Pith. sign in

REVIEW 2 major objections 5 minor 7 cited by

Full characterization of measurement-induced transitions of a superconducting qubit

T0 review · 2 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read High-frequency transmon readout leakage is dominated by one-photon inelastic scattering, with a parameter-free rate formula matching experiment to about 25 percent.

desk verdict First clean identification of single-photon Raman leakage in high-frequency readout, with a parameter-free rate that matches to 25%—the impedance-model caveat is real but minor. read the letter →

arxiv 2506.05306 v1 pith:AOUBPRB4 submitted 2025-06-05 quant-ph cond-mat.mes-hall

Thomas Connolly , Pavel D. Kurilovich , Vladislav D. Kurilovich , Charlotte G. L. B{o}ttcher , Sumeru Hazra , Wei Dai , Andy Z. Ding , Vidul R. Joshi
show 7 more authors
Heekun Nho Spencer Diamond Daniel K. Weiss Valla Fatemi Luigi Frunzio Leonid I. Glazman Michel H. Devoret
This is my paper · ORCID
classification quant-phcond-mat.mes-hall PACS 85.25.-j03.67.Lx
keywords measurement-inducedtransitionstransmonqubitdispersivereadoutquantumnon-demolitioninelasticphotonscatteringACStarkshiftleakageimpedanceengineering
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 claims that the dominant mechanism by which strong high-frequency readout corrupts a transmon qubit is a Raman-like inelastic scattering: one readout photon gives a two-level excitation to the transmon and emerges as a lower-frequency photon. The authors derive a parameter-free rate formula for this process and verify it against measured transition rates across qubit frequencies and drive powers. They also map the other, resonant mechanisms—material defects, spurious modes, six-wave mixing, and multi-excitation resonances—so the full set of transitions that break quantum non-demolition readout is characterized. If correct, the work identifies a concrete design target: suppress dissipation at the scattered-photon frequency to reduce leakage, and it predicts a linear-in-power leakage cost for faster readout.

What carries the argument

The engine of the argument is the transmon's fourth-order Josephson nonlinearity, $-E_J \varphi^4/4!$, treated with Fermi's Golden Rule after diagonalizing the linearized transmon-plus-environment Hamiltonian into normal modes. The phase $\varphi$ is decomposed into a dressed qubit mode and dressed environment modes with coefficients $\mu_k$ linked to the impedance; the AC Stark shift $\delta\omega$ fixes the drive amplitude, and $\mathrm{Re}Z[\omega_{\rm out}]$ fixes the environment density of states at the scattered-photon frequency. This conversion turns a many-body scattering calculation into Eq. (1), a rate expressed entirely in measured quantities. The same machinery, extended to higher order, also yields the rates of two-photon and two-photon-emission processes and the resonant six-wave-mixing feature.

What would settle it

Measure the microwave field leaving the readout channel during a calibrated drive and look for a narrow spectral line at $\omega_{\rm out} = \omega_{\rm in} - \omega_{2,0}$ (or $\omega_{\rm in} - \omega_{3,1}$) whose power grows linearly with drive power at the rate predicted by Eq. (1). Absence of that line, or a proportionality coefficient that disagrees with an independently measured $\mathrm{Re}Z[\omega_{\rm out}]$, would falsify the inelastic-scattering picture. Alternatively, install a notch filter at $\omega_{\rm out}$ and observe whether $\Gamma_{0\to 2}$ and $\Gamma_{1\to 3}$ drop while other transitions remain unchanged.

Watch

Extended reading notes

Core claim

The central discovery is that in the regime $\omega_{\rm res} \gg \omega_q$, the dominant readout-induced transition is $|0\rangle \to |2\rangle$ (and $|1\rangle \to |3\rangle$) caused by inelastic scattering of a single drive photon through the transmon's four-wave-mixing nonlinearity. The rate is $\Gamma_{m\to m+2} = (m+1)(m+2)\,(\omega_q/\omega_{\rm out})\,(2\pi \mathrm{Re}Z[\omega_{\rm out}]/R_Q)\,\delta\omega$, where $\delta\omega$ is the measured AC Stark shift (a power proxy), $\omega_{\rm out} = \omega_{\rm in} - \omega_{m+2,m}$, and $\mathrm{Re}Z[\omega_{\rm out}]$ is the dissipative impedance of the transmon island at the scattered-photon frequency. The authors show that this formula agrees with measured rates without free parameters to within about 25%, explains why the earlier high-frequency readout could not be improved by raising power, and accounts for the observed linear power scaling. Additional resonant features are identified as material-defect resonances, a six-wave-mixing process involving a roughly 27 GHz spurious mode, and multi-excitation resonances such as $|1\rangle \to |8\rangle$.

Load-bearing premise

The predicted rate relies on the assumption that the circuit's dissipation at the scattered-photon frequency is captured by a lumped-element model of the transmon's electrical environment; the authors put the resulting uncertainty at about 25 percent, and if the true dissipation at that frequency differs, the coefficient in the formula would change even though the mechanism and its linear power dependence would survive.

