Pith. sign in

REVIEW 3 major objections 4 minor 49 references

A third quantum dot lets a spin qubit be fast and coherent at the same time.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

In a GaAs triple quantum dot, tuning the third dot's orbital level plus neural-network frequency feedback yields a 99.7% pi/2-gate fidelity in 4 ns (randomized benchmarking).

T0 review reviewed 2026-08-05 challenge →

load-bearing objection A useful triple-dot tuning architecture and a plausible feedback scheme, but the headline 99.7% gate fidelity rests on an RB fit that never reaches saturation and on an inferred T2*, so the number should be read as provisional. the 3 major comments →

arxiv 2508.21723 v1 pith:NYGRPZJC submitted 2025-08-29 cond-mat.mes-hall quant-ph

High fidelity flopping-mode single spin operation with tuning inter-dot orbital levels

Yuta Matsumoto , Xiao-Fei Liu , Arne Ludwig , Andreas D. Wieck , Keisuke Koike , Takefumi Miyoshi , Takafumi Fujita , Akira Oiwa This is my paper
classification cond-mat.mes-hall quant-ph
keywords spin qubitflopping-mode EDSRtriple quantum dotGaAsrandomized benchmarkingmachine learning feedbackcoherence timeRabi frequency
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

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 speed-coherence trade-off that usually limits spin qubits can be broken by adding a third quantum dot to the standard double-dot flopping-mode design. The extra dot gives a tunable knob on the inter-dot orbital energy levels, so the Rabi frequency and the coherence time can be made maximal at the same operating point rather than at different ones. The authors combine this device-level tuning with a machine-learning feedback loop that estimates and corrects the qubit's fluctuating frequency from past single-shot measurements, and they report a pi/2 gate fidelity of 99.72% at a 4.05 ns gate time, measured by randomized benchmarking in a GaAs device. If right, this means high-fidelity fast spin control need not rely on strong spin-orbit materials or precisely positioned micromagnets, and can instead be tuned electrically in each qubit.

Core claim

The central claim is that extending flopping-mode electric dipole spin resonance from a double quantum dot to a triple quantum dot provides a new electrical tuning parameter—the energy of the third dot's orbitals—that allows Rabi frequency and coherence time to be optimized simultaneously. At the sweet spot, with tunnel couplings and micro-magnet gradients chosen so that the sweet spot is broad compared to the charge noise, the paper reports Rabi frequencies above 100 MHz (up to about 271 MHz when orbital levels are brought closer) while maintaining a T2* of about 580 ns under feedback. A feedforward neural network trained on simulated Ramsey data processes 62 single-shot outcomes from past

What carries the argument

The central object is the triple-quantum-dot Hamiltonian with charge and spin terms, where the electron spin is hybridized with orbital states via transverse micro-magnet gradients near anti-crossings. The third dot acts as a tunable lever on the inter-dot orbital energy spacing of the center double dot, reshaping the hybridization gap and creating a sweet spot where the Rabi frequency and coherence are both large. The feedback arm is a feedforward neural network (two hidden layers, 300 neurons each, sigmoid activations) that maps past Ramsey single-shot outcomes to an estimated qubit-frequency shift, trained on simulated data generated with a measured noise power spectral density.

Load-bearing premise

The feedback network's training data and the reported coherence time both rely on an assumed noise model taken from earlier measurements, plus the assumption that frequency fluctuations are Gaussian and quasi-static; if either does not hold in this device, the claimed coherence extension is overstated.

