Pith. sign in

REVIEW 3 major objections 6 minor 32 references

Approaching the Fundamental Limit of Single-Shot Qubit Frequency Tracking with an Adiabatic Tangentially-Modulated Pulse

T0 review · 3 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

Pith's one-line read A single ATM shot matches the sensitivity of a 100-shot Bayesian Ramsey estimate, and the pulse keeps that sensitivity under large amplitude errors.

desk verdict A genuinely new pulse shape with useful empirical design rules and solid numerics, but the 'fundamental limit' framing and 'derived' scaling outrun what is actually shown. read the letter →

arxiv 2608.06636 v1 pith:AAGA2DBS submitted 2026-08-06 quant-ph

classification quant-ph
keywords adiabaticpulsequbitfrequencytrackingdiscriminationRamseyinterferometryShinnar-LeRouxdetuningsensitivityamplitudenoiserobustnessquantumcontrol
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

The paper introduces the adiabatic tangentially-modulated (ATM) pulse, a single-shot qubit drive that converts the unknown detuning between drive and qubit into a sigmoidal, near-binary transition probability. Its central claim is that one ATM shot detects this detuning with the same sensitivity as a 100-shot Bayesian Ramsey estimate, while covering a monotonic frequency window and tolerating large amplitude errors. If true, this would let frequency feedback loops update at single-shot speed and track noise components up to two orders of magnitude higher in frequency than Ramsey-based tracking. The paper derives and verifies in simulation two design rules: sensitivity grows as $S\approx 0.9\sqrt{\dot{\Omega}(\tau_T)}$ with the fall gradient, and the detuning window grows linearly with the maximum chirped frequency.

What carries the argument

The central object is the ATM pulse: an amplitude envelope $\Omega(t)$ with tangent rise and fall segments plus a constant middle segment, and a driving frequency $\omega_D(t)$ that chirps linearly from $\omega_D^{\max}$ to zero during the middle segment. The detuning enters through the polar angle $\theta(t)=\arctan(\Omega(t)/\Delta)$ of the Hamiltonian on the Bloch sphere; the rise and chirp prepare the qubit in an instantaneous eigenstate whose latitude is detuning-dependent, and the tangent fall acts as an adiabatic-to-non-adiabatic switch that projects high-lying states upward and low-lying states downward. The paper locates the sensitivity edge by evaluating the standard adiabatic condition at the end of the pulse, giving the bound $\dot{\Omega}(\tau_T)/(2\Delta^2)\ll 1$, from which the scaling $S\approx 0.9\sqrt{\dot{\Omega}(\tau_T)}$ follows with an empirical constant.

What would settle it

Concretely: simulate or measure the ATM transition edge for a fixed fall time $\tau_f$ while sweeping the fall gradient $\dot{\Omega}(\tau_T)$, and check whether the edge width obeys $S\approx 0.9\sqrt{\dot{\Omega}(\tau_T)}$; a clear deviation breaks the central scaling claim. A second direct test is to compare one 30 µs ATM shot with a 100-shot Bayesian Ramsey estimate on the same qubit noise; if ATM sensitivity does not match or exceed it, the headline tracking claim is falsified.

Watch

Extended reading notes

Core claim

The paper claims that an adiabatic pulse built from a tangent-shaped amplitude rise, a constant amplitude plateau, and a tangent-shaped fall, combined with a piecewise-linear frequency chirp, maps every detuning in a designed window onto one of two well-separated outcome classes. The transition between classes is sharp, and its width is set by the final amplitude fall gradient while the window extent is set by the chirp range, so sensitivity and dynamic range become independent design parameters. The paper further claims that this single-shot binary readout, at 30 µs pulse length, matches the sensitivity of a 100-shot Bayesian Ramsey estimate and remains stable under quasistatic amplitude noise up to ±10 dB, whereas a comparable Shinnar–Le Roux binary pulse degrades severely. It concludes that the ATM pulse enables faster, lower-floor frequency tracking of qubit noise than conventional Ramsey feedback.

