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REVIEW 3 major objections 6 minor 1 cited by

Assessing the Influence of Broadband Instrumentation Noise on Parametrically Modulated Superconducting Qubits

T0 review · 3 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Injected broadband flux noise dephases a flux-modulated transmon at a rate that grows linearly with the noise power spectral density.

desk verdict 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. read the letter →

arxiv 1908.11370 v1 pith:RYBV6HBO submitted 2019-08-29 quant-ph

E. Schuyler Fried , Prasahnt Sivarajah , Nicolas Didier , Eyob A. Sete , Marcus P. da Silva , Blake R. Johnson , Colm A. Ryan This is my paper · ORCID
classification quant-ph
keywords superconductingqubitstransmonfluxnoisedephasingACsweetspotparametrictwo-qubitgatesbroadbandCPMGspectroscopy
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

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.

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 (3)
  1. [Section IV, Eq. (6) and Fig. 6] 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.
  2. [Section III, Fig. 5 and Section IV] 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.
  3. [Section V, Fig. 7] 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.
minor comments (6)
  1. [Eq. (4) and Fig. 5 axes] 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.
  2. [Section II, Fig. 3] 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.
  3. [Fig. 7] 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.
  4. [Section IV, Table II] 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.
  5. [Throughout] 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'.
  6. [Fig. 1] 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.

Circularity Check

2 steps flagged · score 4.0 of 10

The T_phi-vs-noise and filtering measurements are genuine external experiments, but the headline -123 dBm/Hz noise-floor specification rests on a same-group self-citation chain plus a single transferred fitted alpha, not an independent prediction.

  1. self citation load bearing [Section IV, Eq. (5) and Table II validation]
    "To determine the instrument noise floor needed to achieve a desired two-qubit gate infidelity, we use the model for relating the coherence time to parametric entangling gate fidelity established in Ref. [1]. ... We find agreement to within 1% of the observed experimental infidelity, lending credence to the use of Eq. (5)."

    Ref. [1] is the same group's prior work (Didier, Sete, Combes, da Silva, arXiv:1807.01310), and the 'validation' is against Ref. [14] (Hong et al.), which also shares several authors with the present paper (Sivarajah, Didier, Sete, da Silva, Johnson). The gate-error relation that converts the fitted dephasing rate into the 1% noise-floor specification is therefore imported from, and benchmarked only against, the authors' own prior work; it is not an external mathematical or experimental anchor for the central quantitative claim.

  2. fitted input called prediction [Section IV, Eq. (6) and Fig. 6]
    "Using the parameters from Table II (assuming that T^{T,bg}_phi refers to the T^T_phi measured without injected noise) and alpha from the data fitted in Fig. 5, we plot the expected gate infidelity as a function of a given noise PSD in Fig. 6. From this data, we conclude that a noise floor of -123 dBm/Hz is sufficient for 1% CZ gate infidelity."

    The plotted E_CZ(S_inj) is Eq. (6), which is obtained by substituting the fitted linear relation 1/T^{ctrl}_phi = alpha S_inj (Eq. (4), with alpha fit to transmon 3 in Fig. 5) into Eq. (5). No CZ gate infidelity under injected broadband noise was measured on the Hong et al. device, and alpha is not recalibrated there. The 1% threshold therefore restates the single fitted alpha through an assumed gate-error formula; it is a parameter-transfer extrapolation presented as a quantitative prediction rather than a test of the model.

full rationale

The paper's core experimental content is self-contained and externally grounded: the injected PSD is measured with a spectrum analyzer, the dephasing times are measured independently, and the fit of Eqs. (3)-(4) to Fig. 5 is a legitimate calibration. The CPMG broadband check (Section II) and the low-pass filtering demonstration (Section V, Fig. 7) are empirical validations, not circular steps. The circularity burden is concentrated in Section IV: the gate-infidelity model Eq. (5) is imported from Ref. [1], whose authors overlap with this paper, and its only check is against Ref. [14], also largely the same team. The quantitative deliverable (Eq. (6), Fig. 6) then plugs the alpha fitted on transmon 3 into that self-cited formula for a different device pair without recalibration or a direct gate-error measurement under injected noise. That makes the -123 dBm/Hz number an extrapolation of the fit, not an independent result. The score of 4 reflects that the central spectroscopy and filtering claims remain independent; only the noise-floor specification is partially circular.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

