Pith. sign in

REVIEW 2 major objections 5 minor 30 references

Assessing fidelity-limiting factors and achieving single-qubit gate fidelity beyond 99.999% in driven silicon spin qubits

T0 review · 2 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read By removing a nearby reservoir, operating at 100 mK, and shaping microwave pulses, a driven $^{28}$Si/SiGe spin qubit reaches a $\pi/2$ gate fidelity of 99.99920(2)\%, with the remaining error dominated by incoherent noise.

desk verdict A strong experimental paper reporting a state-of-the-art silicon spin-qubit gate fidelity and two practically important benchmarking artifacts; the central claim holds up, with minor caveats about RB extraction assumptions and missing data. read the letter →

arxiv 2608.11072 v1 pith:QYMNM2C2 submitted 2026-08-11 cond-mat.mes-hall quant-ph

Kenta Takeda , Akito Noiri , Takashi Nakajima , Leon C. Camenzind , Takashi Kobayashi , Giordano Scappucci , Seigo Tarucha This is my paper · ORCID
classification cond-mat.mes-hallquant-ph
keywords siliconspinqubitssingle-qubitgatefidelityrandomizedbenchmarkingpurityspin-lockingcoherenceoff-resonantdrivingpulseshaping28Si/SiGequantumdots
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 is trying to establish that a driven silicon spin qubit can be pushed to a $\pi/2$ gate fidelity above 99.999%, and that the remaining error is governed by decoherence rather than by poor control. The authors report a fidelity of 99.99920(2)% in a $^{28}$Si/SiGe spin qubit after fixing three problems: a nearby reservoir shortens the spin-locking coherence time $T_{1\rho}$, microwave heating shifts the qubit frequency, and rectangular pulses off-resonantly excite the neighboring qubit used in parity readout, which distorts randomized benchmarking. Removing the reservoir, operating at 100 mK, and using Gaussian pulse shapes suppress all three effects. If correct, the work turns a record number into a reproducible recipe for high-fidelity single-qubit gates in larger silicon arrays.

What carries the argument

The load-bearing object is the spin-locking coherence time $T_{1\rho}$, the decay time of a qubit under continuous microwave irradiation, connected to noise by $T_{1\rho}^{-1} = \frac12 T_1^{-1} + \frac{(2\pi)^2}{2} S_\parallel(f_{\rm Rabi})$, where $S_\parallel$ is the longitudinal noise spectral density at the Rabi frequency. Reservoir proximity enters through a capacitive coupling factor $\eta(d)^2$ that scales the induced voltage noise. A second mechanism is off-resonant driving in randomized benchmarking: with parity readout, the reference qubit's extra depolarization $q$ adds to the target qubit's depolarizing parameter $p$, so the joint decay looks worse than the true fidelity; the synchronization condition $t_g(n)=\sqrt{4n^2-1}/(4|\Delta f|)$ reveals the 7.9 ns periodicity, and Gaussian pulses suppress the artifact. Purity benchmarking closes the argument by comparing the decay of $\mathrm{Tr}(\rho^2)$ with the RB decay, separating coherent from incoherent error.

What would settle it

Run interleaved randomized benchmarking experiments that isolate $X_{\pi/2}$ and $Y_{\pi/2}$ rotations, or run randomized benchmarking with only $X_{\pi/2}$ gates; if the inferred per-rotation error differs from $8.6(3)\times10^{-6}$ by more than the error bars, the equal-splitting, gate-independent assumption fails and the headline fidelity is not the average. A second check is to look for curvature or non-exponential tails in the randomized-benchmarking decay, which would signal noise that remembers previous pulses.

Watch

Extended reading notes

Core claim

The central claim is that, in a $^{28}$Si/SiGe single-spin qubit, a $\pi/2$ rotation fidelity of 99.99920(2)% is achievable, and the fidelity is limited by incoherent noise. The paper identifies the mechanisms that previously stood in the way: proximal reservoirs degrade the driven coherence time $T_{1\rho}$ via capacitive coupling and longitudinal noise at the Rabi frequency; microwave drive heats the device and shifts the qubit resonance; and rectangular pulses create spectral sidelobes that off-resonantly depolarize the parity-readout partner, adding a spurious decay to the benchmarking signal. With the reservoir depleted, operation at 100 mK, and Gaussian pulses, the measured RB decay rate is $\varepsilon_{\rm RB}=8.6(3)\times10^{-6}$ per $\pi/2$ gate, the purity decay rate is $\varepsilon_{\rm PB}=7.1(2)\times10^{-6}$, giving a coherent contribution of only $1.5(4)\times10^{-6}$ and confirming decoherence as the dominant error.

