{"id":"32f3db43-8d80-4fae-a9f4-6c3f8d914b65","arxiv_id":"1908.11370","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Injected broadband flux noise was used to calibrate a dephasing model linking instrument noise power spectral density to parametric two-qubit gate infidelity, and harmonic filtering was shown to restore AC sweet spot coherence.","lead":"Researchers at Rigetti injected controlled broadband noise into the magnetic flux control of superconducting qubits and measured how that noise shortens qubit coherence during parametric modulation. They used the resulting model to state a noise floor for two-qubit gate error and showed that filtering between harmonics restores coherence.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The quantitative noise-floor claim rests on a single fitted α transferred from transmon 3 to the Hong et al. device, with no direct entangling-gate check; if α is device/line-specific, the -123 dBm/Hz spec shifts.","rationale":"The experimental core is solid: the CPMG validation in Section II demonstrates a broadband noise source, the ACSS recovery in Fig. 4 is clear, the additive-rate fit in Fig. 5 is plausible, and the filtering result in Fig. 7 provides direct qualitative confirmation of the second-harmonic noise channel. These are real evidence and I do not dispute them. However, the headline quantitative deliverable, the -123 dBm/Hz noise floor, is not supported by an end-to-end measurement. It is produced by splicing together α from transmon 3 with T1 and Tphi values from a different device pair (Hong et al., Table II) via Eq. 6. Since α includes chain attenuation and qubit sensitivity, its transfer is the single least-secure step. A direct measurement of α on the relevant device, or a measured E_CZ(S_inj) curve, would settle this. This concern reinforces rather than changes the reader's conditional verdict; no rejection is warranted.","tokens_in":9380,"tokens_out":4993,"duration_ms":52124,"concrete_test":"Repeat the Section III/Fig. 5 protocol on the tunable qubit of the Hong et al. pair used in Table II (or on a second independent device with the same flux-control chain): fit α, recompute Eq. 6 with that α, and compare the PSD at which E_CZ crosses 1% with the claimed -123 dBm/Hz. As a direct cross-check, measure the CZ gate error under injected broadband noise at that PSD and compare with Eq. 6's prediction; agreement within, say, 20% would confirm transferability and validate the noise-floor specification.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's practical deliverable, a -123 dBm/Hz noise floor for 1% CZ infidelity (Eq. 6, Fig. 6), depends on Eq. 4 being calibrated with a single value of α fit to transmon 3 (Fig. 5) and then applied without recalibration to the different tunable transmon in the Hong et al. pair of Table II. Eq. 4 states that α accounts for both qubit-frequency sensitivity to drive amplitude and the attenuation from the instrument output to the SQUID loop; both are device- and control-chain-specific. No error bars are given for α, no repeated-device measurements are shown, and no CZ gate infidelity under injected broadband noise is reported. The internal consistency of the Tphi(S_inj) fit on one qubit does not constrain the transfer. A factor-of-2 error in α changes the inferred 1% threshold by 3 dB, moving the specification substantially. The paper itself in Section V caveats that the filtering mitigation applies 'assuming the noise is coming down the signal line,' acknowledging the environmental-coupling alternative, but even granting that caveat, the α transfer remains unchecked. This is the weakest load-bearing step for the quantitative central claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports an experimental study of dephasing in a flux-tunable transmon operated at the AC sweet spot (ACSS) under controlled broadband noise injected through the flux control line. The authors first validate the noise source with a CPMG-based spectrometer, showing that the measured dephasing times converge for different pulse numbers when injected broadband noise dominates. They then measure T_phi at the ACSS as a function of injected noise PSD, fit the data to an additive background-plus-control rate model with a single parameter alpha, and use that model together with a previously derived gate-infidelity formula to predict that a noise floor of about -123 dBm/Hz is sufficient for a 1% CZ gate infidelity. Finally, they