Editorial extensions

If this is right

  • High-frequency readout power can no longer be increased indefinitely: the leakage rates $\Gamma_{0\to 2}$ and $\Gamma_{1\to 3}$ grow linearly with power, so QND fidelity has a power-dependent ceiling set by Eq. (1).
  • Engineering the readout channel to reduce $\mathrm{Re}Z$ at $\omega_{\rm out}$, for example by filtering the transmission line at that frequency, should suppress the dominant leakage without changing the readout tone.
  • In the simplified resonator-coupled form, $\Gamma_{m\to m+2} \propto \kappa\chi\,\delta\omega/\omega_q^2$, so boosting readout speed through larger resonator linewidth $\kappa$ or larger dispersive shift $\chi$ directly raises the inelastic-leakage rate; designs must balance speed against this cost.
  • The resonant mechanisms are individually identifiable: material-defect resonances appear when the Stark-shifted qubit frequency matches a defect, the roughly 27 GHz mode produces a power-cubed six-wave-mixing peak, and multi-excitation resonances appear when $\omega_{\rm in}$ matches a high-lying transition such as $|1\rangle \to |8\rangle$.
  • The characterization carries over to other strong off-resonant drives on transmons, including parametric gates and control of linear oscillators routed through the same readout channel.

Reading between the lines

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

  • Beyond the paper's readout setting, the same single-photon down-conversion should occur whenever a transmon is strongly driven off-resonantly and its environment has dissipation at $\omega_{\rm in} - 2\omega_q$; parametric gates and bosonic-control pulses may therefore carry a similar power-linear leakage floor.
  • A direct spectral test would detect the predicted lower-frequency photon: measuring the output field at $\omega_{\rm out}$ should show an additional tone whose power grows linearly with drive power and whose coefficient matches Eq. (1).
  • The residual roughly 25% discrepancy could plausibly be resolved by an independent measurement of $\mathrm{Re}Z[\omega_{\rm out}]$, such as reflection spectroscopy of the transmon island environment at that frequency, rather than relying on the lumped-element model.
  • Because the rate prefactor is $(m+1)(m+2)$, higher excited transmon states leak faster under the same drive; for multilevel or bosonic encodings, this predicts leakage accelerating as the quantum state uses higher levels.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. This paper reports an experimental and theoretical study of measurement-induced transitions in a high-frequency dispersively read transmon (ω_res ≫ ω_q). The central claim is that the dominant leakage mechanism at readout powers is an inelastic (Raman-like) scattering process in which one readout photon is converted into a transmon |m⟩→|m+2⟩ excitation plus a lower-frequency photon, with rate given by Eq. (1), Γ_{m→m+2} = (m+1)(m+2)(ω_q/ω_out)(2π ReZ[ω_out]/R_Q) δω. The authors measure Γ_{0→2} and Γ_{1→3} over a range of powers and qubit frequencies, report linear-in-power scaling and agreement with the 'parameter-free' prediction to about 25%, and identify additional resonant mechanisms: TLS-mediated relaxation/excitation, a six-wave process involving a ~27 GHz spurious mode, and multi-excitation resonances at high qubit frequencies. The paper argues that the inelastic process explains the power-dependent leakage that limited the high-frequency readout of Ref. [5] and proposes impedance engineering at ω_out as a mitigation.

Significance. The result is significant for circuit QED: it identifies a mechanism distinct from the previously studied multi-excitation resonances, gives a quantitative expression that can be used for design, and provides an extensive dataset over qubit frequency and power. The paper's strengths include two independent derivations of Eq. (1) (normal-mode decomposition in the supplement and a T-matrix calculation in Supplement VI) that agree in the transmon limit; the use of independently measured δω, κ, χ, and ω_q with no parameter fitted to the transition-rate data; and explicit falsifiable predictions such as linear-in-power scaling and the channel selection |0⟩→|2⟩, |1⟩→|3⟩. If the quantitative agreement survives a sharper test of the environment model, this will be a useful reference for readout and for other strong off-resonant drives.

major comments (2)
  1. [Section IV and Supplementary II.D] The claim that Eq. (1) is parameter-free and in good agreement with data rests on ReZ[ω_out] being computed from the lumped-element model of Fig. S3 rather than being measured. The authors themselves state in Section IV that the residual ~25% discrepancy is due to 'imperfect knowledge of Z[ω] away from the resonator frequency.' Because ω_out = ω_in − ω_{m+2,m} lies several GHz away from the resonator peak, and because the data in Figs. 2(e) and 3 are compared at fixed drive frequency, the absolute proportionality coefficient in Eq. (1) is not yet tested independently of the impedance model. I recommend adding a drive-frequency sweep at fixed qubit frequency and fixed AC Stark shift δω, so that Γ_{m→m+2} is mapped as a function of ω_out through the resonator Lorentzian; this would directly validate Eq. (S19) and separate model error from the inelastic-scattering mechanism.
  2. [Fig. 2(e) and Fig. 3] The central quantitative comparison is presented without error bars on Γ_{m→m+2}, and the agreement is characterized only as 'about 25%' in Section III. Without statistical uncertainties on the rates or an explicit error budget for the inputs δω, κ, χ, and ReZ[ω_out], the reader cannot judge whether the 25% discrepancy is significant or whether the claimed linear-in-power scaling is verified within noise. The authors should add error bars (or shaded uncertainty bands) to Figs. 2(e) and 3, and state the dominant systematic uncertainties in the rate extraction and in the Stark-shift calibration.
minor comments (5)
  1. [Section II] The sentence 'To probe the the unwanted transitions caused by the drive' contains a duplicated 'the' and should be corrected.
  2. [Section IV] The text 'Combined with the prefactor ∝ ωq in Eq. (2)' appears to refer to Eq. (1), since Eq. (2) as numbered in Section III is the matrix-element formula and does not contain the ω_q prefactor.
  3. [Eq. (1) and Section II] The symbol δω is introduced as the absolute value of the AC Stark shift, but the Stark shift itself is stated to be negative; please clarify the sign convention so that Eq. (1) is unambiguous.
  4. [Introduction] The phrase 'decapitate quantum error correction protocols' is unusual; 'compromise' or 'severely degrade' would be more standard English.
  5. [Section V and Supplementary IV] The spurious-mode frequencies ω_s/2π = 26.72 GHz and ω_s'/2π = 24.15 GHz are inferred from frequency-matching conditions rather than from independent spectroscopy; a direct measurement of these modes would strengthen the 'full characterization' claim.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: Eq. (1) is derived from first principles and compared against independently calibrated data, with no transition-rate data used to set parameters.