What would settle it

Measure the free-induction decay directly under the same feedback protocol (fit Ramsey fringes with a Gaussian envelope rather than inferring T2* from frequency-fluctuation statistics): if the fitted T2* comes out well below 580 ns, or if the trained FNN performs no better than a Bayesian estimator with the same number of single-shot measurements on the real device, the central claims fail.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • A pi/2 gate fidelity of 99.72% at 4.05 ns in GaAs shows that fast, high-fidelity single-qubit control is achievable even in a material whose coherence is normally limited by nuclear spins.
  • The third-dot tuning parameter is electrical and per-device, so the same control strategy can be applied to each qubit in an array without depending on material-specific spin-orbit strength or precise micromagnet positioning.
  • The FNN feedback protocol reduces measurement overhead compared with Bayesian estimation, making noise characterization practical for multi-qubit devices where correlated noise matters.
  • The combined device-plus-feedback recipe is transferable to Si and Ge quantum-dot platforms, where the same flopping-mode orbital effects exist.
  • The match between the measured fidelity improvement and the quasi-static frequency-noise estimate identifies residual high-frequency charge noise as the next target for suppression.
  • The error-budget analysis implies that shortening the feedback loop's 3.36 ms total delay would directly cut the remaining gate infidelity.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the reported T2* value, derived from frequency-fluctuation statistics, is validated by direct Ramsey decay fitting, the method offers a fast coherence proxy that avoids long averaging and could be used to screen many qubits quickly.
  • The observed noise-spectrum crossover from 1/f to 1/f^2 suggests charge noise dominates above about 2 Hz and nuclear spin noise below; a similar FNN analysis on pairs of qubits could map correlated low-frequency noise across an array.
  • The residual infidelity is attributed to frequency noise faster than the feedback delay; reducing the estimation and NCO-update latency could push the fidelity beyond 99.72%.
  • The same orbital-level-tuning idea could generalize to two-qubit gates in triple-dot arrays, where the third dot tunes the hybridization of both qubits.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The manuscript reports a GaAs triple-quantum-dot (TQD) flopping-mode electron dipole spin resonance (EDSR) qubit. The authors argue that the third dot provides an additional tunable parameter—the inter-dot orbital energy level—that allows simultaneous optimization of Rabi frequency and coherence time. They report Rabi frequencies exceeding 100 MHz (up to ~271 MHz), a noise PSD showing 1/f charge noise above 2 Hz and 1/f^2 nuclear noise below, and an FNN-based feedback scheme that they claim outperforms Bayesian estimation and extends T2* from 52 ns to 580 ns. Using randomized benchmarking with a pi/2-only Clifford composition and piecewise-constant (PWC) pulse optimization, they report a pi/2 gate fidelity of 99.72% at a gate time of 4.05 ns, which they quote as 99.7% in the abstract.

Significance. If the central claims hold, the TQD flopping-mode architecture would be a significant step toward scalable, electrically tunable spin qubits that do not rely on strong intrinsic spin-orbit interaction or precise micromagnet placement. The FNN feedback protocol also addresses a practical measurement-overhead problem in multi-qubit arrays. The paper's strengths include direct EDSR spectroscopy and Rabi measurements, noise PSD characterization, real-time feedback implementation on FPGA/GPU, PWC pulse optimization, and randomized benchmarking data. However, the headline numbers rest on two load-bearing assumptions: (i) the randomized-benchmarking decay is fit without an observed saturation baseline, and (ii) the FNN is trained on simulated noise whose PSD is taken from a prior device. Both need to be validated experimentally before the quantitative conclusions can be accepted.