demonstrate that placing a low-pass filter between the fundamental and second harmonic of the AC flux drive greatly increases T_phi at the ACSS, confirming the predicted second-harmonic noise channel.","tokens_in":9621,"tokens_out":3608,"duration_ms":37894,"significance":"If the central quantitative claim holds, the paper provides a practical method for translating a spectrum-analyzer measurement of instrumentation noise on the flux line into an entangling-gate infidelity budget, and it experimentally confirms the higher-harmonic dephasing channel predicted by Didier et al. The strongest parts of the work are the external and controlled injection of broadband noise, the internal consistency of the T_phi(S_inj) fit in Fig. 5, and the direct filtering demonstration in Fig. 7. However, the headline noise-floor specification is built on a single fitted alpha that is transferred from one transmon to a different device with no direct entangling-gate check and no reported uncertainty; this limits the strength of the practical conclusion unless the transferability is demonstrated or the claim is reframed as an illustrative estimate.","major_comments":[{"comment":"The quantitative noise-floor claim of -123 dBm/Hz for 1% CZ infidelity depends on transferring the fitted coefficient alpha from transmon 3 (Fig. 5) to the tunable qubit of the Hong et al. device described in Table II. As stated in the text around Eq. (4), alpha accounts for both the qubit-frequency sensitivity to drive amplitude and the attenuation from the instrument output to the SQUID loop; both are device- and control-chain-specific. No measurement of alpha on the Hong et al. device, no repeated-device characterization, and no direct entangling-gate infidelity measurement under injected noise is reported. A factor-of-two error in alpha shifts the inferred 1% threshold by about 3 dB, which is material to the specification. The authors should either recalibrate alpha on the target channel/device, provide a device-to-device variation bound from multiple qubits, or explicitly reframe the -123 dBm/Hz number as an illustrative prediction with a stated sensitivity analysis.","section":"Section IV, Eq. (6) and Fig. 6"},{"comment":"The fitted value of alpha is never reported, and no uncertainties are given for the fit or for the T_phi data in Figs. 3, 5, and 7. Since Eq. (6) is linear in alpha and the noise-floor threshold is logarithmically sensitive to alpha, the absence of a confidence interval means the reader cannot assess how robust the -123 dBm/Hz prediction is. Please report the fitted alpha with its uncertainty, show error bars or confidence bands on the key figures, and state the resulting uncertainty in the inferred noise floor.","section":"Section III, Fig. 5 and Section IV"},{"comment":"The filtering demonstration is presented as a confirmation of the second-harmonic dephasing channel, but it is based on a single transmon and single filter configuration without error bars or repeated measurements. Given that the authors themselves note that the mitigation assumes the noise is coming down the signal line, the claim would be strengthened by at least one repetition on a second device or by a quantitative comparison of the observed T_phi improvement with the model prediction. As written, this section is suggestive rather than definitive, though it is not the central quantitative deliverable.","section":"Section V, Fig. 7"}],"minor_comments":[{"comment":"Equation (4) uses S_inj as if it were a linear power spectral density, while all reported values and figure axes use dBm/Hz. Please clarify the units in Eq. (4) and state explicitly that the linear PSD is used in the fit.","section":"Eq. (4) and Fig. 5 axes"},{"comment":"The numerical calculations in Fig. 3 use 'a static background 1/f noise spectrum' but the amplitude and corner frequency of that 1/f noise are not specified; please provide these parameters so the comparison is reproducible.","section":"Section II, Fig. 3"},{"comment":"The horizontal axis is labeled 'Noise Power (dBm)' but the text describes total noise power; the integration bandwidth used to compute total power should be stated.","section":"Fig. 7"},{"comment":"The phrase 'We find agreement to within 1% of the observed experimental infidelity' is ambiguous: the measured and coherence-limited infidelities are 1.2% and 0.9%, respectively, a difference of 0.3 percentage points. Please state the comparison