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REVIEW 3 major objections 5 minor 1 cited by

Baseband control of single-electron silicon spin qubits in two dimensions

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Baseband hopping gates control single-electron silicon spin qubits at 99.50% fidelity.

desk verdict First silicon single-electron hopping-spin qubit demonstration with a credible 99.5% X90 lower bound; the main residual risk is the odd-parity RB branch artifact, but the paper is honest and worth refereeing. read the letter →

arxiv 2412.05171 v1 pith:RBHTSQGY submitted 2024-12-06 cond-mat.mes-hall

Florian K. Unseld , Brennan Undseth , Eline Raymenants , Yuta Matsumoto , Saurabh Karwal , Oriol Pietx-Casas , Alexander S. Ivlev , Marcel Meyer
show 4 more authors
Amir Sammak Menno Veldhorst Giordano Scappucci Lieven M. K. Vandersypen
This is my paper · ORCID
classification cond-mat.mes-hall
keywords spinqubitssiliconbasebandcontrolhoppinggatequantumdotarrayEDSRcrosstalknanomagnet
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish that single-electron spin qubits in silicon can be controlled entirely with baseband voltage pulses by hopping the electron between quantum dots whose quantization axes point in different directions, and that this control is already good enough for quantum processors. The load-bearing result is a lower bound of $F^{\mathrm{hop}}_{X90}=99.50(6)\%$ on the fidelity of the hopping X90 gate, measured on one qubit in a $2\times2$ $^{28}$Si/SiGe quantum dot array. That value is statistically the same as the $99.54(4)\%$ average fidelity of the same device's microwave-driven EDSR gates. The authors argue this matters because baseband hopping avoids the microwave heating and transient resonance shifts that make EDSR crosstalk hard to calibrate in two-dimensional arrays, and because the quantization-axis tips needed for hopping can be engineered with periodic nanomagnets. If true, this gives a concrete path for scaling silicon spin qubits into two dimensions without an external solenoid.

What carries the argument

The hopping gate is a sequence of two transfers between dots with non-collinear quantization axes, executed by fast detuning ramps: the charge follows the ground state adiabatically while the spin direction is transferred diabatically, keeping its orientation rather than tracking the changing quantization axis. The rotation accumulates from Larmor precession during intervals $t_1$ and $t_2$ in the two dots, plus an idling time $t_{\mathrm{add}}$ that keeps the rotation axis consistent across repeated cycles. The unitary $U=\big(R_z(\omega_{\mathrm{init}}(t_2'+t_{\mathrm{add}}))\,R_\theta(\omega_{\mathrm{tip}}t_1')\,R_z(\omega_{\mathrm{init}}t_2')\,R_\theta(\omega_{\mathrm{tip}}t_1')\big)^r$ is fitted to measured parity oscillations to extract the tip angle $\theta$, and the X90 gate is calibrated by adjusting timing parameters to give a periodicity of four under repeated application. The fidelity claim comes from randomized benchmarking with a Clifford set built from X90 hopping gates and physical Z-rotations, using the odd-parity branch of the readout.

What would settle it

Run interleaved randomized benchmarking on Q1 with the hopping X90 as the interleaved gate at the same low-field setting: if the interleaved fidelity is more than one standard error below the attributed $99.50(6)\%$ bound, the assumption that all randomized-benchmarking error comes from X90 fails and the quoted number is not a true gate fidelity.

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Extended reading notes

Core claim

The central claim is that a silicon single-electron spin can be coherently rotated by shuttling it back and forth between two dots in an inhomogeneous micromagnet stray field and letting it precess for controlled times in the two non-collinear quantization axes. At the low external field used for hopping, the micromagnet produces measured quantization-axis tips of $37.3(2)^\circ$ and $47.5(2)^\circ$ for the two measured dot pairs. By attributing all randomized-benchmarking error to the constituent X90 hopping gates, the odd-parity data give $F^{\mathrm{hop}}_{X90}=99.50(6)\%$, comparable to the EDSR average fidelity of $99.54(4)\%$, while Hahn-echo coherence times nearly double and the hopping gate adds no transient pulse-induced resonance shift. The paper also proposes a periodic iron nanomagnet pattern that would create roughly $90^\circ$ quantization-axis tips on a 100 nm dot pitch, so that hopping control could be engineered over an arbitrarily large two-dimensional array without a solenoid.

Load-bearing premise

The fidelity bound rests on the randomized-benchmarking analysis of the odd-parity branch being faithful, even though the even-parity branch shows an unexplained oscillatory artifact that could indicate state leakage or non-Markovian errors affecting both branches.