major comments (3)
  1. [II.C, Fig. 4(d), Supplemental D] The headline pi/2 gate fidelity of 99.72% is extracted from a randomized-benchmarking decay that is not observed to saturate at the high-fidelity operating point. The authors disclose in Supplemental D that 'observing complete decay saturation was challenging' and that zero-saturation behavior was verified only under 'relatively low-fidelity conditions' (Fig. S5(a)). For p_c ≈ 0.997, the fit F(m)=A+B·p_c^m is strongly degenerate with the baseline B, so a small error in the unsataturated baseline produces a large relative error in 1−p_c. Moreover, the difference between feedback-only (99.56±0.03%) and feedback+PWC (99.72±0.18%) is 0.16±0.18 percentage points, i.e., not statistically significant. The abstract's '99.7%' is therefore not separately established over the feedback-only value. The authors should provide a saturated RB curve at the reported operating point, or an analysis that ex
  2. [II.B, Supplemental C] The FNN is trained exclusively on simulated Ramsey data whose noise fluctuations are generated using a power spectral density taken from prior work (Ref. [26]), not from the present device. The claimed superiority of FNN over Bayesian estimation (Fig. 3(b) and Fig. S4) is therefore a simulation result conditioned on a PSD that may not match the actual temporal noise correlations in this GaAs TQD. If the real device has different noise statistics, the FNN output—and hence the inferred T2* extension—will be biased. The authors should validate the FNN on experimental noise traces, e.g., by comparing predicted versus measured frequency deviations over time, or by training on a PSD extracted from the same device.
  3. [II.B, Fig. 3(f)] The claim that T2* increases from 52.42±2.13 ns to 580±10 ns under feedback is not obtained from a direct Ramsey decay fit. Instead, T2* is inferred from the standard deviation of frequency fluctuations via T2* = sqrt(2)/(2πσ_f), which assumes quasi-static Gaussian frequency noise. The measured PSD (Fig. 3(c)) shows 1/f and 1/f^2 components, and the sparse-sampling protocol (62 points sampled at 1-ns increments) does not rule out non-Gaussian or non-quasi-static contributions. A direct Ramsey measurement under feedback, or a quantitative test of the Gaussian quasi-static assumption, is needed to support the coherence-extension claim. The agreement between the predicted gate-error reduction from σ_f and the observed RB improvement is a useful consistency check, but it does not validate the T2* relation by itself.
minor comments (4)
  1. [Supplemental C, Eq. (4)] The expression P(m_k|Δω)=α(p_↓)+β is not a well-formed probability. The roles of α, β, and p_↓ should be defined explicitly, and the equation should be rewritten so that the dependence on the Ramsey signal model is clear.
  2. [Fig. 4(d)] The error bars in the RB data are not defined in the main text. State explicitly whether they are standard errors over the 30 random sequences and how the fitted parameters and their uncertainties were obtained.
  3. [Fig. 2(d)] The operating point for the RB measurement is stated to be at MW power 4 dBm, while Fig. 2(d) shows Rabi frequencies at 10 dBm. The relation between the 271 MHz point and the operating point used for the fidelity measurement should be clarified.
  4. [Throughout] Several typographical errors distract from the presentation, e.g., 'fideliy' (Introduction), 'whereras' (Section II.A), 'ploted' (Section II.A), 'additonal' (Section II.A), and inconsistent spacing in 'di fferent'. A careful proofreading pass is recommended.

Circularity Check

0 steps flagged

No significant circularity: the headline fidelity and Rabi/coherence data are measured and externally benchmarked; the FNN model-dependence concerns the auxiliary coherence-extension claim but is not definitional circularity.

full rationale

The paper's central claims rest on measured quantities: Rabi frequencies and T2* from pulsed EDSR/Ramsey, and π/2 gate fidelity from randomized benchmarking. The TQD Hamiltonian in Eqs. (1)-(3) is used to interpret the data and motivate tuning, but the reported fRabi, T2*, and RB fidelity are not computed from that Hamiltonian via built-in equivalence; they are experimental observables. The PWC pulse optimization uses a cost function defined as RB sequence fidelity at sequence length 5, and the final 99.72% is extracted from a full RB decay curve. This creates a statistical selection/overfitting risk (especially with the disclosed absence of complete decay saturation in Supplemental D), but it is not a case of a fitted parameter being renamed as a prediction: the final fidelity is not derived solely from the cost function. The FNN feedback claim is the most model-dependent part: the network is trained on simulated Ramsey data generated using a noise PSD from prior work (Ref. [26]), and the T2* = 580 ± 10 ns under feedback is inferred from the standard deviation of FNN-estimated frequency fluctuations via T2* = sqrt(2)/(2πσ_f) rather than from a direct Ramsey decay fit. This makes the quantitative coherence extension dependent on the fidelity of the training noise model and on the Gaussian quasi-static assumption. However, the raw Ramsey oscillations in Fig. 3(e)-(f) independently show suppression of period fluctuations with feedback, so the effect is not constructed solely from the estimator's training data. No step exhibits an equation-level reduction where a predicted quantity equals its own input by definition, and no load-bearing argument reduces to a self-citation chain. The self-citations to [26] and [34] provide external experimental data and standard formulas, not an imported uniqueness theorem. The RB saturation and PWC cost-function concerns are correctness/statistical caveats, not circularity.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 0 invented entities

The central claims rest on a standard spin-qubit Hamiltonian with parameters fitted to the device, plus a neural-network estimator trained on simulated noise. No new physical entities are introduced. The main model-dependence is the assumed noise PSD used for FNN training and the quasi-static Gaussian relation used to convert frequency noise into a coherence time.