Load-bearing premise

The design rule rests on the standard adiabatic condition correctly marking where the transition edge sits; the paper itself notes that quantitative adiabatic conditions do not guarantee adiabaticity, so if another non-adiabatic mechanism sets the edge, the scaling relations would not be reliable.

Editorial extensions

If this is right

  • A single ATM shot can replace a 100-shot Bayesian Ramsey average, so frequency feedback can run at single-shot rate instead of after lengthy averaging.
  • At optimal gain the closed-loop white-noise floor is set by $S^2/(4f_s)$, allowing tracking of noise components up to roughly two orders of magnitude higher in frequency than Ramsey feedback.
  • Sensitivity and dynamic range are independently adjustable: choose the fall gradient for edge width and the maximum chirp frequency $\omega_D^{\max}$ for window extent.
  • The scaling $S_{\min}\approx 0.85/\tau_f$ gives a concrete design rule: longer fall time directly buys finer minimum sensitivity.
  • The same pulse retains its response under quasistatic amplitude fluctuations approaching $\pm10$ dB, unlike an SLR-derived binary response.

Reading between the lines

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

  • An extension the paper leaves implicit: because the response window is monotonic, ATM could be paired with a binary-search controller to turn each shot into one bit of a frequency estimate; the paper lists adaptive gain only as an outlook.
  • A testable extension is to check whether the empirical constant $0.9$ in $S\approx 0.9\sqrt{\dot{\Omega}(\tau_T)}$ remains fixed across chirp rates and amplitude envelopes or shifts with pulse shape; the paper demonstrates only one pulse family.
  • Since the construction is geometric in the Bloch-sphere picture, the same tangent-rise/linear-chirp/tangent-fall pulse might act as a frequency discriminator in any coherent two-level sensor, though the paper does not demonstrate that transfer.
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

3 major / 6 minor

Summary. The paper introduces an Adiabatic Tangentially-Modulated (ATM) pulse for single-shot qubit frequency tracking. The pulse maps qubit detuning onto a sigmoidal, near-binary transition probability via a tangent-shaped amplitude envelope and a piecewise-linear frequency chirp. The authors propose that the sensitivity of the response is governed by the final fall gradient of the amplitude, while the detuning range is set by the maximum chirp frequency. They present scaling relations, compare the pulse to Shinnar–Le Roux (SLR) binary pulses under amplitude noise, and benchmark its frequency-tracking performance against single-shot and Bayesian Ramsey feedback. The paper includes numerical simulations, a noise power spectral density analysis, and an appendix with explicit pulse parameters sufficient for reimplementation.

Significance. If the central scaling relations hold, the ATM pulse would provide a single-shot detuning discriminator with independently tunable sensitivity and range and strong robustness to amplitude calibration errors, which is a practically useful combination for qubit frequency tracking. The manuscript contains reproducible pulse parameters (Appendix E), detailed numerical simulations of the pulse response and noise performance, and a transparent comparison with SLR pulses. However, the main quantitative claim — that sensitivity scales as the square root of the fall gradient with a universal coefficient 0.9 — rests on an empirical fit rather than a derived result, and the adiabaticity analysis is incomplete. The paper would be significantly strengthened by an out-of-sample test or a derivation of the proportionality constant from a non-adiabatic transition model.