Editorial extensions

If this is right

  • Hopping gates are baseband operations that do not produce the transient, schedule-dependent phase pickup of EDSR; the hopping decoupling pulse contributes only a constant phase shift.
  • Operating at the low fields needed for hopping nearly doubles Hahn-echo coherence, from roughly 30 µs to 49 µs for Q1 and from 21 µs to 44 µs for Q4.
  • Because hopping addressability comes from local quantization-axis tips rather than frequency separation, the proposed nanomagnet array can work at zero external field and remove the solenoid from the cryostat.
  • Tip angles between 45° and 135° allow a single shuttling cycle to implement a Hadamard-class gate, making the design tolerant to magnet and dot placement variation.
  • The dominant estimated error, a 0.1–1% Landau–Zener probability of non-adiabatic charge transfer at the anticrossing, is attributed to limited tunnel-coupling tunability, so improving tunnel coupling should raise the fidelity beyond the quoted bound.

Reading between the lines

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

  • The paper's bound assumes the Z-rotation shoulders of each Clifford are nearly error-free compared with the X90; an interleaved randomized-benchmarking measurement of the hopping X90 alone would test that assumption directly.
  • If non-adiabatic charge transfer really is the dominant error, a straightforward prediction is that the same hopping gate with tunnel coupling increased to 50–100 µeV should beat 99.5% fidelity; the paper leaves this as an outlook rather than a tested claim.
  • The unexplained even-parity randomized-benchmarking artifact suggests parity-based benchmarking may be contaminated by state leakage or readout crosstalk; if so, odd-parity lower bounds should be treated as conservative bounds rather than point estimates in fault-tolerance analysis.
  • The periodic nanomagnet landscape of roughly 90° tips and decoherence sweet spots could double as a built-in parking and shuttling map for idling spins and long-range qubit transport, which the paper does not develop further.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. Unseld et al. report operation of a 2x2 28Si/SiGe quantum dot array in two control regimes: conventional micromagnet-based EDSR of four qubits at high field, and baseband hopping-spin control of single-electron spin qubits at reduced field. The central result is a quoted lower bound on the fidelity of an X90 hopping gate, F_hop_X90 = 99.50(6)%, extracted from odd-parity randomized benchmarking of Q1, which the authors compare with the device's average EDSR single-qubit fidelity of 99.54(4)%. The paper also reports improved Hahn-echo coherence at low field, absence of the transient pulse-induced resonance shift for hopping control, and a proposed periodic nanomagnet design for scalable two-dimensional hopping control.

Significance. If the hopping fidelity claim holds, this is a valuable experimental demonstration: it shows that a single-electron silicon spin qubit can be controlled with baseband-only pulses at fidelity competitive with resonant EDSR, avoiding microwave heating and transient crosstalk and opening a concrete route toward two-dimensional silicon spin arrays. Strengths of the paper include direct measurement of hopping-induced coherent oscillations and quantization-axis tip angles, an honest discussion of device limitations, and public availability of data and scripts. The nanomagnet architecture proposal is clearly labeled as illustrative but rests on plausible OOMMF simulations. The main caveat is that the headline fidelity depends on a single randomized-benchmarking branch with an unresolved oscillatory artifact.