full rationale

The central claim, Eq. (1), is a parameter-free prediction derived via Fermi's Golden Rule from the transmon Hamiltonian with the Josephson nonlinearity treated as a perturbation (main text Section III, Eqs. (2)-(3); Supplementary Sections II.A-II.C). The final rate is expressed in terms of the independently calibrated AC Stark shift delta-omega and the computed dissipative impedance ReZ[omega_out]; no transition-rate measurement is used to fit any parameter. delta-omega is calibrated by separate qubit spectroscopy (Supplementary Section V.C), and ReZ[omega_out] is obtained from a lumped-element circuit model whose parameters (eta, E_C, kappa) are determined by independent spectroscopy and resonance measurements. The residual ~25% discrepancy is explicitly attributed by the authors to imperfect knowledge of Z[omega] away from the resonator frequency (Section IV); this is an assumption about the environment model, not a circular reduction. Self-citations to the authors' prior work [5] and [1] are used for context and for the standard dispersive-shift relation in a simplified auxiliary formula (Supplementary II.E), but the main result Eq. (1) does not depend on those citations. No fitted input is renamed as a prediction, no uniqueness theorem is imported from the authors' own work, and the identification of the dominant inelastic-scattering mechanism is validated by independent scaling checks. The central derivation chain is therefore self-contained; any remaining concern is a correctness/calibration caveat, not circularity.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central rate formula rests on standard circuit-QED ingredients (nonlinear transmon Hamiltonian, linear environment characterized by impedance, Fermi's Golden Rule) and uses independently measured calibrations. No parameter is fitted to the measured transition rates. The secondary mechanisms invoke inferred environmental modes and defects whose frequencies are matched to data. The paper introduces no new particles or forces.

free parameters (3)
  • Spurious mode frequency ω_s/2π for the six-wave process = 26.72 GHz
    Inferred from the resonance condition 3ω_in = ω_{3,1}[δω] + ω_s that fits the sharp feature in Γ_{1→3} (Fig. 4e); used to identify a higher-order process, not part of the central Raman formula.
  • Spurious mode frequency ω_s'/2π = 24.15 GHz
    Inferred from the resonance condition for the feature in Γ_{1→4+} (Fig. 4g) and Γ_{0→4+}; also non-central.
  • Lumped-element circuit parameters (C_q, C_c, C_res, L_res, L_tr, R) = not listed; calibrated from resonator and qubit spectroscopy
    Used to compute ReZ[ω_out] in Eq. (1). These are fitted to independent spectroscopic data, not to the measured transition rates, so the leakage prediction retains its parameter-free character. They introduce model dependence in the theory line.
assumptions (5)
  • standard math The transmon is described by the standard circuit-QED Hamiltonian H = 4E_C(N−n_g)^2 − E_J cos φ, and its non-linearity can be treated perturbatively via the −E_J φ^4/4! term.
    Invoked in Section III and Supplementary II; standard for transmon in the EJ/EC >> 1 regime.
  • standard math The environment (transmission line and readout resonator) is a linear bosonic bath characterized by an impedance Z[ω]; the Kubo formula relates ReZ[ω] to the mode coupling.
    Used in Supplementary II.C-D to connect the microscopic coupling to measurable impedance.
  • domain assumption The drive is a large-amplitude coherent state, so the photon number n_in is a c-number and the AC Stark shift δω = (ω_q/2)|μ_in|^2 n_in.
    Used in Supplementary II.C.1 to express the rate in terms of the measured Stark shift.
  • domain assumption The transition rates are extracted assuming exponential (Markovian) decay over the pulse duration, with state assignment thresholds that lump all states above |4>.
    Underlies the rate measurements in Section II and Supplementary IV/V; if the dynamics are non-exponential or the assignment biased, rates could be distorted.
  • ad hoc to paper Sharp resonant features in the rates are caused by two-level-system defects and by package modes with frequencies inferred from frequency-matching conditions.
    Sections V and Supplementary IV interpret the stripe/peak structure without direct spectroscopic detection of the defects or modes; the mode frequencies are chosen to match the features.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Full characterization of measurement-induced transitions of a superconducting qubit." pith.science (2026). https://pith.science/paper/AOUBPRB4

@misc{pith2026250605306,
  author       = {Pith},
  title        = {Pith review of: Full characterization of measurement-induced transitions of a superconducting qubit},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AOUBPRB4}},
  note         = {Machine review of arXiv:2506.05306}
}
read the original abstract

Repeated quantum non-demolition measurement is a cornerstone of quantum error correction protocols. In superconducting qubits, the speed of dispersive state readout can be enhanced by increasing the power of the readout tone. However, such an increase has been found to result in additional qubit state transitions that violate the desired quantum non-demolition character of the measurement. Recently, the readout of a transmon superconducting qubit was improved by using a tone with frequency much larger than the qubit frequency. Here, we experimentally identify the mechanisms of readout-induced transitions in this regime. In the dominant mechanism, the energy of an incoming readout photon is partially absorbed by the transmon and partially returned to the transmission line as a photon with lower frequency. Other mechanisms involve the excitation of unwanted package modes, decay via material defects, and, at higher qubit frequencies, the activation of undesired resonances in the transmon spectrum. Our work provides a comprehensive characterization of superconducting qubit state transitions caused by a strong drive.