Load-bearing premise

The headline fidelity assumes the noise that makes randomized benchmarking decay is the same from pulse to pulse and has no memory, and that the error per Clifford gate divides evenly among the average 3.25 $\pi/2$ rotations; if the noise remembers previous pulses or favors certain rotations, the quoted 99.99920(2)% may not equal the true average gate fidelity.

Editorial extensions

If this is right

  • With the reservoir depleted and Gaussian pulses, single-qubit randomized benchmarking at $f_{\rm Rabi}=3$ MHz should consistently return fidelities above 99.999%, rather than the 99.9% level commonly reported.
  • Operating at 100 mK reduces the transient microwave-induced frequency shift to below 50 kHz, so long sequences of tens of thousands of $\pi/2$ pulses no longer accumulate a coherent detuning error.
  • Rectangular-pulse randomized benchmarking combined with parity readout systematically under-reports fidelity for any qubit pair separated by tens of MHz; pulse shaping is therefore a prerequisite for trustworthy multi-qubit benchmarks in this architecture.
  • Because the purity decay rate is close to the randomized-benchmarking decay rate, further improvement in this device will come mainly from lengthening $T_{1\rho}$ and reducing incoherent noise, not from better pulse calibration.

Reading between the lines

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

  • The off-resonant artifact is unlikely to be confined to this device: any parity-readout architecture with a shared drive line and qubits separated by tens of MHz will see the same inflated randomized-benchmarking decay, so comparing IZ and ZZ readouts is a cheap diagnostic for it.
  • The reservoir-proximity dependence of $T_{1\rho}$ implies that qubits sitting next to charge sensors in dense arrays will have uneven driven coherence; sparse layouts with shuttling, or reservoirs far from qubits, should produce more homogeneous fidelities.
  • Purity benchmarking's low cost makes it a natural tool for two-qubit error budgets, separating coherent cross-talk from decoherence in CNOT or CZ gates rather than only single-qubit rotations.
  • If heating scales with total microwave power, scaling to many simultaneously driven qubits will require baseband or low-frequency control; a direct test is to measure the qubit frequency shift while increasing the number of concurrently driven qubits.
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. The paper reports single-qubit gate fidelities above 99.999% in a 28Si/SiGe spin qubit, with a headline π/2 rotation fidelity of 99.99920(2)% extracted from randomized benchmarking (RB). The authors identify two main sources of error: (i) proximity to a grounded reservoir, which degrades the driven coherence time T1ρ, and (ii) off-resonant driving of the reference qubit during parity-readout RB, which creates a benchmarking artifact that can be mistaken for qubit error. They show that removing a proximal reservoir, operating at 100 mK to suppress microwave-induced frequency shifts, and using Gaussian-shaped pulses rather than rectangular pulses mitigate these effects. Purity benchmarking is used to separate incoherent and coherent contributions, and the authors conclude that the residual error is predominantly incoherent, with a coherent error per π/2 rotation of about 1.5(4)×10^-6.

Significance. If the reported fidelity is taken at face value, this is a state-of-the-art result for single-qubit control in silicon spin qubits: an infidelity near 8×10^-6 exceeds previous demonstrations by roughly an order of magnitude. The paper is also valuable for identifying and isolating a subtle benchmarking artifact (off-resonant driving of a parity-readout ancilla) that could otherwise corrupt high-fidelity RB claims, and for connecting driven coherence (T1ρ) to device geometry through the reservoir-proximity study. A clear strength is that the central fidelity is a direct experimental measurement with stated statistical error bars, not a derived quantity from a fitted model, and the RB-versus-purity comparison provides evidence for the incoherent-limited claim. The supporting capacitance model and the off-resonant-driving simulation are explicitly presented as fitted or approximate, and they do not feed back into the headline fidelity extraction.