major comments (3)
  1. [Section IV.A, Eqs. (10)-(11)] The central design rule S ≈ 0.9√˙Ω(τ_T) is not derived: Eq. (10) explicitly states that C is an empirical proportionality constant, and Eq. (11) is a fit to the same simulations shown in Fig. 4(a) that are then used to claim agreement. This is not an independent confirmation, so the phrase 'derived scaling relations' in the Abstract and Conclusions overstates the result. The authors should either derive C from a microscopic non-adiabatic model (e.g., a Landau–Zener transition calculation during the fall segment) or explicitly present the relations as empirical design rules and support them with out-of-sample validation, for example by predicting S for a parameter set not used in the fit.
  2. [Section IV.A and Appendix B] The adiabatic condition analysis is incomplete. Equation (B12) evaluates the adiabatic parameter only at t = τ_T with ˙φ_D = 0, but during the chirp segment ˙φ_D = -ω_D^max/τ_c ≠ 0, and the full expression in Eq. (B11) contains ˙φ_D-dependent terms that are never checked. The sensitivity edge may therefore be set by non-adiabatic transitions during the chirp rather than by the fall gradient. The paper itself cites Tong et al. [24] for the fact that Eq. (8) does not guarantee adiabaticity, so identifying the edge with the breakdown of Eq. (9) is an assumption, not a derivation. The authors should verify adiabaticity across the full pulse and test whether the scaling S ≈ 0.9√˙Ω remains valid when the chirp rate is varied independently of the fall gradient.
  3. [Section VI, Fig. 6 and Abstract] The headline claim that a single ATM shot achieves sensitivity comparable to a 100-shot Bayesian Ramsey estimate is not a resource-fair comparison. The ATM pulse in Fig. 6(b) has a duration of 30 μs, whereas a 100-shot Bayesian Ramsey estimate requires at least 100 separate excitation-readout cycles; the text states that the time per cycle is dominated by readout, so the total measurement time differs by orders of magnitude. The authors should state explicitly whether the comparison is per-shot or per-unit-time, or restrict the claim to sensitivity per shot, otherwise the comparison is likely to mislead readers about the achievable tracking bandwidth.
minor comments (6)
  1. [Section III] The sentence 'The final tangential fall plays the an important role' contains a typo; it should read 'plays an important role'.
  2. [Section IV.A] The sentence 'These design parameters allow the ATM pulse to allow different experimental constraints' is grammatically awkward; consider rephrasing to 'These design parameters allow the ATM pulse to accommodate different experimental constraints'.
  3. [Section VI, Eqs. (16)-(17)] The variables G and f_s are used in Eqs. (16) and (17) but are not defined in the main text. The authors should define the feedback gain G and the sampling rate f_s before using them in the noise floor expressions.
  4. [Appendix D] The derivation of E[S_xx(f_k)] = S²/(4 f_s) is terse. In particular, the step 'every shot will perfectly bounce between 0 and S²/4' and the resulting expectation value E[x_n²] = S²/8 should be explained more explicitly, since the assumption of a 50% probability for ±S/2 is not stated before it is used.
  5. [Title and Abstract] The phrase 'Fundamental Limit' in the title is not supported by a derived bound. The paper presents scaling relations and empirical fits, not a fundamental limit. Consider rephrasing the title to avoid implying that a rigorous bound has been established.
  6. [Appendix E] The pulse parameters are listed clearly, but the relationship between β_r, β_f and the stated endpoint slopes ˙Ω(0), ˙Ω(τ_T) would be easier to verify if the equations linking these quantities were repeated here rather than only in the main text.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the sensitivity coefficient is explicitly empirical, the range law follows from the chirp construction, and the adiabaticity caveat is a robustness concern, not a circular reduction.