free parameters (5)
  • alpha, beta (Ramsey measurement model) = alpha = 0.32, beta = 0.23
    Parameters in P(mk|Delta omega) = alpha(p_down) + beta used to generate simulated training data for the FNN and to implement Bayesian estimation; fitted to experimental readout characteristics (Supplemental).
  • FNN architecture and trained weights = 2 hidden layers, 300 neurons each, sigmoid activation; weights trained on simulated data
    The neural network estimator's weights are fit to data generated from the assumed noise model; the claimed estimation advantage over Bayesian is shown for this architecture and training set (Fig. 3b, Fig. S3).
  • PWC pulse I/Q amplitudes = optimized over 4.05 ns at 40 CMA-ES iterations, population 20
    The pi/2 pulse envelope components are optimized with cost function = RB sequence fidelity at length 5; the optimized pulse is then used in the reported 99.72% fidelity measurement.
  • TQD Hamiltonian parameters (2t23, 2t34, bz, bx, epsilon23, epsilon34) = 2t23 = 16 GHz, 2t34 = 25 GHz, bz(2-3) = 0.05 mT, bx(2-3) = 0.2 mT, epsilon = 15 ueV, etc.
    Used to compute the energy diagram in Fig. 1(d); inferred from transport/EDSR spectroscopy, not independently predicted.
  • Noise PSD model for FNN training = 1/f and 1/f^2 crossover at 2 Hz from prior measurement [26]
    The training data for the FNN is generated from this assumed PSD; the coherence improvement claim depends on this model.
axioms (5)
  • domain assumption The single-electron TQD Hamiltonian (Eqs. 2-3) with spin-charge coupling and micro-magnet field gradients captures the device physics.
    The sweet-spot analysis and Rabi/T2 dependences are interpreted through this model (Section II.A).
  • domain assumption The micro-magnet field-gradient simulation (bx > 50 mT, bz ~ 0 at symmetry) represents the actual device at the operating point.
    Simulation in Supplemental B; the paper notes bz can be up to 100 mT when dots are asymmetric, requiring experimental adjustment via EDSR spectroscopy.
  • standard math The relation T2* = sqrt(2)/(2*pi*sigma_f) holds for Gaussian quasi-static frequency noise.
    Used to convert measured sigma_f into the reported T2* = 580 ± 10 ns (Section II.B).
  • standard math Randomized benchmarking decays as an exponential with depolarizing parameter p and the standard fidelity formula Faverage = (1+p)/2 applies.
    Used in Fig. 4(d) and the fidelity analysis; the paper itself prints the formula in garbled form.
  • ad hoc to paper The simulated Ramsey data used to train the FNN faithfully reproduces the real device's noise statistics.
    The FNN's advantage over Bayesian is established on 100,000 simulated datasets; experimental transfer is assumed (Fig. 3b).

reviewed 2026-08-05 · how reviews work

0 comments
Cite this review

Pith. "Pith review of High fidelity flopping-mode single spin operation with tuning inter-dot orbital levels." pith.science (2026). https://pith.science/paper/NYGRPZJC

@misc{pith2026250821723,
  author       = {Pith},
  title        = {Pith review of: High fidelity flopping-mode single spin operation with tuning inter-dot orbital levels},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NYGRPZJC}},
  note         = {Machine review of arXiv:2508.21723}
}
Share X Bluesky LinkedIn Reddit HN
abstract