Figures

Figures reproduced from arXiv: 2506.05306 by the authors.

Figure 1
Figure 1. Transmon state transitions caused by inelastic scat [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Transition rates of the transmon in the presence of the drive. The qubit is tuned to frequency [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Transition rates Γ0→2 and Γ1→3 as a function of qubit frequency controlled with flux bias. Both plots show rates measured at three different values of AC Stark shift δω. Grey dashed line indicates the working point of Ref. [5]. Solid lines show the prediction of the inelastic scattering theory, Eq. (1), where Z[ω] is computed within the lumped element model of the device. The deviations between the theory and experi… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Full characterization of undesired drive-induced transitions of a transmon qubit. (a-d) Transition rates from [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 7 Pith papers

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

  1. Collapse and Inversion of the Josephson Potential in a Strongly Driven Superconducting Circuit

    quant-ph 2026-07 conditional novelty 7.0 of 10

    The Josephson potential of a transmon collapses and inverts under a strong fast flux drive, dynamically stabilizing the qubit at φ=π, as shown by spectroscopy and readout.

  2. Readout-Induced Leakage in Superconducting Circuits with Nonlinear Couplings

    quant-ph 2026-06 conditional novelty 6.0 of 10

    Native nonlinear qubit-readout couplings alone neither eliminate nor reliably suppress readout-induced leakage; auxiliary modes reintroduce multiphoton channels whose rates vary by orders of magnitude over <7% frequen...

  3. Single-Step Phase-Engineered Pulse for Active Readout Cavity Reset in Superconducting Circuits

    quant-ph 2025-12 conditional novelty 6.0 of 10

    A single phase-engineered reset segment appended to a square readout pulse empties the circuit-QED cavity ~6× faster than free decay with no extra hardware and no extra backaction.

  4. The Pound-Drever-Hall Method for Superconducting-Qubit Readout

    quant-ph 2025-12 conditional novelty 6.0 of 10

    Three-tone Pound-Drever-Hall readout cancels microwave phase drift in a transmon and tolerates strong detuned sidebands, pointing to a 14 dB readout-gain path.

  5. Suppression of measurement-induced state transitions in cos{\phi}-coupling transmon readout

    quant-ph 2025-09 conditional novelty 6.0 of 10

    A cos-phi-coupled transmon readout is experimentally free of measurement-induced state transitions up to roughly 300 photons, with flux-controlled activation of specific transitions.

  6. High-power readout of a transmon qubit using a nonlinear coupling

    quant-ph 2025-07 conditional novelty 6.0 of 10

    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.

  7. Mitigation of Measurement-Induced State Transitions via a Fast-Load and Fast-Clear Readout

    quant-ph 2026-07 conditional novelty 5.0 of 10

    State-independent fast-load/fast-clear three-step pulses suppress ng-dependent measurement-induced state transitions in transmons and minimize ng-averaged readout and post-readout errors.

Reference graph

Works this paper leans on

83 extracted references · 61 canonical work pages · cited by 7 Pith papers

  1. [1]

    A. Y. Kitaev, Fault-tolerant quantum computation by anyons, Annals of Physics 303, 2 (2003)

    2003

  2. [2]

    Kitaev, Anyons in an exactly solved model and be- yond, Annals of Physics January Special Issue, 321, 2 (2006)

    A. Kitaev, Anyons in an exactly solved model and be- yond, Annals of Physics January Special Issue, 321, 2 (2006)

    2006

  3. [3]

    D. Sank, Z. Chen, and M. Khezri et al., Measurement- Induced State Transitions in a Superconducting Qubit: Beyond the Rotating Wave Approximation, Physical Re- view Letters 117, 190503 (2016)

    2016

  4. [4]

    Khezri and A

    M. Khezri and A. Opremcak et al., Measurement-induced state transitions in a superconducting qubit: Within the rotating-wave approximation, Physical Review Applied 20, 054008 (2023)

    work page 2023

  5. [6]

    Thorbeck, Z

    T. Thorbeck, Z. Xiao, A. Kamal, and L. C. Govia, Readout-Induced Suppression and Enhancement of Su- perconducting Qubit Lifetimes, Physical Review Letters 132, 090602 (2024)

    2024

  6. [7]

    M. F. Dumas, B. Groleau-Paré, A. McDonald, M. H. Muñoz-Arias, C. Lledó, B. D’Anjou, and A. Blais, Measurement-Induced Transmon Ionization, Physical Review X 14, 041023 (2024)

    work page 2024

  7. [8]

    N. Ofek, A. Petrenko, R. Heeres, P. Reinhold, Z. Leghtas, B. Vlastakis, Y. Liu, L. Frunzio, S. M. Girvin, L. Jiang, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, Ex- tending the lifetime of a quantum bit with error correc- tion in superconducting circuits, Nature 536, 441 (2016)

    2016

  8. [9]

    Google Quantum AI, Suppressing quantum errors by scaling a surface code logical qubit, Nature 614, 676 (2023)

    2023

Show all 83 references
  1. [10]

    V. V. Sivak, A. Eickbusch, B. Royer, S. Singh, I. Tsiout- sios, S. Ganjam, A. Miano, B. L. Brock, A. Z. Ding, L. Frunzio, S. M. Girvin, R. J. Schoelkopf, and M. H. De- voret, Real-time quantum error correction beyond break- even, Nature 616, 50 (2023)

    2023

  2. [11]