full rationale

Walking the derivation chain, I find no step in which a predicted quantity is equivalent by construction to an input or to a self-citation. The central scaling S ∝ sqrt(Omega_dot(tau_T)) is grounded in the standard adiabatic condition Eq. (8), evaluated in Appendix B at t = tau_T with phi_dot_D = 0 (Eqs. B11-B13), giving Eq. (9) Omega_dot(tau_T)/(2 Delta^2) << 1. The paper then explicitly introduces C as 'an empirical proportionality constant' (Eq. 10) and reports S ≈ 0.9 sqrt(Omega_dot(tau_T)) as the simulated relationship (Eq. 11); it does not claim to have predicted the coefficient from first principles. The 'agreement' is therefore an in-sample calibration of a free constant, not a fitted parameter renamed as a prediction. Equations (12)-(13) are also empirical fits used as design rules, with no pretense of derivation from the adiabatic theorem; the abstract's phrase 'derive scaling relations' overstates their status, but this is a presentation issue rather than circularity. The range relation Delta_range ≈ omega_D^max (Eq. 14) follows from the piecewise linear chirp in Eq. (6) sweeping the drive frequency from omega_D^max to zero, so it is definitional, not a fitted prediction. The paper's caveat that the quantitative adiabatic condition 'does not always guarantee the validity of the adiabatic approximation' (ref. [24], quoted in Section IV.A) is a genuine limitation of anchoring the sensitivity edge to Eq. (8), and it weakens the theoretical justification; however, it does not make the scaling relation equal to its inputs. No load-bearing self-citation exists: author-affiliated references appear in the experimental motivation (coherence, noise environment) and are not the source of the pulse construction or scaling relations. The ATM-vs-Ramsey and ATM-vs-SLR comparisons are external benchmark simulations with fixed, stated pulse parameters (Appendix E), so they do not reduce to the fitted design rules.

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

The central claims rest on empirical constants fitted to simulation, on a heuristic adiabaticity criterion, and on idealized two-level simulations. No new physical entities are introduced.

free parameters (3)
  • C (sensitivity proportionality constant) = 0.9 (Eq. 11)
    Defined in Eq. (10) as 'an empirical proportionality constant' and set to 0.9 to match the simulation curve.
  • S_min prefactor = 0.85 (Eq. 12)
    Empirical fit relating the minimum sensitivity to 1/tao_f.
  • dOmega(Smin) prefactor = 0.41 (Eq. 13)
    Empirical fit relating the fall gradient at the minimum sensitivity to 1/tao_f^2.
assumptions (5)
  • domain assumption Rotating-wave approximation (Appendix A)
    The lab-frame Hamiltonian is converted to Eq. (A4) by dropping counter-rotating terms, which is standard but an approximation.
  • ad hoc to paper The standard adiabatic condition, Eq. (8), locates the sensitivity edge
    Used to derive S proportional to sqrt(dOmega(taoT)); the paper itself notes in Section IV.A that quantitative conditions do not guarantee validity of the adiabatic approximation.
  • domain assumption Quasistatic uniform-in-dB amplitude noise model
    The Monte Carlo comparison with SLR assumes slow calibration drift dominates, with delta uniformly distributed over a dB window.
  • domain assumption Noiseless closed-loop controller assumptions in Appendix D
    The intrinsic tracker noise derivation assumes no Larmor noise, starting on resonance, gain S/2, and equal probability of +/-S/2 detuning; this yields E[Sxx] = S^2/(4fs).
  • domain assumption Ideal two-level evolution with no decoherence or readout noise in the main simulations
    All fidelity and tracking claims are for closed two-level evolution; experimental imperfections such as T1, T2, and readout errors are not included.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Approaching the Fundamental Limit of Single-Shot Qubit Frequency Tracking with an Adiabatic Tangentially-Modulated Pulse." pith.science (2026). https://pith.science/paper/AAGA2DBS

@misc{pith2026260806636,
  author       = {Pith},
  title        = {Pith review of: Approaching the Fundamental Limit of Single-Shot Qubit Frequency Tracking with an Adiabatic Tangentially-Modulated Pulse},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AAGA2DBS}},
  note         = {Machine review of arXiv:2608.06636}
}
read the original abstract

Understanding and mitigating noise in two level quantum systems is essential for achieving high fidelity qubit control. Conventional frequency tracking techniques, such as Ramsey interferometry, are fundamentally limited by trade offs between sensitivity, bandwidth, and dynamic range. Here we introduce the adiabatic tangentially-modulated (ATM) pulse, a pulse derived from quantum adiabatic theory that maps qubit detuning onto a sigmoidal, near-binary response. Using numerical simulations supported by analytical modelling, we show that pulse sensitivity and detuning range can be independently engineered through simple design parameters. We derive scaling relations governing these quantities and demonstrate their agreement with simulation. A single shot ATM measurement achieves sensitivity comparable to that obtained from multi-shot Ramsey averaging, enabling tracking of substantially higher frequency noise components with a lower closed-loop white-noise floor. In addition, this pulse exhibits strong robustness to amplitude fluctuations compared with binary response pulses derived from the Shinnar-Le Roux formalism. Together, these properties establish the ATM pulse as a promising approach for robust qubit frequency tracking.