Fast spin manipulation and long spin coherence time in quantum dots are essential features for high fidelity semiconductor spin qubits. However, generally it has not been well established how to optimize these two properties simultaneously, because these two properties are usually not independent from each other. Therefore, the scheme for high fidelity operation by simultaneous tuning Rabi frequency and coherence time, which does not rely on the material-dependent strong spin-orbit interaction and the local magnetic field gradient limiting their scalability, are strongly demanded. Here, we demonstrate an approach to achieve high-fidelity spin control by tuning inter-dot spin-orbit coupling in a GaAs triple quantum dot (TQD), where the third dot provides precise control over orbital energy levels. In an electrically stable charge state with optimized tunnel coupling, we achieve Rabi frequencies exceeding 100 MHz while maintaining coherence through proper tuning of the inter-dot orbital levels of the TQD. By implementing a machine learning-based feedback control that efficiently estimates qubit frequency using past measurement data, we characterize and mitigate the impact of low frequency noise on qubit coherence with minimal measurement overhead. Finally, we demonstrate a $\pi$/2 gate fidelity of 99.7\% with a gate time of 4 ns through randomized benchmarking, even in a GaAs quantum dot device where electron spin coherence is typically limited by strong hyperfine interaction with nuclear spins. Our approach provides a scalable strategy for high-fidelity spin control in semiconductor quantum dot arrays by utilizing device-specific parameters rather than relying on material properties or external field gradients.

Figures

Figures reproduced from arXiv: 2508.21723 by Akira Oiwa, Andreas D. Wieck, Arne Ludwig, Keisuke Koike, Takafumi Fujita, Takefumi Miyoshi, Xiao-Fei Liu, Yuta Matsumoto.

Figure 1
Figure 1. Figure 1: FIG. 1. Characteristics of the single qubit control speed and coherence time: (a)SEM picture of quadruple quantum dot device similar to [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Dependence of the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Performance of the measurement based feedback control of spin qubits (a) The scheme of the FNN based feedback control of [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Single qubit fidelity evaluation using randomized benchmarking (a) Measurement protocol of RB with the feedback cycle. After [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

49 extracted references · 30 canonical work pages · 2 internal anchors

  1. [1]

    Veldhorst, M. et al. An addressable quantum dot qubit with fault-tolerant control-fidelity. Nature Nanotechnology 9, 981–985 (2014). URL https://doi.org/10.1038/nnano. 2014.216

    doi:10.1038/nnano 2014

  2. [2]

    Yoneda, J. et al. A quantum-dot spin qubit with coherence lim- ited by charge noise and fidelity higher than 99.9%. Nature Nanotechnology 13, 102–106 (2018). URL https://doi. org/10.1038/s41565-017-0014-x

    doi:10.1038/s41565-017-0014-x 2018

  3. [3]

    Huang, W. et al. Fidelity benchmarks for two-qubit gates in silicon. Nature 569, 532–536 (2019). URL https://doi. org/10.1038/s41586-019-1197-0

    work page doi:10.1038/s41586-019-1197-0 2019

  4. [4]

    Xue, X. et al. Quantum logic with spin qubits crossing the surface code threshold. Nature 601, 343–347 (2022). URL https://doi.org/10.1038/s41586-021-04273-w . 10 FIG. S1. Simulated magnetic field induced by micro-magnets. a) Schematic diagram of the micro-magnet design. White circles indicate the intended positions of quantum dots, red rectangles represe...

    doi:10.1038/s41586-021-04273-w 2022

  5. [5]

    M˛ adzik, M. T. et al. Precision tomography of a three-qubit donor quantum processor in silicon. Nature 601, 348–353 (2022). URL https://doi.org/10.1038/ s41586-021-04292-7

    work page 2022

  6. [6]

    Noiri, A. et al. Fast universal quantum gate above the fault- tolerance threshold in silicon. Nature 601, 338–342 (2022). URL https://doi.org/10.1038/s41586-021-04182-y

    doi:10.1038/s41586-021-04182-y 2022

  7. [7]

    Mills, A. R. et al. Two-qubit silicon quantum proces- sor with operation fidelity exceeding 99%. Science Advances 8, eabn5130 (2022). URL https://www. science.org/doi/abs/10.1126/sciadv.abn5130. https://www.science.org/doi/pdf/10.1126/sciadv.abn5130

    doi:10.1126/sciadv.abn5130 2022

  8. [8]

    Yang, C. et al. Silicon quantum processor unit cell operation above one kelvin. arXiv preprint arXiv:1902.09126 (2019)

    work page internal anchor Pith review Pith/arXiv arXiv 1902

  9. [9]

    Petit, L. et al. Universal quantum logic in hot silicon qubits. arXiv preprint arXiv:1910.05289 (2019)

    work page internal anchor Pith review Pith/arXiv arXiv 1910

  10. [10]

