{"id":"93d5b8cf-cf53-4718-998b-e641735b72c0","arxiv_id":"1908.09556","paper_version":3,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":1,"one_line_summary":"A transmon qudit using Ramsey interferometry infers on-chip microwave amplitude and frequency from ac Stark shifts of the first two transitions, enabling broadband transfer function characterization.","lead":"Superconducting qudit sensors can measure the amplitude and frequency of microwave signals arriving on a chip using time-resolved Ramsey fringes that reveal the ac Stark shifts of higher transmon levels. The method maps the transfer function of the microwave line over hundreds of megahertz and could improve calibration of quantum gate pulses.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Amplitude extraction rests entirely on unvalidated lookup-table simulations; no independent on-chip amplitude calibration is reported, so the claimed ΔAF precision is not yet established.","rationale":"The paper's central claim is that the on-chip amplitude and frequency can be inferred from ac Stark shifts of two transmon transitions using numerically generated lookup tables. The frequency part is well supported by the direct comparison in Fig. 3a. The amplitude part, however, is only as good as the lookup-table model, because the on-chip amplitude is not known a priori: PF,apl is set at the source, and everything between source and chip is the transfer function the sensor is supposed to characterize. The only validation of the amplitude channel would be an independent measurement of AF, and none is reported. The simulation-uncertainty analysis in the Supplementary correctly propagates the error in ω1 and ω2, but it assumes these are the only simulation-input errors; Eq. (1) itself drops the readout resonator, and there is no stated convergence test on the number of transmon levels or the master-equation time step. Since the lookup tables are the inversion kernel, a model bias would systematically shift every extracted AF. This does not invalidate the frequency sensing or the relative amplitude response, but it does mean the absolute amplitude claim and the quoted ΔAF are conditional on the model. A resonant Rabi calibration is a straightforward check that would either confirm the model or reveal the bias. For these reasons I would accept the paper only conditional on such an independent amplitude validation (or an equivalent full-resonator simulation comparison).","tokens_in":11560,"tokens_out":13080,"duration_ms":145390,"concrete_test":"Measure resonant Rabi oscillations on the 0-1 transition using the same drive line: the Rabi frequency gives an independent, lookup-table-free calibration of the on-chip AF (up to the known transmon matrix element). Then, at several frequencies and powers in the range of Fig. 3c, apply a calibrated field off-resonantly and run the sensor; compare the extracted AF,ex with the Rabi-calibrated value. If the deviations exceed ΔAF/2π = 3.4 MHz, the lookup-table model is biased and the amplitude claim requires revision.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The frequency channel is validated by comparing ω_F,ex with the applied source frequency (Fig. 3a), but the amplitude channel has no independent ground truth: the applied power at the source is not the on-chip AF, and the transfer function of Fig. 3c is precisely the unknown quantity the sensor is meant to report, so it cannot provide a self-calibration. The lookup tables are generated by master-equation simulations of Eq. (1) that explicitly neglect the readout resonator, and the Supplementary's 'Simulation Uncertainty' section bounds only the effect of uncertainty in ω1 and ω2, concluding the error is at most 2σR,i. That argument does not cover model-form error—neglected resonator-mediated dressing, truncated level basis, or gate-pulse modeling—and a systematic lookup-table bias would propagate directly into AF,ex, undermining the headline amplitude uncertainty ΔAF/2π = 3.4 MHz. The paper does not supply any independent calibration of AF against, for example, resonant Rabi oscillations.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports a time-resolved microwave-field sensor based on a superconducting transmon qudit. A continuous microwave tone detuned from the first two qudit transitions produces ac Stark shifts Δ1 and Δ2 that are measured via Ramsey interferometry. The measured shifts are inverted using lookup tables generated by QuTiP master-equation simulations of Eq. (1) to extract the on-chip field frequency ωF and amplitude AF. The authors validate the frequency channel by comparing extracted and applied source frequencies over a 450 MHz range, and they use the extracted amplitude to display the transfer function of the microwave line. They report an order-of-magnitude precision improvement over the earlier spectroscopic implementation, with ΔAF/2π = 3.4 MHz and ΔωF/2π = 25 MHz for about one-minute measurement times, and they discuss sensor limits, the Ramsey noise floor, TLS fluctuations, and a phase-measurement scheme.","tokens_in":11737,"tokens_out":8601,"duration_ms":98364,"significance":"This is a useful and timely contribution to in-situ calibration of microwave control lines in circuit QED. The paper's strengths