Figures

Figures reproduced from arXiv: 2608.06636 by the authors.

Figure 1
Figure 1. Construction of the adiabatic tangentially [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. ATM pulse evolution resulting detuning dependent [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. (a) Simulated ATM fall pulse sensitivity [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figures from the paper (3 more)
Figure 5
Figure 5. Figure 5: Monte Carlo analysis of robustness to quasistatic [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 6
Figure 6. Figure 6: Comparison of Ramsey and ATM detuning sen [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 7
Figure 7. Figure 7: Noise power spectral density of simulated Larmor [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

32 extracted references · 25 canonical work pages

  1. [24]

    Comparat, General conditions for quantum adiabatic evolution, Phys

    D. Comparat, General conditions for quantum adiabatic evolution, Phys. Rev. A80, 012106 (2009)

  2. [1]

    High-gain regime Starting withG≥S/2we have found the closed-loop noise floor of ATM tracking rises smoothly according to Pfloor N = G2 fs .(16) Ontheotherhand, Ramseytracking, seeninFigure 7(a), aliases at low frequencies which is attributed to the pre- viously mentioned periodicity of the detuning response. At gains this large a random shift in the Larmo...

  3. [2]

    This results in the tracker being unable to keep pace with fast changes in detuning; this manifests as a low-pass filter whose cut- off scales with the gain

    Low-gain regime Now withG≤S/2we see that the closed-loop noise floor bottoms out dependent on the sensitivity only as: Pfloor N = S2 4fs .(17) In this situation the applied gainGis small relative to the sensitivitySmeaning the per shot correction is small compared to typical noise fluctuations. This results in the tracker being unable to keep pace with fa...

  4. [3]

    Takeda, J

    K. Takeda, J. Yoneda, T. Otsuka, T. Nakajima, M. R. Delbecq, G. Allison, Y. Hoshi, N. Usami, K. M. Itoh, S. Oda, T. Kodera, and S. Tarucha, Optimized elec- trical control of a si/sige spin qubit in the presence of an induced frequency shift, npj Quantum Information4, 10.1038/s41534-018-0105-z (2018). 11

  5. [4]

    Proctor, M

    T. Proctor, M. Revelle, E. Nielsen, K. Rudinger, D. Lob- ser, P. Maunz, R. Blume-Kohout, and K. Young, Detect- ing and tracking drift in quantum information processors, Nature Communications11, 10.1038/s41467-020-19074- 4 (2020)

  6. [5]

    K. W. Chan, W. Huang, C. H. Yang, J. C. C. Hwang, B. Hensen, T. Tanttu, F. E. Hudson, K. M. Itoh, A. Laucht, A. Morello, and A. S. Dzurak, Assessment of a silicon quantum dot spin qubit environment via noise spectroscopy, Phys. Rev. Appl.10, 044017 (2018)

  7. [6]

    M. M. E. K. Shehata, G. Simion, R. Li, F. A. Mo- hiyaddin, D. Wan, M. Mongillo, B. Govoreanu, I. Radu, K. De Greve, and P. Van Dorpe, Modeling semiconductor spin qubits and their charge noise environment for quan- tum gate fidelity estimation, Physical Review B108, 10.1103/physrevb.108.045305 (2023)

  8. [7]

    Capannelli, B

    K. Capannelli, B. Undseth, I. Fernández de Fuentes, E. Raymenants, F. K. Unseld, O. Pietx-Casas, S. G. J. Philips, M. T. Mądzik, S. V. Amitonov, L. Tryputen, G. Scappucci, and L. M. K. Vandersypen, Tracking spin qubit frequency variations over 912 days, npj Quantum Information11, 10.1038/s41534-025-01134-6 (2025)