major comments (2)
  1. [Methods, Randomized benchmarking; Fig. 5a] The headline value 99.99920(2)% is obtained by fitting the per-Clifford RB decay and converting to a per-π/2 error by dividing by 3.25, the average number of π/2 rotations per Clifford gate. This conversion is exact only if every primitive π/2 gate (Xπ/2, Yπ/2, and the four-pulse identity) has the same error rate and if the noise is Markovian and gate-independent. The manuscript does not provide an experimental test of these assumptions at the 10^-6 level, and the microwave-induced frequency shifts described in the section on heating are a known time-dependent, potentially non-Markovian error source. I ask the authors to quantify the systematic uncertainty in the per-π/2 fidelity from gate-dependent errors and non-Markovianity, for example by measuring primitive gate fidelities directly or by interleaved RB, or by demonstrating that the RB decay is single-exponential over the full range of m with residuals consistent with the model.
  2. [Methods, Error budgeting (purity benchmarking); Supplementary Fig. 5] The final RB and purity-benchmarking data are taken with ZZ parity readout, so the reference qubit Q1 is always present during the sequence. The methods section explicitly concedes that single-qubit-space GST and PB 'fail to account for off-resonant rotations of the reference qubit,' and the justification for using Gaussian pulses under ZZ readout rests on a simulation (Supplementary Fig. 5) rather than an experimental comparison. If the simulated off-resonant depolarization q is an underestimate, the observed RB decay includes a contribution that is not part of Q2's per-gate error, and the RB-versus-purity decomposition could also be affected. I request an experimental bound on q at the Gaussian-pulse operating point (for example, repeating the IZ-versus-ZZ comparison of Fig. 4d with Gaussian pulses) or an explicit sensitivity analysis of the simulation to its assumptions (noise amplitude A, waiting time, pulse truncation).
minor comments (5)
  1. [Methods, Randomized benchmarking] The conversion from per-Clifford decay to per-π/2 fidelity is described only in prose; please state the explicit relation used (e.g., ε_π/2 = ε_Clifford / 3.25 or p_π/2 = p_Clifford^(1/3.25)) so that the reader can reproduce the number.
  2. [Data availability] The Data availability section contains the placeholder '{URL}' for the Zenodo record; a working DOI should be provided before publication.
  3. [Supplementary Fig. 9] The sentence 'Modifying the 500 nm offset in the reservoir geometry changes these constants but does not affect the overall result' is vague; please state explicitly which aspect is robust (the functional form T1ρ ∝ (η^2 + B)^-1, the qualitative distance scaling, or the value of the exponent).
  4. [Abstract and main text] Several occurrences of 'π/2' appear as 'π22' in the abstract and main text; the final version should use the correct mathematical notation.
  5. [Methods, Error budgeting] The caveat that single-qubit-space GST and PB fail to account for off-resonant rotations of the reference qubit is important and should also appear in the main-text discussion of the error budget, not only in the Methods.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the reported 99.99920(2)% fidelity is a direct randomized-benchmarking measurement, and the supporting simulations and error-budget analysis do not feed fitted parameters back into the headline number.

full rationale

The central claim is a measured randomized-benchmarking depolarizing parameter, not a quantity derived from a fitted model. The Methods section ('Randomized benchmarking') states that Clifford gates are decomposed into π/2 rotations with an average of 3.25 rotations per Clifford, and the quoted π/2 fidelity is obtained from the standard single-exponential fit F(m)=V p^m to measured return probabilities (Fig. 5a). The gate-independence/Markovian assumption underlying RB is a modeling assumption, not a circular input; it affects interpretation but does not make the measurement equal to its inputs. The purity-benchmarking comparison (εRB−εPB) is an independent experimental protocol run in the same session and is used only to attribute the already-measured error to coherent versus incoherent sources. The off-resonant-driving simulation calibrates A=17 kHz to a separate Ramsey T2* measurement and adds a constant offset equal to the average IZ-readout decay; the oscillatory q contribution that demonstrates the artifact is predicted from the simulation rather than fitted to the ZZ data, so it is not a fitted input dressed as a prediction. Self-citations (Ref. 13 for the device and Clifford decomposition) are conventional and do not carry the evidential weight of the fidelity claim; the device identity is not used to infer the new fidelity. No equation in the paper reduces by construction to its own input, and no load-bearing argument depends on an unverified self-citation. The derivation chain is self-contained against direct experimental benchmarking.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The paper's central fidelity claim is an experimental measurement and does not depend on the fitted models; the fitted models support secondary mechanistic explanations (reservoir coupling, off-resonant artifact) and are appropriately flagged by the authors as approximate. No new physical entities are introduced.