are the direct frequency validation over 450 MHz, the quantitative error analysis (Ramsey fit standard errors, shot-noise scaling, TLS frequency-fluctuation estimates, and simulation uncertainty for input parameters), and the concrete Ramsey-based protocol with clear sensor limits. If the amplitude channel can be independently validated, the demonstrated order-of-magnitude precision gain over Ref. [18] and the broadband transfer-function measurement would justify publication in a good quantum-engineering journal.","major_comments":[{"comment":"The amplitude channel is not independently calibrated, so the headline amplitude uncertainty ΔAF/2π = 3.4 MHz is not yet established. The applied source power PF,apl is not a ground truth for the on-chip amplitude AF, and the transfer function shown in Fig. 3c is precisely the quantity the sensor is meant to measure; therefore Fig. 3c cannot serve as a self-calibration. The lookup tables are generated by master-equation simulations of Eq. (1) that explicitly neglect the readout resonator, and the Supplementary 'Simulation Uncertainty' analysis varies only ω1 and ω2, concluding that the error is at most 2σR,i. That argument does not bound model-form error from the neglected resonator, the truncated level basis, or the modeling of the gate pulses. A systematic bias in the lookup tables would shift AF,ex without affecting the statistical shaded error bars, and the successful frequency validation in Fig. 3a does not rule this out because the frequency contours of the lookup table can remain accurate even if the amplitude scaling is wrong. I request an independent amplitude check, for example resonant Rabi oscillations at a known transition frequency to calibrate the on-chip drive amplitude, or a full-system simulation including the readout resonator that quantifies the model-form error.","section":"Lookup table calculations; Fig. 3c; Supplementary 'Simulation Uncertainty'"}],"minor_comments":[{"comment":"The expression PF,ex = AF,ex ℏωF,ex appears dimensionally inconsistent as written; please specify the unit conversion used to obtain a value in dBm.","section":"Results, Example extraction"},{"comment":"The claim of an 'energy sensitivity on the order of 10^-4' is never defined; please state which measured quantity this refers to and how it is derived.","section":"Abstract"},{"comment":"The sentence 'the qudit ground state is not effected' contains a typo; 'effected' should be 'affected'.","section":"Supplementary Information, Unprocessed sensor data"},{"comment":"The text refers to 'the full system Hamiltonian in Eq. (1)', but Eq. (1) neglects the readout resonator; this wording is misleading and should be revised to 'the qudit Hamiltonian' or similar.","section":"Methods, Lookup table calculations"},{"comment":"The distinction between upper and lower sensor limits in Eq. (3) would be clearer if the text explicitly stated that the first inequality is an upper bound set by the sampling rate and the second is a lower bound set by the maximum Ramsey delay, and why the lower bound is controlled by Δ2.","section":"Results, Eq. (3)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a solid incremental experimental demonstration, and the requested amplitude validation appears feasible within the scope of the paper. If the authors can supply an independent cross-check of the extracted on-chip amplitude, I would support acceptance. The overlap with Ref. [18] is substantial, but the time-resolved implementation, the order-of-magnitude precision improvement, and the transfer-function measurement constitute a clear advance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my read on 1908.09556. The paper is a solid, honest experimental follow-up to Schneider et al., but the stress-test note is right about the main caveat: only the frequency channel gets independent validation.\n\nWhat's new is the time-resolved implementation. The earlier spectroscopic sensor used steady-state ac Stark shifts; this one uses Ramsey fringes on the first two transmon transitions and gets an order-of-magnitude precision improvement, with uncertainties of ΔA_F/2π = 3.4 MHz and Δω_F/2π = 25 MHz for comparable measurement time. The Ramsey scheme is nontrivial because the second transition's π-pulse depends on the first shift, so the measurement order is fixed. They build lookup tables from full master-equation simulations rather than perturbation theory, and they include a reasonable uncertainty budget: Ramsey fit error, noise floor, TLS fluctuation estimate, and a simulation-uncertainty check. The frequency sweep over 450 MHz matches the applied source, and the inferred transfer function shows clear frequency-dependent structure from the readout resonator and cables.\n\nThe soft spot is exactly the one the stress-tester flags. The amplitude channel has no independent ground truth. The source power is not the on-chip amplitude, and the transfer function of Fig. 3c is the unknown they are trying to infer, so it cannot validate the extraction. The lookup tables come from simulations of Eq. (1) that neglect the readout resonator, and the supplementary simulation-uncertainty section only bounds the effect of qudit frequency uncertainty, not model-form error. That means the quoted amplitude precision is conditional on the simulation being faithful. That is not a fatal flaw — driven-transmon master-equation simulations are usually reliable in this regime, and the dispersive resonator is likely a small effect — but a referee should ask for an independent amplitude cross-check, e.g. resonant Rabi oscillations, or a softened claim.