Show all 32 references
  1. [8]

    Hensen, W

    B. Hensen, W. W. Huang, C. H. Yang, K. W. Chan, J. Yoneda, T. Tanttu, F. E. Hudson, A. Laucht, K. M. Itoh, T. D. Ladd, A. Morello, and A. S. Dzurak, A silicon quantum-dot-coupled nuclear spin qubit, Nature Nan- otechnology15, 13 (2020)

  2. [9]

    C. H. Yang, K. W. Chan, R. Harper, W. Huang, T. Evans, J. C. C. Hwang, B. Hensen, A. Laucht, T. Tanttu, F. E. Hudson, S. T. Flammia, K. M. Itoh, A. Morello, S. D. Bartlett, and A. S. Dzurak, Silicon qubit fidelities approaching incoherent noise limits via pulse engineering, Na...

  3. [10]

    M.D.Shulman, S.P.Harvey, J.M.Nichol, S.D.Bartlett, A. C. Doherty, V. Umansky, A. Yacoby, and J. R. Petta, Suppressing qubit dephasing using real-time hamiltonian estimation, Nature Communications5, 5156 (2014)

  4. [11]

    N. F. Ramsey, A molecular beam resonance method with separated oscillating fields, Phys. Rev.78, 695 (1950)

  5. [12]

    C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys.89, 035002 (2017)

  6. [13]

    Steinacker, N

    P. Steinacker, N. Dumoulin Stuyck, W. H. Lim, T. Tanttu, M. Feng, S. Serrano, A. Nickl, M. Candido, J. D. Cifuentes, E. Vahapoglu, S. K. Bartee, F. E. Hud- son, K. W. Chan, S. Kubicek, J. Jussot, Y. Canvel, S. Beyne, Y. Shimura, R. Loo, C. Godfrin, B. Raes, S. Baudot, D. Wan, ...

  7. [14]

    Vepsäläinen, R

    A. Vepsäläinen, R. Winik, A. H. Karamlou, J. Braumüller, A. D. Paolo, Y. Sung, B. Kannan, M. Kjaergaard, D. K. Kim, A. J. Melville, B. M. Niedzielski, J. L. Yoder, S. Gustavsson, and W. D. Oliver, Improving qubit coherence using closed-loop feedback, Nature Communications13, 1...

  8. [15]

    Nakajima, A

    T. Nakajima, A. Noiri, K. Kawasaki, J. Yoneda, P. Stano, S. Amaha, T. Otsuka, K. Takeda, M. R. Delbecq, G. Al- lison, A. Ludwig, A. D. Wieck, D. Loss, and S. Tarucha, Coherence of a Driven Electron Spin Qubit Actively De- coupled from Quasistatic Noise, Physical Review X10, 01...

  9. [16]

    Dumoulin Stuyck, A

    N. Dumoulin Stuyck, A. E. Seedhouse, S. Serrano, T. Tanttu, W. Gilbert, J. Y. Huang, F. Hudson, K. M. Itoh, A. Laucht, W. H. Lim, C. H. Yang, A. Saraiva, and A. S. Dzurak, Silicon spin qubit noise characterization using real-time feedback protocols and wavelet analysis, Applie...

  10. [17]

    M. O. Hecht, K. Saurav, E. Vlachos, D. A. Lidar, and E. M. Levenson-Falk, Beating the ramsey limit on sens- ing with deterministic qubit control, Nature Communi- cations16, 10.1038/s41467-025-58947-4 (2025)

  11. [18]

    J. S. Rojas-Arias, Y. Kojima, K. Takeda, P. Stano, T. Nakajima, J. Yoneda, A. Noiri, T. Kobayashi, D. Loss, and S. Tarucha, The origins of noise in the zeeman splitting of spin qubits in natural-silicon devices (2024), arXiv:2408.13707 [cond-mat.mes-hall]