    Google Quantum AI, Quantum error correction below the surface code threshold (2024), arXiv:2408.13687 [quant- ph]

    2024 arXiv

  3. [12]

    A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Mar- quardt, and R. J. Schoelkopf, Introduction to quantum noise, measurement, and amplification, Reviews of Mod- ern Physics 82, 1155 (2010)

    2010

  4. [13]

    Blais, R.-S

    A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation, Physical Review A 69, 062320 (2004)

    2004

  5. [14]

    Wallraff, D

    A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, Strong coupling of a single photon to a super- conducting qubit using circuit quantum electrodynamics, Nature 431, 162 (2004)

    2004

  6. [15]

    Mallet, F

    F. Mallet, F. R. Ong, A. Palacios-Laloy, F. Nguyen, P. Bertet, D. Vion, and D. Esteve, Single-shot qubit read- out in circuit quantum electrodynamics, Nature Physics 5, 791 (2009)

    2009

  7. [16]

    M. D. Reed, L. DiCarlo, B. R. Johnson, L. Sun, D. I. Schuster, L. Frunzio, and R. J. Schoelkopf, High-Fidelity Readout in Circuit Quantum Electrodynamics Using the Jaynes-Cummings Nonlinearity, Physical Review Letters 105, 173601 (2010)

    2010

  8. [17]

    Jeffrey, D

    E. Jeffrey, D. Sank, J. Mutus, T. White, J. Kelly, R. Barends, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A. Megrant, P. O’Malley, C. Neill, P. Roushan, A. Vainsencher, J. Wenner, A. Cleland, and J. M. Marti- nis, Fast Accurate State Measurement with Supercon- ducting Qubits, P...

    2014

  9. [18]

    Walter, P

    T. Walter, P. Kurpiers, S. Gasparinetti, P. Mag- nard, A. Potočnik, Y. Salathé, M. Pechal, M. Mon- dal, M. Oppliger, C. Eichler, and A. Wallraff, Rapid High-Fidelity Single-Shot Dispersive Readout of Super- conducting Qubits, Physical Review Applied 7, 054020 (2017)

    2017

  10. [19]

    Dassonneville, T

    R. Dassonneville, T. Ramos, V. Milchakov, L. Planat, E. Dumur, F. Foroughi, J. Puertas, S. Leger, K. Bharad- waj, J. Delaforce, C. Naud, W. Hasch-Guichard, J. Garcia-Ripoll, N. Roch, and O. Buisson, Fast High- Fidelity Quantum Nondemolition Qubit Readout via a Nonperturbative ...

    2020

  11. [20]

    Swiadek, R

    F. Swiadek, R. Shillito, P. Magnard, A. Remm, C. Hellings, N. Lacroix, Q. Ficheux, D. C. Zanuz, G. J. Norris, A. Blais, S. Krinner, and A. Wallraff, Enhancing Dispersive Readout of Superconducting Qubits through Dynamic Control of the Dispersive Shift: Experiment and Theory, PR...

    2024

  12. [21]

    P. A. Spring, L. Milanovic, Y. Sunada, S. Wang, A. F. van Loo, S. Tamate, and Y. Nakamura, Fast multiplexed superconducting qubit readout with intrinsic Purcell fil- tering (2024), arXiv:2409.04967 [quant-ph]

    2024 arXiv

  13. [22]

    Gambetta, W

    J. Gambetta, W. A. Braff, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, Protocols for optimal readout of qubits using a continuous quantum nondemolition mea- surement, Physical Review A 76, 012325 (2007)

    2007

  14. [23]

    Zhang, B

    Y. Zhang, B. J. Lester, Y. Y. Gao, L. Jiang, R. J. Schoelkopf, and S. M. Girvin, Engineering bilinear mode coupling in circuit QED: Theory and experiment, Phys- ical Review A 99, 012314 (2019)

    2019

  15. [24]

    Petrescu, M

    A. Petrescu, M. Malekakhlagh, and H. E. Türeci, Life- time renormalization of driven weakly anharmonic su- perconducting qubits. II. The readout problem, Physical Review B 101, 134510 (2020)

    2020

  16. [25]

    Hanai, A

    R. Hanai, A. McDonald, and A. Clerk, Intrinsic mech- anisms for drive-dependent Purcell decay in supercon- ducting quantum circuits, Physical Review Research 3, 043228 (2021)

    2021

  17. [26]

    Bista, M

    A. Bista, M. Thibodeau, K. Nie, K. Chow, B. K. Clark, and A. Kou, Readout-induced leakage of the fluxonium qubit (2025), arXiv:2501.17807 [quant-ph]

    2025

  18. [27]

    Lescanne, L

    R. Lescanne, L. Verney, Q. Ficheux, M. H. Devoret, B. Huard, M. Mirrahimi, and Z. Leghtas, Escape of a Driven Quantum Josephson Circuit into Unconfined States, Physical Review Applied 11, 014030 (2019) , pub- lisher: American Physical Society

    2019

  19. [28]

    Hazra, W

    S. Hazra, W. Dai, T. Connolly, P. D. Kurilovich, Z. Wang, L. Frunzio, and M. H. Devoret, Benchmark- ing the readout of a superconducting qubit for repeated measurements (2024), arXiv:2407.10934

    2024 arXiv

  20. [29]

    Aliferis and B

    P. Aliferis and B. M. Terhal, Fault-tolerant quantum computation for local leakage faults, Quantum Info. Comput. 7, 139 (2007)

    2007

  21. [30]

    A. G. Fowler, Coping with qubit leakage in topological codes, Physical Review A 88, 042308 (2013)

    2013

  22. [31]