\n\nI trust the paper's honesty: it explicitly says the simplified model is inadequate and gives a quantitative, if partial, uncertainty analysis. Data and code are available only on request, which limits independent verification but is common in this field.\n\nFor a cQED experimentalist working on pulse calibration, this is directly useful. For a theory reading group, it's less central. I would send it to peer review, and I would accept it after an amplitude cross-check or a revised claim. The paper deserves a serious referee.","headline":"A useful, honest experimental follow-up: Ramsey-based ac-Stark sensing improves precision by an order of magnitude, but the amplitude channel lacks independent ground truth and should be tempered or cross-checked.","tokens_in":12294,"tokens_out":3227,"would_cite":true,"duration_ms":34427,"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":"Ac Stark shifts of a transmon qudit reveal the amplitude and frequency of an on-chip microwave field.","keywords":["transmon qudit","ac Stark shift","Ramsey interferometry","microwave sensing","transfer function","superconducting circuits","lookup table inversion","quantum sensing"],"falsifier":"Apply a known microwave tone at several amplitudes and frequencies, including a tone near the readout resonator at 6.878 GHz and amplitudes around A_F/2pi = 0.75 GHz where the simulation predicts 22.7% population of the |2> state, and compare the sensor's extracted amplitude to an independently calibrated cryostat attenuation model; agreement within the quoted uncertainties would confirm the lookup-table model, while systematic deviations beyond those uncertainties would falsify it.","tokens_in":11388,"feed_emoji":"📡","tokens_out":4580,"duration_ms":48874,"temperature":0.7,"pith_summary":"This paper shows that a single superconducting transmon, used as a multilevel sensor, can determine both the frequency and the amplitude of a microwave field arriving at the chip by measuring how that field shifts the energies of its first two transitions. The shifts are read out through Ramsey fringes, which raises the precision by an order of magnitude over the earlier spectroscopic scheme. Over a span of several hundred megahertz, the sensor reports field frequency and amplitude with uncertainties of 25 MHz and 3.4 MHz, respectively, at an energy sensitivity around $10^{-4}$. Such on-chip metrology matters because conventional electronics cannot probe signals at the millikelvin stage, and knowing the transfer function from source to sample would let experimenters correct distorted microwave pulses before they reach the qubit.","feed_headline":"A transmon qudit reads microwave amplitude and frequency","feed_subtitle":"Ramsey fringes of Stark shifts give on-chip field values to about 0.5% accuracy in one minute.","key_machinery":"The load-bearing object is a pair of lookup tables: numerical master-equation simulations of the full transmon Hamiltonian that map field frequency and amplitude onto the expected Stark shifts of the first two transitions. A Ramsey sequence on each transition supplies the measured shifts, and the tables are searched for the field parameters whose predicted shifts match both measurements. These numerical tables replace the analytic perturbation-theory version from the earlier sensing work, which is not accurate enough when frequency shifts are resolved at the few-kilohertz level.","core_discovery":"The central claim is that the ac Stark shifts of the first two transmon transitions, measured via Ramsey interferometry and inverted through pre-computed lookup tables, uniquely determine the frequency and amplitude of an unknown on-chip microwave field. The paper verifies this by sending a known tone across a 450 MHz range and showing that the extracted frequencies track the applied frequencies, while the extracted amplitudes trace the frequency-dependent attenuation of the transfer function. Compared with the prior spectroscopic implementation, the time-resolved approach reduces the uncertainties to $\\Delta$ omega_F/2pi = 25 MHz and $\\Delta$ A_F/2pi = 3.4 MHz in about a minute of measurement time. The method is limited to fields above the first qudit transition and below the power where higher transmon levels become substantially populated.","pith_inferences":["Because the lookup tables are generated numerically, the same sensor concept could be retuned to other transmon frequencies or higher qudit levels simply by regenerating the tables, extending the measurable band without changing the measurement logic.","A practical phase sensor built on the supplement's two-detuned-pulse idea would likely need a clearer readout signal than this sample's noise floor permits, suggesting that readout improvement is the natural next step.","Temporal fluctuations of the qudit frequencies from two-level-system noise could be the dominant systematic error in field extraction; continuously