major comments (3)
  1. [Methods, Randomized Benchmarking; Fig. 4(f)] The headline result F_hop_X90 = 99.50(6)% is derived from the odd-parity Clifford decay F_hop_Clif,odd = 99.01(11)%, while the even-parity branch yields F_hop_Clif,even = 99.49(7)% and, as the authors state, 'contains a small oscillatory artifact that persists even with substantial averaging' whose origin they are unsure of. The two branches differ by 0.48% in Clifford fidelity, far larger than the 0.06% error bar quoted on the X90 bound. Choosing the lower-fidelity branch is conservative only with respect to the even/odd branch difference; it does not protect against a mechanism such as state leakage, readout crosstalk, or non-Markovian phase error that could bias both branches. Because the comparison to EDSR rests on this number, the authors should provide an interleaved randomized benchmarking measurement of the X90 gate, a leakage or parity-loss check during the RB protocol, or an explicit model showing that the artifact cannot affect the odd branch. Without one of these, the claimed lower bound is not established at the stated precision.
  2. [Abstract and Section III] The abstract compares the one-qubit hopping lower bound on Q1 with the EDSR average fidelity averaged over all four qubits, 99.54(4)%. Only the Q1 hopping gate was benchmarked; the Q4 hopping gate could not be faithfully benchmarked because pulsing gate P3 degrades readout. A one-qubit result is therefore not equivalent to a device-average comparison. The authors should either benchmark hopping gates on additional qubits or restrict the claim to 'comparable to the EDSR fidelity of this device' with the one-qubit sample size explicitly stated; as written, the comparison in the abstract is stronger than the data support.
  3. [Methods, Randomized Benchmarking] The quoted uncertainty on F_hop_X90 is the fitting standard deviation of the odd-branch Clifford decay only. The unresolved even-branch artifact and the 0.48% discrepancy between the parity branches constitute a systematic uncertainty that is not reflected in the quoted 99.50(6)% value. At minimum, the systematic spread should be reported or the authors should explicitly state that the quoted uncertainty captures only statistical fit error and that the systematic contribution is unresolved.
minor comments (5)
  1. [Fig. 3(b) caption] The labels '(lower)' and '(upper)' in the caption are ambiguous; please rephrase to identify clearly which panel shows T2* and which shows T2^H.
  2. [Methods, Eq. (1)] The ordering of t2 and tadd in the first Rz factor of Eq. (1) should be double-checked against the pulse diagram in Fig. 4(a); as written it is not obvious why tadd appears only in the first factor.
  3. [Page 5 and throughout] Use a space between numerical values and units, e.g., 'fRabi ≈ 2 MHz' instead of 'fRabi ≈2 MHz'.
  4. [Supplementary Information, Section V] The sentence 'The data in a-b) was collected' should read 'The data in a-b) were collected'.
  5. [Fig. 3(a) caption] The shaded area is described as a 'generous estimate of uncertainty' but no quantitative definition is given; please specify what the shaded band represents and how the ±15 nm out-of-plane displacement was chosen.

Circularity Check

1 steps flagged · score 1.0 of 10

No significant circularity: the headline hopping-gate fidelity is a direct measurement with a stated conservative attribution, and the only fitted-input/prediction overlap is a non-load-bearing micromagnet calibration.

  1. fitted input called prediction [Section III (Baseband Operation), Fig. 3 caption and accompanying text]
    "The dashed line shows the predicted homogeneous polarization of the micromagnet as extracted by fitting the measured qubit frequencies to a simplified micromagnet model ... From the extracted micromagnet polarization in panel a) we extract c) the driving gradient along the y-axis and d) the decoherence gradient magnitude at the center of the plunger gates."

    The polarization parameter is a least-squares fit to the measured qubit frequencies at each field setting, so the driving and decoherence gradients computed from it are calibrated outputs rather than independent predictions. Calling the resulting frequency behavior 'predicted by simulations' overstates the test because the model is constrained by the very frequencies it is used to explain. This is a genuine but minor fitted-input-called-prediction issue. It is not load-bearing for the central claim: the hopping X90 fidelity, the coherence times, and the PIRS comparison are direct measurements, not outputs of this magnet model.

full rationale

The central result, F^hop_X90 = 99.50(6)%, is obtained from odd-parity Clifford randomized benchmarking of Q1 with the conversion F_X90 = 1 - (1 - F_Clif)/2 justified by the stated assumption that Z rotations are brief and relatively error-free. That is a conservative attribution rule, not a derivation of the measured decay from the claimed fidelity; the decay itself is new data from this device. The unresolved even-parity RB artifact is acknowledged by the authors ('we are unsure of the true origin of this artifact'), and using the lower odd-parity branch is conservative; this is a measurement-methodology caveat, not circularity. Tip angles are explicitly obtained by fitting a unitary model and are labeled as fits. The hopping-control protocol and Hamiltonian are adapted from prior work including Ref. [25], which involves some overlapping authors, but the silicon implementation, measured Rabi-like oscillations, RB decay, coherence data, and crosstalk comparison are independent experimental content; no load-bearing argument reduces to a self-citation. The micromagnet polarization is fit to measured frequencies and then used to interpret gradient changes; this is a calibration and interpretation step, and the paper mostly phrases it as 'compatible with' rather than as an independent prediction, so it does not undermine the headline claims. Overall, no central claim is equivalent to its inputs by construction.

Assumptions & free parameters 6 free parameters · 5 assumptions · 1 invented entities

The central experimental claims use external measurements (Ramsey, Hahn echo, randomized benchmarking, PIRS) and are not circular. However, derived field gradients and tip angles come from a micromagnet model whose polarization is fit to measured qubit frequencies, so those derived quantities are calibrated rather than independent predictions. The hopping gate fidelity is a measured quantity, not derived from the model, so the circularity burden is low.