free parameters (3)
  • Reservoir T1ρ fit constants A and B = determined from fit in log(T1ρ) space (Supp Fig. 9)
    The claimed scaling T1ρ^-1 ∝ η(d)^2 + const uses two dimensionless constants fit to the measured T1ρ at a few reservoir distances; the fit has significant uncertainty per the paper's own statement.
  • Low-frequency noise amplitude A = 17 kHz
    Chosen to reproduce Ramsey T2* in the off-resonant driving simulation (Methods/Supp); a fitted input, not independently measured.
  • Simulation offset for resonant qubit decay = 2.5e-4
    Constant offset added to simulated off-resonant decay to match the average IZ readout results; fitted to the same data.
assumptions (6)
  • domain assumption T1ρ^-1 = (1/2)T1^-1 + ((2π)^2/2)S∥(f_Rabi), with T1^-1 = ((2π)^2/2)S⊥(f_Larmor)
    Used in Fig. 2d/e to attribute T1ρ changes to reservoir noise PSDs; standard rotating-frame relaxation formula from Ithier et al.
  • standard math Randomized benchmarking decay is exponential and the per-Clifford depolarizing parameter is the same for all Clifford gates
    The RB fits use F(m)=Vp^m; this assumes Markovian, gate-independent errors.
  • standard math Purity benchmarking: √P decay rate equals the depolarizing rate, so coherent error is εRB - εPB
    Used in Fig. 5f to separate coherent and incoherent errors; from Feng et al. and Yang et al.
  • ad hoc to paper The reservoir can be modeled as a grounded infinitesimally thin conducting sheet with image-charge screening
    Supplementary capacitive coupling model; used to explain T1ρ distance dependence, but not independently validated.
  • domain assumption 1/f charge noise with amplitude A=17 kHz
    Assumed noise model in the off-resonant driving simulation; the amplitude is chosen to match T2* rather than measured directly.
  • domain assumption Micromagnet simulation with cobalt saturation 1.8 T and nominal gate-stack dimensions
    Used to argue anisotropy of field gradients explains selective T1ρ degradation; simulation assumptions are not experimentally verified.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Assessing fidelity-limiting factors and achieving single-qubit gate fidelity beyond 99.999% in driven silicon spin qubits." pith.science (2026). https://pith.science/paper/QYMNM2C2

@misc{pith2026260811072,
  author       = {Pith},
  title        = {Pith review of: Assessing fidelity-limiting factors and achieving single-qubit gate fidelity beyond 99.999% in driven silicon spin qubits},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QYMNM2C2}},
  note         = {Machine review of arXiv:2608.11072}
}
abstract

In semiconductor single-spin qubits, high-fidelity quantum gates have been demonstrated; however, achieving consistent performance remains challenging due to variations in driven qubit coherence, which is less explored than free-evolution coherence such as $T_2^*$. Here, we report single-qubit gate fidelities above 99.999%, achieved by dramatically extending the driven-spin coherence time and suppressing off-resonant driving effects that are detrimental to accurate fidelity benchmarking. We demonstrate that removing proximal reservoirs significantly enhances the spin-locking coherence time ($T_{1\rho}$), a critical metric for qubits under microwave driving. Furthermore, we reveal that in typical spin qubit setups using parity readout and rectangular pulses, off-resonant excitation of neighboring qubits causes substantial benchmarking artifacts. By optimizing device conditions to mitigate microwave-induced degradation and implementing spectrally tailored pulse shaping, we achieve a ${\pi}/2$ gate fidelity of 99.99920(2)%, with remaining errors primarily limited by incoherent noise. These results showcase the mechanisms that bound fidelity benchmarking in state-of-the-art silicon spin qubits and provide practical guidelines for achieving and verifying high fidelities in these systems.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

30 extracted references · 20 canonical work pages

  1. [1]

    Neyens, S. et al. Probing single electrons across 300 -mm spin qubit wafers. Nature 629, 80–85 (2024)

    work page 2024

  2. [2]

    Elsayed, A. et al. Low charge noise quantum dots with industrial CMOS manufacturing. Npj Quantum Inf. 10, 70 (2024)

    2024

  3. [3]

    A digitally controlled silicon quantum processing unit

    Members of the HRL Quantum Team and Collaborators et al. A digitally controlled silicon quantum processing unit. Nature 655, 1154–1159 (2026)

    work page 2026

  4. [4]

    Yoneda, J. et al. A quantum-dot spin qubit with coherence limited by charge noise and fidelity higher than 99.9%. Nat. Nanotechnol. 13, 102–106 (2018)

    2018

  5. [5]

    Veldhorst, M. et al. An addressable quantum dot qubit with fault -tolerant control-fidelity. Nat. Nanotechnol. 9, 981–985 (2014)

    work page 2014

  6. [6]

    Xue, X. et al. Quantum logic with spin qubits crossing the surface code threshold. Nature 601, 343–347 (2022)

    2022

  7. [7]

    Noiri, A. et al. Fast universal quantum gate above the fault-tolerance threshold in silicon. Nature 601, 338–342 (2022)

    2022

  8. [8]

    Mills, A. R. et al. Two-qubit silicon quantum processor with operation fidelity exceeding 99%. Sci. Adv. 8, eabn5130 (2022)

    work page 2022

Show all 30 references
  1. [9]