explicitly.","section":"Section IV, Table II"},{"comment":"There are several typos and small errors: 'Arbitary' in Section II, 'dramatric' in the Fig. 7 caption, and 'N. Dider' in reference [14] should be 'N. Didier'.","section":"Throughout"},{"comment":"The near-negligible slope of the noise PSD is quoted without accounting for the analyzer's own noise floor; a sentence explaining how the correction affects the quoted slope would improve clarity.","section":"Fig. 1"}],"recommendation":"major_revision","confidential_remarks":"The paper is a competent experimental study with an internally consistent central measurement, but the headline -123 dBm/Hz specification rests on an uncalibrated transfer of a single fitted alpha from one transmon to another device, and the fitted alpha itself is not reported with uncertainty. The authors can address this either by recalibrating alpha on the target device or by repositioning the noise-floor number as an illustrative estimate with a sensitivity analysis; the latter may be the more realistic path given the available data."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThis is a competent experimental study from the Rigetti group, and the core measurement is real: they inject broadband noise through the flux line, watch T_phi at the AC sweet spot degrade, and fit the additive rate model 1/T_phi = 1/T_bg + alpha*S_inj. The fit is clean, the CPMG convergence in Fig. 3 is a sensible validation that the noise is broadband, and the filtering demonstration in Fig. 7 is a concrete, useful confirmation of the Didier et al. prediction. The paper is worth reading if you care about practical noise requirements for parametric CZ gates.\n\nWhat is genuinely new is the experimental mapping between an instrument PSD measured at room temperature and qubit dephasing at the ACSS, plus the demonstration that placing a low-pass filter between the fundamental and second harmonic recovers coherence. That is a practical engineering result, and the paper is honest that it assumes the noise comes down the signal line.\n\nThe soft spot is the quantitative noise-floor claim. The -123 dBm/Hz number for 1% CZ infidelity comes from Eq. (6), which uses a single value of alpha fitted on transmon 3 (Fig. 5) and then applies it to the different tunable transmon in the Hong et al. pair. No error bars on alpha, no repeated-device measurement, no entangling-gate error measured under injected noise. A factor-of-two shift in alpha moves the threshold by 3 dB. The internal consistency of the T_phi fit on one qubit does not constrain the transfer. So the spec is a reasonable estimate, but it is not a calibrated requirement. This should be stated more carefully or backfilled with additional data.\n\nAlso, the figures lack error bars, and the paper does not provide raw data or uncertainty propagation for the derived infidelity curve. Minor but worth noting. The reliance on prior work from the same group is not a flaw per se; the equations are published and the new measurements are the contribution.\n\nBottom line: this paper deserves a serious referee. It is a useful engineering contribution with a clear central result and honest caveats. The main revision should be to either directly measure the gate error under injected noise or at least give error bars and a sensitivity analysis on alpha. With that, the quantitative framework would be much stronger.\n\nI would bring it to a reading group and likely cite it in work on control-line noise requirements.\n\n— Your initials","headline":"A solid, useful experimental paper whose quantitative noise-floor spec rests on a single fitted alpha transferred across devices; worth sending to referees but the -123 dBm/Hz number should be treated as indicative, not a hard specification.","tokens_in":10167,"tokens_out":954,"would_cite":true,"duration_ms":11375,"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":"Injected broadband flux noise dephases a flux-modulated transmon at a rate that grows linearly with the noise power spectral density.","keywords":["superconducting qubits","transmon","flux noise","dephasing","AC sweet spot","parametric two-qubit gates","broadband noise","CPMG spectroscopy"],"falsifier":"Repeat the $T_\\varphi$-versus-injected-noise measurement on a second uncalibrated qubit and compare the predicted dephasing rates, or directly measure CZ gate error under injected noise against Eq. (6); a mismatch beyond the fitted accuracy would falsify the