    Zwerver, A. M. J. et al. Qubits made by advanced semiconduc- tor manufacturing. Nature Electronics5, 184–190 (2022). URL https://doi.org/10.1038/s41928-022-00727-9

    doi:10.1038/s41928-022-00727-9 2022

  11. [11]

    Vandersypen, L. M. K. et al. Interfacing spin qubits in quan- tum dots and donors—hot, dense, and coherent. npj Quantum Information 3, 34 (2017). URL https://doi.org/10.1038/ s41534-017-0038-y

    work page 2017

  12. [12]

    Li, R. et al. A crossbar network for silicon quantum dot qubits. Science Advances 4, eaar3960 (2018). URL https:// www.science.org/doi/abs/10.1126/sciadv.aar3960. https://www.science.org/doi/pdf/10.1126/sciadv.aar3960

    doi:10.1126/sciadv.aar3960 2018

  13. [13]

    & Harrington, J

    Raussendorf, R. & Harrington, J. Fault-tolerant quantum com- putation with high threshold in two dimensions.Phys. Rev. Lett. 98, 190504 (2007). URL https://link.aps.org/doi/10. 1103/PhysRevLett.98.190504

    work page 2007

  14. [14]

    C., Koppens, F

    Nowack, K. C., Koppens, F. H. L., Nazarov, Y . V . & Vander- sypen, L. M. K. Coherent control of a single electron spin with electric fields. SCIENCE 318, 1430–1433 (2007)

    work page 2007

  15. [15]

    van den Berg, J. W. G. et al. Fast spin-orbit qubit in an indium antimonide nanowire. Phys. Rev. Lett. 110, 066806 (2013). URL https://link.aps.org/doi/10. 1103/PhysRevLett.110.066806. 11 FIG. S3. Evaluation of the expected dephasing rate from the FNN based estimation as a function of (a) the free evolution time of the Ramsey measurement for the initial m...

    work page 2013

  16. [16]

    W., Franke, D

    Hendrickx, N. W., Franke, D. P., Sammak, A., Scappucci, G. & Veldhorst, M. Fast two-qubit logic with holes in germanium. Nature 577, 487–491 (2020). URL https://doi.org/10. 1038/s41586-019-1919-3

    work page 2020

  17. [17]

    G., Obata, T

    Tokura, Y ., van der Wiel, W. G., Obata, T. & Tarucha, S. Coher- ent single electron spin control in a slanting zeeman field.Phys. Rev. Lett. 96, 047202 (2006). URL https://link.aps.org/ doi/10.1103/PhysRevLett.96.047202

    doi:10.1103/physrevlett.96.047202 2006

  18. [18]

    Yoneda, J. et al. Fast electrical control of single electron spins in quantum dots with vanishing influence from nuclear spins. Physical review letters 113, 267601 (2014)

    work page 2014

  19. [19]

    Hendrickx, N. W. et al. A four-qubit germanium quantum pro- cessor. Nature 591, 580–585 (2021). URL https://doi. org/10.1038/s41586-021-03332-6

    doi:10.1038/s41586-021-03332-6 2021

  20. [20]

    Yoneda, J. et al. Robust micromagnet design for fast electrical manipulations of single spins in quantum dots. Applied Physics Express 8, 084401 (2015). URL https://dx.doi.org/10. 7567/APEX.8.084401

    work page 2015

  21. [21]

    Dumoulin Stuyck, N. I. et al. Low dephasing and ro- bust micromagnet designs for silicon spin qubits. Applied Physics Letters 119 (2021). URL https://doi.org/10. 1063/5.0059939. 094001, https://pubs.aip.org/aip/apl/article- pdf/doi/10.1063/5.0059939/13318369/094001_1_online.pdf

    work page doi:10.1063/5.0059939/13318369/094001_1_online.pdf 2021

  22. [22]

    Huang, P. & Hu, X. Fast spin-valley-based quantum gates in si with micromagnets. npj Quantum Information 7, 162 (2021). URL https://doi.org/10.1038/s41534-021-00500-4

    work page doi:10.1038/s41534-021-00500-4 2021

  23. [23]