tracking omega_1 and omega_2 during a sensor run should tighten the reported uncertainties.","One could test whether the method extends beyond continuous tones to pulsed or multi-tone microwave fields, by comparing the Ramsey-derived amplitudes against an independent, calibrated power measurement in the time domain."],"forward_implications":["The sensor measures the amplitude of the microwave transfer function from source to chip over a band of several hundred megahertz, exposing frequency-dependent distortion from the readout resonator and cable resonances.","Because both frequency and amplitude come from the same two shift measurements, the method can characterize arbitrary microwave fields, not just tones whose parameters are already known.","Combined with the phase-sensitive extension outlined in the supplemental material, the scheme could yield the full complex transfer function needed for digital pulse pre-distortion and higher gate fidelities.","The achieved energy sensitivity near 10^-4 makes weak fields detectable, with the ultimate floor in this device set by a noise offset of about 2.2 kHz on the second transition.","The one-minute measurement time can plausibly shrink to seconds using parametric amplifiers and active reset, both already demonstrated in similar circuit-QED setups."],"supporting_citations":[{"why":"Establishes the multilevel ac Stark sensing concept and supplies the analytic lookup tables that this paper replaces with numerical simulations.","marker":"[18]"},{"why":"Provides the transmon Hamiltonian and eigenstates used to compute the Stark shifts and transition matrix elements.","marker":"[27]"},{"why":"Documents the coherence and decay of higher transmon levels, which sets the maximum Ramsey delay and motivates the damping term in the fits.","marker":"[30]"},{"why":"Shot-noise scaling is used to model how the Ramsey fit error decreases with the number of averages.","marker":"[31]"},{"why":"Low-frequency noise from single two-level-system fluctuators motivates the estimation of qudit-frequency fluctuation uncertainty.","marker":"[34]"},{"why":"The master-equation simulations that generate the lookup tables are performed with this quantum dynamics toolbox.","marker":"[53, 54]"}],"fun_headline_variants":["Transmon qudit senses microwave amplitude and frequency via Stark shifts","On-chip microwave field calibration using a transmon qudit","Ramsey fringes of qudit levels measure microwave fields","Qudit ac Stark shifts give amplitude and frequency of microwaves","Time-resolved microwave sensing with a superconducting transmon"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The sensor's calibration charts are computed by a simulation that ignores the readout resonator and uses only the two measured qudit transition frequencies, so if that model's predicted Stark shifts do not match what the real device feels, the extracted amplitude and frequency will be systematically wrong.","fun_headline_variants_meta":{"raw":{"variants":["Transmon qudit senses microwave amplitude and frequency via Stark shifts","On-chip microwave field calibration using a transmon qudit","Ramsey fringes of qudit levels measure microwave fields","Qudit ac Stark shifts give amplitude and frequency of microwaves","Time-resolved microwave sensing with a superconducting transmon"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000824,"raw_usage":{"total_tokens":3557,"prompt_tokens":854,"completion_tokens":2703,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":470,"completion_tokens_details":{"reasoning_tokens":2620}},"tokens_in":470,"tokens_out":2703,"duration_ms":19295,"temperature":1.0,"reasoning_tokens":2620,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T11:07:25.843173+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Apply a known microwave tone at several amplitudes and frequencies, including a tone near the readout resonator at 6.878 GHz and amplitudes around A_F/2pi = 0.75 GHz where the simulation predicts 22.7% population of the |2> state, and compare the sensor's extracted amplitude to an independently calibrated cryostat attenuation model; agreement within the quoted uncertainties would confirm the lookup-table model, while systematic deviations beyond those uncertainties would falsify it.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the multilevel ac Stark sensing concept and supplies the analytic lookup tables that this paper replaces with numerical simulations."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the transmon Hamiltonian and eigenstates used to compute the Stark shifts and transition matrix elements."},{"cited_title":"Concentric transmon qubit featuring fast tunability and an anisotropic magnetic dipole moment","cited_arxiv_id":null,"evidence_quote":"Documents the coherence and decay of higher transmon levels, which sets the maximum Ramsey delay and motivates the damping term in the fits."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shot-noise scaling is used to model how the Ramsey fit error decreases with the number of averages."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Low-frequency noise from single two-level-system fluctuators motivates the estimation of qudit-frequency fluctuation uncertainty."}],"review_version":1}