    Ghosh, A

    J. Ghosh, A. G. Fowler, J. M. Martinis, and M. R. Geller, Understanding the effects of leakage in superconducting quantum-error-detection circuits, Physical Review A 88, 062329 (2013)

    2013

  23. [32]

    Suchara, A

    M. Suchara, A. W. Cross, and J. M. Gambetta, Leakage suppression in the Toric code, Quantum Info. Comput. 15, 997 (2015)

    2015

  24. [33]

    Magnard, P

    P. Magnard, P. Kurpiers, B. Royer, T. Walter, J.-C. Besse, S. Gasparinetti, M. Pechal, J. Heinsoo, S. Storz, A. Blais, and A. Wallraff, Fast and Unconditional All- Microwave Reset of a Superconducting Qubit, Physical Review Letters 121, 060502 (2018)

    2018

  25. [34]

    C. C. Bultink, T. E. O’Brien, R. Vollmer, N. Muthusub- ramanian, M. W. Beekman, M. A. Rol, X. Fu, B. Tarasin- ski, V. Ostroukh, B. Varbanov, A. Bruno, and L. Di- Carlo, Protecting quantum entanglement from leakage and qubit errors via repetitive parity measurements, Sci- ence ...

    2020

  26. [35]

    B. M. Varbanov, F. Battistel, B. M. Tarasinski, V. P. Ostroukh, T. E. O’Brien, L. DiCarlo, and B. M. Terhal, Leakage detection for a transmon-based surface code, npj Quantum Information 6, 1 (2020)

    2020

  27. [36]

    McEwen et al., Removing leakage-induced correlated errors in superconducting quantum error correction, Na- ture Communications 12, 1761 (2021)

    M. McEwen et al., Removing leakage-induced correlated errors in superconducting quantum error correction, Na- ture Communications 12, 1761 (2021)

    2021

  28. [37]

    K. C. Miao and M. McEwen et al., Overcoming leakage in quantum error correction, Nature Physics 19, 1780 (2023)

    2023

  29. [38]

    Shillito, A

    R. Shillito, A. Petrescu, J. Cohen, J. Beall, M. Hauru, M. Ganahl, A. G. Lewis, G. Vidal, and A. Blais, Dynam- ics of Transmon Ionization, Physical Review Applied 18, 034031 (2022)

    2022

  30. [39]

    X. Xiao, J. Venkatraman, R. G. Cortiñas, S. Chowdhury, and M. H. Devoret, A diagrammatic method to compute the effective Hamiltonian of driven nonlinear oscillators (2023), arXiv:2304.13656

    2023 arXiv

  31. [40]

    Cohen, A

    J. Cohen, A. Petrescu, R. Shillito, and A. Blais, Remi- niscence of Classical Chaos in Driven Transmons, PRX Quantum 4, 020312 (2023)

    2023

  32. [41]

    K. N. Nesterov and I. V. Pechenezhskiy, Measurement- induced state transitions in dispersive qubit-readout schemes, Physical Review Applied 22, 064038 (2024)

    2024

  33. [42]

    Y. Y. Gao, B. J. Lester, Y. Zhang, C. Wang, S. Rosen- blum, L. Frunzio, L. Jiang, S. Girvin, and R. J. Schoelkopf, Programmable Interference between Two Microwave Quantum Memories, Physical Review X 8, 021073 (2018) , publisher: American Physical Society

    2018

  34. [43]

    B. J. Chapman, S. J. de Graaf, S. H. Xue, Y. Zhang, J. Teoh, J. C. Curtis, T. Tsunoda, A. Eickbusch, A. P. Read, A. Koottandavida, S. O. Mundhada, L. Frunzio, M. Devoret, S. Girvin, and R. Schoelkopf, High-On-Off- Ratio Beam-Splitter Interaction for Gates on Bosonically Encoded...

    2023

  35. [44]

    Y. Lu, A. Maiti, J. W. O. Garmon, S. Ganjam, Y. Zhang, J. Claes, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, High-fidelity parametric beamsplitting with a parity- protected converter, Nature Communications 14, 5767 (2023)

    2023

  36. [45]

    Eickbusch, V

    A. Eickbusch, V. Sivak, A. Z. Ding, S. S. Elder, S. R. Jha, J. Venkatraman, B. Royer, S. M. Girvin, R. J. Schoelkopf, and M. H. Devoret, Fast universal control of an oscillator with weak dispersive coupling to a qubit, Nature Physics 18, 1464 (2022)

    2022

  37. [46]

    See supplementary materials

  38. [47]

    S. E. Nigg, H. Paik, B. Vlastakis, G. Kirchmair, S. Shankar, L. Frunzio, M. H. Devoret, R. J. Schoelkopf, and S. M. Girvin, Black-Box Superconducting Cir- cuit Quantization, Physical Review Letters 108, 240502 (2012)

    2012

  39. [48]

    Singh, G

    S. Singh, G. Refael, A. Clerk, and E. Rosenfeld, Impact of Josephson junction array modes on fluxonium readout (2025), arXiv:2412.14788 [cond-mat]

    2025

  40. [49]

    Kishmar, P

    M. Kishmar, P. D. Kurilovich, A. Klots, T. Connolly, I. L. Aleiner, and V. D. Kurilovich, Quasiparticle-induced decoherence of a driven superconducting qubit (2025), arXiv:2505.00769 [quant-ph]

    2025 arXiv

  41. [50]