    Gilbert, W. et al. On-demand electrical control of spin qubits. Nature Nanotechnology 18, 131–136 (2023). URL https:// doi.org/10.1038/s41565-022-01280-4

    work page doi:10.1038/s41565-022-01280-4 2023

  24. [24]

    Croot, X. et al. Flopping-mode electric dipole spin resonance. Phys. Rev. Research 2, 012006 (2020). URL https://link. aps.org/doi/10.1103/PhysRevResearch.2.012006

    doi:10.1103/physrevresearch.2.012006 2020

  25. [25]

    Hu, R.-Z. et al. Flopping-mode spin qubit in a Si-MOS quantum dot. Applied Physics Letters 122 (2023). URL https://doi.org/10.1063/5. 0137259. 134002, https: //pubs.aip.org/aip/apl/article- pdf/doi/10.1063/5.0137259/16786030/134002_1_online.pdf

    doi:10.1063/5 2023

  26. [26]

    Nakajima, T. et al. Coherence of a driven electron spin qubit actively decoupled from quasistatic noise. Phys. Rev. X 10, 011060 (2020). URL https://link.aps.org/doi/10. 1103/PhysRevX.10.011060

    work page 2020

  27. [27]

    Shulman, M. D. et al. Suppressing qubit dephasing using real- time hamiltonian estimation. Nature Communications 5, 5156 (2014). URL https://doi.org/10.1038/ncomms6156

    doi:10.1038/ncomms6156 2014

  28. [28]

    Struck, T. et al. Low-frequency spin qubit energy split- ting noise in highly purified 28si /sige. npj Quantum Infor- mation 6, 40 (2020). URL https://doi.org/10.1038/ s41534-020-0276-2 . 12 30 45 60 (a) 30 45 60 (b) 30 40 50 60 (c) 0 1 2 3 4 5 6 7 Real time (s) 32 40 48 (d) f (MHz) FIG. S4. Estimated deviations from the experimental qubit frequency, wher...

    work page 2020

  29. [29]

    Yoneda, J. et al. Noise-correlation spectrum for a pair of spin qubits in silicon. Nature Physics 19, 1793–1798 (2023). URL https://doi.org/10.1038/s41567-023-02238-6

    doi:10.1038/s41567-023-02238-6 2023

  30. [30]

    & Vandersypen, L

    Koppens, F., Nowack, K. & Vandersypen, L. Spin echo of a single elec- tron spin in a quantum dot.Physical Review Letters 100, 236802 (2008)

    work page 2008

  31. [31]

    M., Nave, C

    Cywi ´nski, L., Lutchyn, R. M., Nave, C. P. & Das Sarma, S. How to enhance dephasing time in superconducting qubits. Phys. Rev. B 77, 174509 (2008). URL https://link.aps. org/doi/10.1103/PhysRevB.77.174509

    doi:10.1103/physrevb.77.174509 2008

  32. [32]

    Wang, Z.-H. et al. Effect of pulse error accumulation on dy- namical decoupling of the electron spins of phosphorus donors in silicon. Phys. Rev. B 85, 085206 (2012). URL https: //link.aps.org/doi/10.1103/PhysRevB.85.085206

    work page doi:10.1103/physrevb.85.085206 2012

  33. [33]

    Keith, D. et al. Ramped measurement technique for robust high-fidelity spin qubit readout. Science Ad- vances 8, eabq0455 (2022). URL https://www. science.org/doi/abs/10.1126/sciadv.abq0455. https://www.science.org/doi/pdf/10.1126/sciadv.abq0455

    doi:10.1126/sciadv.abq0455 2022

  34. [34]

    Benito, M. et al. Electric-field control and noise protec- 13 FIG. S5. Test runs of Randomized benchmarking a) The sequence fidelity as a function of the number of applied clliford gates with bad fidelity condition. We confirmed that the di fference between the up-spin and down-spin decay curves saturates to zero. b) RB data with different Clifford compos...

    work page 2019

  35. [35]

    Studenikin, S. et al. Electrically tunable e ffective g-factor of a single hole in a lateral gaas /algaas quantum dot. Communi- cations Physics 2, 159 (2019). URL https://doi.org/10. 1038/s42005-019-0262-1

    work page 2019

  36. [36]