No new entities are introduced. The central claims rest on standard dephasing and gate-error formulas from prior literature, one fitted linear coefficient alpha, and the assumption that injected broadband noise reaches the SQUID through the flux control line. The free-parameter count is small, but the single alpha carries the weight of the gate infidelity extrapolation.

free parameters (1)
  • alpha (α) = not stated numerically
    Single coefficient fit in Fig. 5 to Eq. (4) on transmon 3, converting injected broadband noise PSD into a control dephasing rate. It is reused unchanged in Eq. (6) for the CZ gate infidelity noise floor.
assumptions (5)
  • domain assumption Eq. (1) CPMG dephasing formula and Eq. (2) filter function correctly describe longitudinal flux noise dephasing.
    Used in Section II to interpret CPMG convergence as broadband noise; taken from Refs. [16] and [19] without proof.
  • domain assumption Background and control noise contributions add as independent rates (Eq. 3).
    Assumes no cross-correlation or nonlinear interference between static background flux noise and injected broadband noise; enters the fit in Fig. 5 and all downstream gate error estimates.
  • domain assumption Control dephasing rate is linear in injected noise PSD with a single coefficient alpha (Eq. 4).
    Assumes transduction from room-temperature PSD to SQUID flux noise is linear and frequency-independent over the relevant band; central to Eq. (6).
  • domain assumption Eq. (5) gives the coherence-limited CZ infidelity for nutation between |11> and |02>.
    Taken from prior theory (Refs. [1]/[20]); validated only indirectly against one measured gate in Hong et al. with agreement to within about 1%.
  • standard math Modulated qubit frequency is periodic and can be Fourier expanded (Eq. 7), with higher harmonic terms carrying nonzero flux sensitivity at the ACSS.
    Used in Section V to motivate filtering between first and second harmonics.

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Cite this review

Pith. "Pith review of Assessing the Influence of Broadband Instrumentation Noise on Parametrically Modulated Superconducting Qubits." pith.science (2026). https://pith.science/paper/RYBV6HBO

@misc{pith2026190811370,
  author       = {Pith},
  title        = {Pith review of: Assessing the Influence of Broadband Instrumentation Noise on Parametrically Modulated Superconducting Qubits},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RYBV6HBO}},
  note         = {Machine review of arXiv:1908.11370}
}
read the original abstract

With superconducting transmon qubits --- a promising platform for quantum information processing --- two-qubit gates can be performed using AC signals to modulate a tunable transmon's frequency via magnetic flux through its SQUID loop. However, frequency tunablity introduces an additional dephasing mechanism from magnetic fluctuations. In this work, we experimentally study the contribution of instrumentation noise to flux instability and the resulting error rate of parametrically activated two-qubit gates. Specifically, we measure the qubit coherence time under flux modulation while injecting broadband noise through the flux control channel. We model the noise's effect using a dephasing rate model that matches well to the measured rates, and use it to prescribe a noise floor required to achieve a desired two-qubit gate infidelity. Finally, we demonstrate that low-pass filtering the AC signal used to drive two-qubit gates between the first and second harmonic frequencies can reduce qubit sensitivity to flux noise at the AC sweet spot (ACSS), confirming an earlier theoretical prediction. The framework we present to determine instrumentation noise floors required for high entangling two-qubit gate fidelity should be extensible to other quantum information processing systems.

Figures

Figures reproduced from arXiv: 1908.11370 by the authors.

Figure 2
Figure 2. FIG. 2. We use a transmon and a CPMG pulse sequence of [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 1
Figure 1. FIG. 1. The noise PSD of the TEK as measured on a Ag [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Experimentally measured (points) and numerically [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Tunable transmon 3’s (ref. Table [PITH_FULL_IMAGE:figures/full_fig_p003_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. We can extrapolate the CZ infidelity as a function [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Dynamical Sweet and Sour Regions in Bichromatically Driven Floquet Qubits

    quant-ph 2025-05 accept novelty 6.0 of 10

    Bichromatic driving of a two-level qubit can create continuous 'doubly sweet spot' manifolds where sensitivity to both DC bias noise and AC drive-amplitude noise is simultaneously minimized.

Reference graph

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