transfer of $\\alpha$. A second check: filter the flux line while injecting no added noise; if $T_\\varphi$ at the ACSS does not change, the remaining noise floor is set by environmental coupling rather than control-line noise, and the filtering prescription would not generalize.","tokens_in":9196,"feed_emoji":"⚛️","tokens_out":8268,"duration_ms":74377,"temperature":0.7,"pith_summary":"This paper tries to show that the dephasing of a flux-modulated transmon qubit at its AC sweet spot—the operating point where the time-averaged frequency is first-order insensitive to flux noise—follows an additive law: the total dephasing rate is the sum of a static background rate and a control rate proportional to the power spectral density of broadband noise injected through the flux line. If the law holds, it converts a room-temperature noise measurement into a predicted two-qubit gate infidelity, yielding concrete instrument noise-floor specifications. The paper reports fits to measured coherence times, derives a noise floor near $-123\\,\\mathrm{dBm/Hz}$ for a CZ gate infidelity of 1%, and demonstrates that low-pass filtering the AC drive between its fundamental and second harmonic greatly increases $T_\\varphi$, confirming that second-harmonic noise is the next leading dephasing channel. The framework is offered as a general way to set noise requirements for control instrumentation on other qubit platforms.","feed_headline":"Flux-line noise floor for 1% CZ gates: -123 dBm/Hz","feed_subtitle":"One fitted rate turns noise readings into gate-error predictions; filtering the second harmonic restores coherence.","key_machinery":"The load-bearing object is the single-coefficient rate law $1/T_\\varphi^{\\rm ctrl} = \\alpha S_{\\rm inj}$, where $\\alpha$ maps a broadband noise PSD measured at room temperature into a dephasing rate at the qubit. Around this sits the Fourier picture of the modulated qubit frequency, $\\omega(t) = \\sum_k \\omega_k \\cos[k(\\omega_m t + \\theta_m)]$: at the AC sweet spot the slope of the fundamental harmonic $d\\omega_0/d\\Phi$ vanishes while harmonics with $k\\geq 2$ keep nonzero sensitivity, so second-harmonic noise is the next leading channel. That same picture motivates placing a low-pass filter between $\\omega_m$ and $2\\omega_m$. The CPMG pulse sequence with its filter function supplies the experimental confirmation that the injected source is broadband across the relevant frequency range.","core_discovery":"The central claim is that at the AC sweet spot of a parametrically modulated transmon, flux-noise dephasing splits into two additive channels, background and control, with $1/T_\\varphi(S_{\\rm inj}) = 1/T_\\varphi^{\\rm bg} + \\alpha S_{\\rm inj}$, where $\\alpha$ encodes the qubit's frequency sensitivity to the drive and the attenuation from instrument output to the SQUID loop. The paper validates the injected noise as broadband using CPMG measurements, fits $\\alpha$ to coherence data under injected noise, and combines the model with a coherence-limited gate fidelity formula to predict that a flux-line noise PSD near $-123\\,\\mathrm{dBm/Hz}$ suffices for 1% CZ gate infidelity. It then shows experimentally that low-pass filtering the AC modulation between the fundamental and second harmonic greatly increases $T_\\varphi$ at the ACSS, confirming the predicted second-harmonic noise channel and establishing passive filtering as a practical mitigation when the noise arrives through the flux line.","pith_inferences":["Because $\\alpha$ is likely device- and channel-specific, the framework is best used as a per-qubit calibration rather than a universal constant; repeating the protocol on each tunable qubit would make the noise-floor prescriptions quantitative for that device.","The filtered-versus-unfiltered coherence comparison at the ACSS doubles as a diagnostic: it separates control-line-delivered noise from noise coupled directly to the SQUID from the environment.","The same additive-rate treatment could be extended to other parametric control schemes—tunable couplers, driven qubits, or modulated resonators—wherever a harmonic of the drive has finite susceptibility to a control-noise spectral density.","A testable extension would combine the CPMG noise spectrometer with the harmonic filter to reconstruct the full flux-noise spectrum at the ACSS rather than only the integrated broadband power."],"forward_implications":["At the AC sweet spot, control-line dephasing is