    Froning, F. N. M. et al. Ultrafast hole spin qubit with gate- tunable spin–orbit switch functionality. Nature Nanotechnol- ogy 16, 308–312 (2021). URL https://doi.org/10.1038/ s41565-020-00828-6

    work page 2021

  37. [37]

    Wang, K. et al. Ultrafast coherent control of a hole spin qubit in a germanium quantum dot. Nature Communica- tions 13, 206 (2022). URL https://doi.org/10.1038/ s41467-021-27880-7

    work page 2022

  38. [38]

    Ferrie, C., Granade, C. E. & Cory, D. G. Adaptive hamiltonian estimation using bayesian experimental design (2012)

    work page 2012

  39. [39]

    & Biercuk, M

    Sastrawan, J., Jones, C., Akhalwaya, I., Uys, H. & Biercuk, M. J. Analytically exploiting noise correlations inside the feed- back loop to improve locked-oscillator performance.Phys. Rev. E 94, 022204 (2016). URL https://link.aps.org/doi/ 10.1103/PhysRevE.94.022204

    work page doi:10.1103/physreve.94.022204 2016

  40. [40]

    & Biercuk, M

    Mavadia, S., Frey, V ., Sastrawan, J., Dona, S. & Biercuk, M. J. Prediction and real-time compensation of qubit decoherence via machine learning. Nature Communications 8, 14106 (2017). URL https://doi.org/10.1038/ncomms14106

    work page doi:10.1038/ncomms14106 2017

  41. [41]

    Werninghaus, M. et al. Leakage reduction in fast supercon- ducting qubit gates via optimal control. npj Quantum In- formation 7, 14 (2021). URL https://doi.org/10.1038/ s41534-020-00346-2

    work page 2021

  42. [42]

    Baum, Y . et al. Experimental deep reinforcement learning for error-robust gate-set design on a superconducting quantum computer. PRX Quantum 2, 040324 (2021). URL https: //link.aps.org/doi/10.1103/PRXQuantum.2.040324

    doi:10.1103/prxquantum.2.040324 2021

  43. [43]

    Takeda, K. et al. Optimized electrical control of a si /sige spin qubit in the presence of an induced frequency shift. npj Quan- 14 (a) (b) TABLE I. Clifford compositions used in this work. (a) A gate set containing π/2 and π rotations around the Bloch sphere (’standard composition (SC)’ ). (b) A gate set containing π/2 rotations around the Bloch sphere (...

    work page 2018

  44. [44]

    The cma evolution strategy: A tutorial

    Hansen., N. The cma evolution strategy: A tutorial. hal- 01297037 (2005)

    work page 2005

  45. [45]

    Takeda, K. et al. A fault-tolerant addressable spin qubit in a natural silicon quantum dot. Science Ad- vances 2, e1600694 (2016). URL https://www. science.org/doi/abs/10.1126/sciadv.1600694. https://www.science.org/doi/pdf/10.1126/sciadv.1600694

    doi:10.1126/sciadv.1600694 2016

  46. [46]

    Rimbach-Russ, M., Philips, S. G. J., Xue, X. & Vandersypen, L. M. K. Simple framework for systematic high-fidelity gate op- erations. Quantum Science and Technology 8, 045025 (2023). URL https://dx.doi.org/10.1088/2058-9565/acf786

    work page doi:10.1088/2058-9565/acf786 2023

  47. [47]

    Philips, S. G. J. et al. Universal control of a six-qubit quantum processor in silicon.Nature 609, 919–924 (2022). URLhttps: //doi.org/10.1038/s41586-022-05117-x

    doi:10.1038/s41586-022-05117-x 2022

  48. [48]

    John, V . et al. A two-dimensional 10-qubit array in germa- nium with robust and localised qubit control. arXiv preprint arXiv:2412.16044 (2024). Revised Feb 2025

    arXiv 2024

  49. [49]

    Lawrie, W. I. L. et al. Simultaneous single-qubit driving of semiconductor spin qubits at the fault-tolerant threshold. Na- ture Communications 14, 3617 (2023). URL https://doi. org/10.1038/s41467-023-39334-3

    work page doi:10.1038/s41467-023-39334-3 2023

This paper was first reviewed by deepseek-v4-flash on August 5, 2026.