.","QNDness errors stay below 4% up to about 300 photons, supporting repeated-measurement protocols, pre-selection, and active feedback at much higher power than standard readout allows.","The derived 377-photon limit gives a concrete design target: increasing it by tuning the hybridization angle $\\theta$, the ancilla charging energy, or the Josephson energy would push the scheme further into the high-power regime."],"supporting_citations":[{"why":"The previous transmon-molecule implementation demonstrating low-power QND readout of the $\\cos\\varphi$-coupling, which this work optimizes.","marker":"[12]"},{"why":"The earlier transmon-molecule sample and its in situ bifurcation readout, whose parameter limits motivate the new sample's design.","marker":"[16]"},{"why":"The theoretical proposal of a diamond-shaped artificial atom whose nonlinear coupling enables nondemolition readout.","marker":"[11]"},{"why":"The transmon model and dispersive-shift formula used to construct the equivalent transverse readout scheme.","marker":"[5]"},{"why":"The standard derivation of the critical photon number that limits dispersive transverse readout, which this scheme bypasses.","marker":"[19, 20]"},{"why":"A state-of-the-art high-fidelity dispersive readout operating in the low-power regime, the main comparison point for fidelity and QNDness.","marker":"[6]"},{"why":"The repeated-measurement protocol used to define and measure the QNDness $P_{\\mathrm{QND}}$.","marker":"[34]"},{"why":"The traveling-wave parametric amplifier used to improve signal-to-noise ratio for the fidelity measurement.","marker":"[26]"}],"fun_headline_variants":["Nonlinear transmon readout hits 99.21% at 89 photons","Transmon readout stays QND at 300 photons without Purcell filter","377-photon limit for transmon readout via cosφ coupling","High-power transmon readout: 99.21% fidelity, no Purcell filter","Nonlinear coupling enables 300-photon QND transmon readout"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The photon-number scale assumes the AC-Stark shift remains linear in readout power above the 200-photon range where it was experimentally verified, so the 300-photon and 377-photon numbers rest on an extrapolation.","fun_headline_variants_meta":{"raw":{"variants":["Nonlinear transmon readout hits 99.21% at 89 photons","Transmon readout stays QND at 300 photons without Purcell filter","377-photon limit for transmon readout via cosφ coupling","High-power transmon readout: 99.21% fidelity, no Purcell filter","Nonlinear coupling enables 300-photon QND transmon readout"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000331,"raw_usage":{"total_tokens":1901,"prompt_tokens":1061,"completion_tokens":840,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":677,"completion_tokens_details":{"reasoning_tokens":738}},"tokens_in":677,"tokens_out":840,"duration_ms":7849,"temperature":1.0,"reasoning_tokens":738,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T20:06:22.771335+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compare an independent photon-number calibration, such as transmitted-power measurement or sideband thermometry, against the Stark-shift scale between 200 and 400 photons; a disagreement would rescale $\\bar{n}_r^{\\mathrm{crit}}$ and the QNDness-versus-power map, while a match would confirm the 377-photon limit.","supporting_citations":[{"cited_title":"All the modes are simulated for1 Joule of stored energy so that the re- sults are comparable","cited_arxiv_id":null,"evidence_quote":"The previous transmon-molecule implementation demonstrating low-power QND readout of the $\\cos\\varphi$-coupling, which this work optimizes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The theoretical proposal of a diamond-shaped artificial atom whose nonlinear coupling enables nondemolition readout."},{"cited_title":"reverse- Kerr","cited_arxiv_id":null,"evidence_quote":"The transmon model and dispersive-shift formula used to construct the equivalent transverse readout scheme."},{"cited_title":"We use its TE101 mode for the transmon molecule read- out scheme","cited_arxiv_id":null,"evidence_quote":"A state-of-the-art high-fidelity dispersive readout operating in the low-power regime, the main comparison point for fidelity and QNDness."},{"cited_title":"Didier, J","cited_arxiv_id":null,"evidence_quote":"The traveling-wave parametric amplifier used to improve signal-to-noise ratio for the fidelity measurement."}],"review_version":1}