    Chowdhury, M

    S. Chowdhury, M. Hays, S. R. Jha, K. Serniak, T. P. Or- lando, J. A. Grover, and W. D. Oliver, Theory of Quasi- particle Generation by Microwave Drives in Supercon- ducting Qubits (2025), arXiv:2505.00773 [quant-ph]

    2025

  42. [51]

    Féchant, M

    M. Féchant, M. F. Dumas, D. Bénâtre, N. Gosling, P. Lenhard, M. Spiecker, W. Wernsdorfer, B. D’Anjou, A. Blais, and I. M. Pop, Offset Charge Dependence of Measurement-Induced Transitions in Transmons (2025), arXiv:2505.00674 [quant-ph]

    2025

  43. [52]

    Full characterization of measurement-i nduced transitions of a superconducting qubit

    Z. Wang, B. D’Anjou, P. Gigon, A. Blais, and M. S. Blok, Probing excited-state dynamics of transmon ionization (2025), arXiv:2505.00639 [quant-ph]. Supplementary information for “Full characterization of measurement-i nduced transitions of a superconducting qubit” Thomas Conno...

    2025 arXiv

  44. [53]

    Relation between the parameters of the drive and the transmon AC Stark shift 6

  45. [54]

    Calculation of the impedance Z[ω] for our device 7 E

    Relation between the parameters of the environment and the impedanc e of the transmon island 7 D. Calculation of the impedance Z[ω] for our device 7 E. Simplified expression for inelastic scattering rate in the case of a high-frequency readout 8 III. Rates of other lowest-order...

  46. [55]

    Simplified expression for the rate of the two-photon process in the case of high-frequency readout 10

  47. [56]

    Inelastic scattering process with two photons leaving into th e environment 10

    Two-photon process in the presence of spurious modes in the devic e 10 B. Inelastic scattering process with two photons leaving into th e environment 10

  48. [57]

    Drive-induced |m⟩ → | m + 1⟩ process with two photons leaving into the environment 11

  49. [58]

    Additional data 12 A

    Drive-induced |m⟩ → | m − 1⟩ process with two photons leaving into the environment 11 IV. Additional data 12 A. Rates of transmon state transitions for qubit initialized in |0⟩ 12 B. Multi-excitation resonances in the transmon spectrum activated b y the drive 13

  50. [59]

    Evidence that feature in Γ 1→4+ stems from |1⟩ → | 8⟩ multi-excitation resonance 14

  51. [60]

    Details of the calibration procedure 15 A

    Splitting of the strongest feature in Γ 1→4+ explained by readout resonator sidebands 15 V. Details of the calibration procedure 15 A. Measurement of qubit and readout resonator frequencies as functions of phase bias 16 B. State assignment at different values of the flux bias 17...

  52. [61]

    Measurement of Rabi amplitude 19

  53. [62]

    Measurement of the qubit lifetime 19 ∗ These two authors contributed equally. tom.connolly@yale.edu, pavel.kurilovich@yale.edu † Present address: Google Quantum AI, 301 Mentor Dr, Goleta, C A93111, USA ‡ Present address: Department of Applied Physics, Stanford U niversity, Sta...

  54. [63]

    extra drive

    Evaluation of the rate in the case of a weak anharmonicity 20 References 21 3 I. EXPERIMENT AL SETUP A. Wiring diagram x2 50Ω -20dB -10dB deviceSPA DAC ADC semiconducting amplifier -20dB SPA SNAIL parametric amplifier high-pass filter low-pass filter band-pass filter infrared ...

  55. [64]

    The term in the Hamiltonian describing the lowest order cor rection to the spectrum due to the nonlinearity is given by H non−lin = −EJ φ4/4!

    Relation between the parameters of the drive and the trans mon AC Stark shift To evaluate the AC Stark shift δω of the |0⟩ → | 1⟩ transition of our transmon, we treat its non-linearity perturba- tively. The term in the Hamiltonian describing the lowest order cor rection to the...

  56. [65]

    two-photon

    Relation between the parameters of the environment and th e impedance of the transmon island Next, we relate parameters νout and µout in Eq. ( S8) to the real part of the impedance of the transmon island. The impedance is measured with respect to ground, see Figure 1 of the ma...

  57. [66]

    First, we focus on the case of a high-frequency readout, ωres ≫ ωq

    Simplified expression for the rate of the two-photon proce ss in the case of high-frequency readout Here, we derive a simplified expression for the rate of the discusse d two-photon process under a set of assumptions. First, we focus on the case of a high-frequency readout, ωres...

  58. [67]

    ( S26) couples the transmon to its electromagnetic environment at frequen cy ωout = 2ωin + ωq

    Two-photon process in the presence of spurious modes in th e device The process captured by Eq. ( S26) couples the transmon to its electromagnetic environment at frequen cy ωout = 2ωin + ωq. In case of dispersive readout, ωin = ωres, frequency scale ωout significantly exceeds b...

  59. [68]

    The matrix element for this process is given by |Mf i| = |⟨Ψf |EJ φ4/4!|Ψi⟩|, |Ψi⟩ ∝ (a† in)nin |m⟩|Ω⟩, |Ψf ⟩ ∝ (a† in)nin−1a† out1 a† out2 |m + 1⟩|Ω⟩

    Drive-induced |m⟩ → | m + 1⟩ process with two photons leaving into the environment We set out by considering the excitation process where the transmon transitions from |m⟩ to |m + 1⟩. The matrix element for this process is given by |Mf i| = |⟨Ψf |EJ φ4/4!|Ψi⟩|, |Ψi⟩ ∝ (a† in)n...