    Mills, A. R. et al. High-Fidelity State Preparation, Quantum Control, and Readout of an Isotopically Enriched Silicon Spin Qubit. Phys. Rev. Appl. 18, 064028 (2022)

    2022

  2. [10]

    Steinacker, P. et al. Industry-compatible silicon spin -qubit unit cells exceeding 99% fidelity. Nature 646, 81–87 (2025)

    2025

  3. [11]

    Maurand, R. et al. A CMOS silicon spin qubit. Nat. Commun. 7, 3–8 (2016)

    2016

  4. [12]

    Maune, B. M. et al. Coherent singlet-triplet oscillations in a silicon -based double quantum dot. Nature 481, 344–347 (2012)

    2012

  5. [13]

    Wu, Y .-H. et al. Simultaneous High-Fidelity Single-Qubit Gates in a Spin Qubit Array. Preprint at https:22arxiv.org2abs22507.11918 (2025)

    2025 arXiv

  6. [14]

    Takeda, K. et al. Rapid single -shot parity spin readout in a silicon double quantum dot with fidelity exceeding 99%. Npj Quantum Inf. 10, 22 (2024)

    2024

  7. [15]

    Undseth, B. et al. Hotter is Easier: Unexpected Temperature Dependence of Spin Qubit Frequencies. Phys Rev X 13, 041015 (2023)

    2023

  8. [16]

    Rimbach-Russ, M., Philips, S. G. J., Xue, X. & Vandersypen, L. M. K. Simple framework for systematic high-fidelity gate operations. Quantum Sci. Technol. 8, 045025 (2023)

    2023

  9. [17]

    G., Obata, T

    Tokura, Y ., Van Der Wiel, W. G., Obata, T. & Tarucha, S. Coherent single electron spin control in a slanting zeeman field. Phys. Rev. Lett. 96, 1–4 (2006)

    2006

  10. [18]

    Zajac, D. M. et al. Resonantly driven CNOT gate for electron spins. Science 359, 439–442 (2018)

    2018

  11. [19]

    G., Tokura, Y

    Ono, K., Austing, D. G., Tokura, Y . & Tarucha, S. Current rectification by Pauli exclusion in a weakly coupled double quantum dot system. Science 297, 1313–1317 (2002)

    2002

  12. [20]

    Ithier, G. et al. Decoherence in a superconducting quantum bit circuit. Phys Rev B 72, 134519 (2005)

    2005

  13. [21]

    Takeda, K. et al. Optimized electrical control of a Si2SiGe spin qubit in the presence of an induced frequency shift. Npj Quantum Inf. 4, 54 (2018)

    2018

  14. [22]

    Feng, G. et al. Estimating the Coherence of Noise in Quantum Control of a Solid -State Qubit. Phys Rev Lett 117, 260501 (2016)

    2016

  15. [23]

    Yang, C. H. et al. Silicon qubit fidelities approaching incoherent noise limits via pulse engineering. Nat. Electron. 2, 151–158 (2019)

    2019

  16. [24]

    Wang, C.-A. et al. Operating semiconductor quantum processors with hopping spins. Science 385, 447–452 (2024)

    2024

  17. [25]

    John, V . et al. Robust and localised control of a 10-spin qubit array in germanium. Nat. Commun. 16, 10560 (2025)

    2025

  18. [26]

    Boter, J. M. et al. Spiderweb Array: A Sparse Spin-Qubit Array. Phys Rev Appl 18, 024053 (2022)

    2022

  19. [27]

    Beer, M. et al. Conveyor-mode electron shuttling through a T -junction in Si2SiGe. Preprint at https:22arxiv.org2abs22601.03942 (2026)

    2026

  20. [28]

    Blumoff, J. Z. et al. Fast and High -Fidelity State Preparation and Measurement in Triple - Quantum-Dot Spin Qubits. PRX Quantum 3, 10352 (2022)

    2022

  21. [29]

    Isolated

    Yan, F. et al. Rotating-frame relaxation as a noise spectrum analyser of a superconducting qubit undergoing driven evolution. Nat. Commun. 4, 2337 (2013). Fig. 1, Basic device properties. a, False-color scanning electron microscope image of the device. The khaki, green, and bl...

    2013

  22. [30]

    Supplementary Fig

    In the experiment, the quantum dot position s are likely misaligned from 𝑧 = 0 due to disorder ; however, such misalignment does not drastically affect the gradients along the x-axis. Supplementary Fig. 4, Coherence times and benchmarking for Q1. a, Summary of coherence time m...

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.