  12. [19]

    Yoneda, K

    J. Yoneda, K. Takeda, T. Otsuka, T. Nakajima, M. R. Delbecq, G. Allison, T. Honda, T. Kodera, S. Oda, Y. Hoshi, N. Usami, K. M. Itoh, and S. Tarucha, A quantum-dot spin qubit with coherence limited by charge noise and fidelity higher than 99.9%, Nature Nanotech- nology13, 102 (2018)

  13. [20]

    Y. Dong, C. Feng, S.-C. Zhang, Y. Zheng, X.-D. Chen, G.-C. Guo, and F.-W. Sun, Breaking the measurement- sensitivity–maximum-range limit of quantum metrology using two sequences, Phys. Rev. Appl.19, 064022 (2023)

  14. [21]

    Shinnar, L

    M. Shinnar, L. Bolinger, and J. S. Leigh, The synthesis of soft pulses with a specified frequency response, Magnetic Resonance in Medicine12, 88 (1989)

  15. [22]

    W. A. Grissom, Z. Cao, and M. D. Does, |b1+|-selective excitation pulse design using the shinnar–le roux algo- rithm, Journal of Magnetic Resonance242, 189 (2014)

  16. [23]

    Kessler, S

    H. Kessler, S. Mronga, and G. Gemmecker, Multi- dimensionalnmrexperimentsusingselectivepulses,Mag- netic Resonance in Chemistry29, 527 (1991)

  17. [25]

    Messiah, Quantum mechanics

    A. Messiah, Quantum mechanics. (1961 - 1962)

  18. [26]

    D. M. Tong, K. Singh, L. C. Kwek, and C. H. Oh, Quan- titative conditions do not guarantee the validity of the adiabatic approximation, Phys. Rev. Lett.95, 110407 (2005)

  19. [27]

    Wei and M

    Z. Wei and M. Ying, Quantum adiabatic computa- tion and adiabatic conditions, Phys. Rev. A76, 024304 (2007)

  20. [28]

    Berritta, J

    F. Berritta, J. Benestad, L. Pahl, M. Mathews, J. A. Krzywda, R. Assouly, Y. Sung, D. K. Kim, B. M. Niedzielski, K. Serniak, M. E. Schwartz, J. L. Yoder, A. Chatterjee, J. A. Grover, J. Danon, W. D. Oliver, and F. Kümmeth, Efficient qubit calibration by binary- search hamilton...

  21. [29]

    F. K. Malinowski, F. Martins, Ł. Cywiński, M. S. Rud- ner, P. D. Nissen, S. Fallahi, G. C. Gardner, M. J. Man- fra, C. M. Marcus, and F. Kümmeth, Spectrum of the NuclearEnvironmentforGaAsSpinQubits,PhysicalRe- view Letters118, 177702 (2017)

  22. [30]

    A.Rower,Exploring Anisotropic Noise and Fast Gates with Superconducting Qubits, Phd thesis, Massachusetts Institute of Technology (2025)

    D. A.Rower,Exploring Anisotropic Noise and Fast Gates with Superconducting Qubits, Phd thesis, Massachusetts Institute of Technology (2025)

  23. [31]

    F. Yan, J. Bylander, S. Gustavsson, F. Yoshihara, K. Harrabi, D. G. Cory, T. P. Orlando, Y. Nakamura, J.- S. Tsai, and W. D. Oliver, Spectroscopy of low-frequency noise and its temperature dependence in a superconduct- ing qubit, Physical Review B85, 174521 (2012)

  24. [32]

    A. E. Seedhouse, N. D. Stuyck, S. Serrano, T. Tanttu, W. Gilbert, J. Y. Huang, F. E. Hudson, K. M. Itoh, 12 A. Laucht, W. H. Lim, C. H. Yang, A. S. Dzurak, and A. Saraiva, Wavelet correlation noise analysis for qubit operation variable time series, Scientific Reports 15, 11065...

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.