  60. [69]

    Similarly to Eq

    Drive-induced |m⟩ → | m − 1⟩ process with two photons leaving into the environment Now we consider a similar process where the transmon transitions |m⟩ → | m − 1⟩ and two photons are emitted into the environment. Similarly to Eq. ( S34), we obtain Γm→m−1 = m64π EJ ℏ δω ∫ ωin+ω...

  61. [70]

    phase-rolls

    Evidence that feature in Γ1→4+ stems from |1⟩ → | 8⟩ multi-excitation resonance The measurement presented in Figure 4(d) of the main text is incapabl e of resolving the final state to which the transmon gets excited to after the drive pulse. This measurement i s performed at a ...

  62. [71]

    phase-roll

    Splitting of the strongest feature in Γ1→4+ explained by readout resonator sidebands As explained above, the feature in Γ 1→4+ around ωq/2π = 1500 MHz stems from the resonance between the drive and the |1⟩ to |8⟩ transition of the transmon. It occurs when the frequency matchin...

  63. [72]

    We deliver this pulse through the readout channel

    Measurement of Rabi amplitude Figure S12(a) shows measured DAC amplitude required to drive the π/2 pulse at different frequencies of our qubit. We deliver this pulse through the readout channel. The measurement shows that our transmission line is poorly matched at the frequency...

  64. [73]

    The relaxation time defined as the inverse rate of transitions from state |1⟩ to state |0⟩ measured in the absence of the drive

    Measurement of the qubit lifetime Figure S12(b) shows how the qubit relaxation time depends on the qubit freq uency. The relaxation time defined as the inverse rate of transitions from state |1⟩ to state |0⟩ measured in the absence of the drive. As is clear from the figure, the ...

  65. [74]

    ( S38) proceeds, we focus on the case of weak anharmonicity

    Evaluation of the rate in the case of a weak anharmonicity To give an example of how the calculation via Eq. ( S38) proceeds, we focus on the case of weak anharmonicity. We show that this approach gives a result consistent with that obtained th rough normal mode decomposition ...

  66. [75]

    P. D. Kurilovich, T. Connolly, C. G. L. Bøttcher, D. K. Weiss, S . Hazra, V. R. Joshi, A. Z. Ding, H. Nho, S. Diamond, V. D. Kurilovich, W. Dai, V. Fatemi, L. Frunzio, L. I. Glazman, and M. H. Devoret, High-frequency readout free from transmon multi-excitation resonances (2025...

    2025 arXiv

  67. [76]

    Lecocq, I

    F. Lecocq, I. M. Pop, Z. Peng, I. Matei, T. Crozes, T. Fournie r, C. Naud, W. Guichard, and O. Buisson, Junction fabrication by shadow evaporation without a suspended bridge, Nanotechnology 22, 315302 (2011)

    2011

  68. [77]

    A. P. M. Place, L. V. H. Rodgers, P. Mundada, B. M. Smitham, M . Fitzpatrick, Z. Leng, A. Premkumar, J. Bryon, A. Vrajitoarea, S. Sussman, G. Cheng, T. Madhavan, H. K. Babla, X . H. Le, Y. Gang, B. J¨ ack, A. Gyenis, N. Yao, R. J. Cava, N. P. de Leon, and A. A. Houck, New mate...

    2021

  69. [78]

    Ganjam, Y

    S. Ganjam, Y. Wang, Y. Lu, A. Banerjee, C. U. Lei, L. Krayzman, K . Kisslinger, C. Zhou, R. Li, Y. Jia, M. Liu, L. Frunzio, and R. J. Schoelkopf, Surpassing millisecond cohere nce in on chip superconducting quantum memories by optimizing materials and circuit design, Nature Co...

    2024

  70. [79]

    Serniak, S

    K. Serniak, S. Diamond, M. Hays, V. Fatemi, S. Shankar, L. Frun zio, R. Schoelkopf, and M. Devoret, Direct dispersive monitoring of charge parity in offset-charge-sensitive transmon s, Physical Review Applied 12, 014052 (2019)

    2019

  71. [80]

    Connolly, P

    T. Connolly, P. D. Kurilovich, S. Diamond, H. Nho, C. G. Bøttc her, L. I. Glazman, V. Fatemi, and M. H. Devoret, Coexistence of Nonequilibrium Density and Equilibrium Energy D istribution of Quasiparticles in a Superconducting Qubit, Physical Review Letters 132, 217001 (2024)

    2024

  72. [81]

    Rehammar and S

    R. Rehammar and S. Gasparinetti, Low-Pass Filter With Ult rawide Stopband for Quantum Computing Applications, IEEE Transactions on Microwave Theory and Techniques 71, 3075 (2023)

    2023

  73. [82]

    S. E. Nigg, H. Paik, B. Vlastakis, G. Kirchmair, S. Shankar, L . Frunzio, M. H. Devoret, R. J. Schoelkopf, and S. M. Girvin, Black-Box Superconducting Circuit Quantization, Physical Review Letters 108, 240502 (2012)

    2012

  74. [83]

    J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Charge-insensitive qubit design derived from the Co oper pair box, Physical Review A 76, 042319 (2007)

    2007

  75. [84]

    Willsch, D

    D. Willsch, D. Rieger, P. Winkel, M. Willsch, C. Dickel, J. Kra use, Y. Ando, R. Lescanne, Z. Leghtas, N. T. Bronn, P. Deb, O. Lanes, Z. K. Minev, B. Dennig, S. Geisert, S. G¨ unzler, S . Ihssen, P. Paluch, T. Reisinger, R. Hanna, J. H. Bae, P. Sch¨ uffelgen, D. Gr¨ utzmacher, ...

    2024

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.