free parameters (6)
  • Micromagnet homogeneous polarization = not stated numerically; inferred by least-squares fit to measured qubit frequencies
    Used to compute driving and decoherence gradients and quantization-axis tips versus external field (Fig. 3a, SI Note II).
  • Quantization axis tip angle theta_1,2 = 37.3(2) deg
    Fit from 2-cycle, 4-repetition spin-hopping pattern to Eq. 2; used to validate the hopping gate model.
  • Quantization axis tip angle theta_4,3 = 47.5(2) deg
    Same fitting method for the Q4-Q3 pair.
  • Timing offsets, frequencies, and SPAM parameters in tip-angle fit = t1_offset, t2_offset, omega_init, omega_tip, A, B; optimized within narrow bounds
    Free parameters in pixel-by-pixel least-squares fit of the hopping pattern (Methods: Tip angle fitting).
  • Tunnel coupling tc = about 40 ueV
    Estimated from interdot transition fits; enters the Landau-Zener estimate of charge-transfer error in SI Note V.
  • Detuning ramp speed v = about 3000 ueV/ns
    Estimated from lever arm and a 5 ns ramp; enters the same Landau-Zener estimate.
assumptions (5)
  • domain assumption The electron g-factor in the silicon quantum well is isotropic with g=2, so the spin quantization axis follows the total magnetic field direction.
    Invoked in SI Note I to compute tip angles and gradients; load-bearing for interpreting the hopping mechanism and nanomagnet simulations.
  • domain assumption Randomized benchmarking decay is exponential under Markovian noise, so the fitted Clifford fidelity represents the average gate error.
    Methods, Randomized Benchmarking; relied on for the 99.50(6)% lower bound.
  • standard math Landau-Zener formula and sudden approximation govern the charge and spin dynamics during shuttling.
    SI Note V uses Eq. S26 and Eq. S28 to justify adiabatic charge transfer with diabatic spin transfer.
  • standard math Schrieffer-Wolff perturbation theory gives the EDSR Rabi and decoherence couplings in Eqs. S2-S3.
    SI Note I; standard quantum perturbation theory for the EDSR Hamiltonian.
  • domain assumption OOMMF zero-temperature energy minimization with Fe material parameters predicts the relaxed magnetization of the proposed nanomagnet array.
    SI Note III; no fabricated nanomagnet array is measured in this paper.
invented entities (1)
  • Periodic Fe nanomagnet pattern (40 nm x 120 nm x 50 nm, roughly 280 nm pitch)
    purpose: Generate deterministic ~90 degree quantization-axis tips and decoherence sweet spots for baseband hopping control in arbitrary large 2D silicon spin arrays.
    Simulated in OOMMF only; no experimental device or stray-field measurement verifies the design. The predicted field maps and tip angles are falsifiable by future fabrication and magnetometry.

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Cite this review

Pith. "Pith review of Baseband control of single-electron silicon spin qubits in two dimensions." pith.science (2026). https://pith.science/paper/RBHTSQGY

@misc{pith2026241205171,
  author       = {Pith},
  title        = {Pith review of: Baseband control of single-electron silicon spin qubits in two dimensions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RBHTSQGY}},
  note         = {Machine review of arXiv:2412.05171}
}
abstract

Micromagnet-enabled electric-dipole spin resonance (EDSR) is an established method of high-fidelity single-spin control in silicon. However, the resulting architectural limitations have restrained silicon quantum processors to one-dimensional arrays, and heating effects from the associated microwave dissipation exacerbates crosstalk during multi-qubit operations. In contrast, qubit control based on hopping spins has recently emerged as a compelling primitive for high-fidelity baseband control in sparse two-dimensional hole arrays in germanium. In this work, we commission a $^{28}$Si/SiGe 2x2 quantum dot array both as a four-qubit device with pairwise exchange interactions using established EDSR techniques and as a two-qubit device using baseband hopping control. In this manner, we can evaluate the two modes of operation in terms of fidelity, coherence, and crosstalk. We establish a lower bound on the fidelity of the hopping gate of 99.50(6)%, which is similar to the average fidelity of the resonant gate of 99.54(4)%. Lowering the external field to reach the hopping regime nearly doubles the measured $T_2^{\mathrm{H}}$, suggesting a reduced coupling to charge noise. Finally, the hopping gate circumvents the transient pulse-induced resonance shift. To further motivate the hopping gate approach as an attractive means of scaling silicon spin-qubit arrays, we propose an extensible nanomagnet design that enables engineered baseband control of large spin arrays.

Figures

Figures reproduced from arXiv: 2412.05171 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
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Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
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Forward citations

Cited by 1 Pith paper

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

  1. A trilinear quantum dot architecture for semiconductor spin qubits

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    A trilinear quantum dot layout with a middle shuttling array could give semiconductor spin qubits two-dimensional connectivity while keeping each dot individually wireable.

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Reviewed August 11, 2026 · model on record in the stance chip above.