fully captured by one fitted coefficient, so a short coherence-versus-noise measurement on a device specifies the instrument noise floor for any target gate error.","For the parameters studied, a flux-line noise PSD near $-123\\,\\mathrm{dBm/Hz}$ sustains 1% CZ gate infidelity, and improving $T_1$ and $T_2$ by tenfold relaxes the requirement to about $-115\\,\\mathrm{dBm/Hz}$.","Placing a low-pass filter between the fundamental and second harmonic of the AC drive restores long coherence at the ACSS whenever the noise is injected down the flux line.","The model predicts a floor on CZ infidelity near 0.83% for the studied device, set by $T_1$ and $T_2$ rather than by broadband control noise."],"supporting_citations":[{"why":"Supplies the AC sweet spot concept and the Fourier-harmonic analysis of the modulated qubit frequency, including the predicted benefit of filtering between the fundamental and second harmonic.","marker":"[1]"},{"why":"Supplies the fixed-tunable qubit pair, CZ gate time, coherence times, and measured gate infidelity used to convert noise PSD into an entangling-gate noise requirement.","marker":"[14]"},{"why":"Supplies the Carr-Purcell-Meiboom-Gill pulse sequence used to test whether the injected noise is broadband.","marker":"[15]"},{"why":"Supplies the CPMG filter-function formalism that relates measured dephasing times to the flux-noise spectrum.","marker":"[16]"},{"why":"Supplies the explicit CPMG filter function and the broadband-plus-1/f dephasing framework used in the numerical and analytical model.","marker":"[19]"}],"fun_headline_variants":["Flux-noise model sets 1% gate error floor: -123 dBm/Hz","Filtering second harmonic boosts transmon coherence at ACSS","Injected noise model predicts two-qubit gate fidelity","Broadband flux noise: dephasing split into two channels","Low-pass filter cuts flux noise sensitivity at ACSS"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the dominant broadband flux noise reaches the qubit through the flux control line, and that one fitted coefficient $\\alpha$, calibrated on a single qubit from room-temperature noise measurements, transfers to other qubits and gate operations without device-specific refitting.","fun_headline_variants_meta":{"raw":{"variants":["Flux-noise model sets 1% gate error floor: -123 dBm/Hz","Filtering second harmonic boosts transmon coherence at ACSS","Injected noise model predicts two-qubit gate fidelity","Broadband flux noise: dephasing split into two channels","Low-pass filter cuts flux noise sensitivity at ACSS"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001237,"raw_usage":{"total_tokens":5088,"prompt_tokens":964,"completion_tokens":4124,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":580,"completion_tokens_details":{"reasoning_tokens":4047}},"tokens_in":580,"tokens_out":4124,"duration_ms":25324,"temperature":1.0,"reasoning_tokens":4047,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T10:17:12.619217+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Repeat the $T_\\varphi$-versus-injected-noise measurement on a second uncalibrated qubit and compare the predicted dephasing rates, or directly measure CZ gate error under injected noise against Eq. (6); a mismatch beyond the fitted accuracy would falsify the transfer of $\\alpha$. A second check: filter the flux line while injecting no added noise; if $T_\\varphi$ at the ACSS does not change, the remaining noise floor is set by environmental coupling rather than control-line noise, and the filtering prescription would not generalize.","supporting_citations":[{"cited_title":"AC flux sweet spots in parametrically-modulated superconducting qubits","cited_arxiv_id":"1807.01310","evidence_quote":"Supplies the AC sweet spot concept and the Fourier-harmonic analysis of the modulated qubit frequency, including the predicted benefit of filtering between the fundamental and second harmonic."},{"cited_title":"Meiboom and D","cited_arxiv_id":null,"evidence_quote":"Supplies the Carr-Purcell-Meiboom-Gill pulse sequence used to test whether the injected noise is broadband."},{"cited_title":"Bylander, S","cited_arxiv_id":null,"evidence_quote":"Supplies the CPMG filter-function formalism that relates measured dephasing times to the flux-noise spectrum."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the explicit CPMG filter function and the broadband-plus-1/f dephasing framework used in the numerical and analytical model."}],"review_version":1}