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Exploiting epitaxial strained germanium for scaling low noise spin qubits at the micron-scale

T0 review · 4 major / 7 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Strained germanium grown on germanium wafers sets a low charge-noise benchmark for hole spin qubits and identifies the 73Ge and 29Si nuclear baths that must be purified to reach long coherence.

desk verdict Solid experimental noise benchmarking on a promising platform: the charge-noise numbers and the first 29Si coherence modulation in Ge/SiGe qubits are the real new results, but the low-frequency noise attribution could use one more discriminating check. read the letter →

arxiv 2411.11526 v2 pith:SLXDME6P submitted 2024-11-18 cond-mat.mes-hall

Lucas E. A. Stehouwer , Cécile X. Yu , Barnaby van Straaten , Alberto Tosato , Valentin John , Davide Degli Esposti , Asser Elsayed , Davide Costa
show 5 more authors
Stefan D. Oosterhout Nico W. Hendrickx Menno Veldhorst Francesco Borsoi Giordano Scappucci
This is my paper · ORCID
classification cond-mat.mes-hall
keywords chargenoisespinqubitsgermaniumquantumwellsGe/SiGeheterostructureshyperfinedynamicaldecouplingholeisotopicpurification
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 argues that growing the strained germanium quantum well on a germanium wafer, rather than on silicon, reduces material disorder enough that even micron-scale multi-dot spin-qubit devices stay quiet. The benchmark it establishes is an average charge noise of $\sqrt{S_0} = 0.3(1)\ \mu\mathrm{eV}/\sqrt{\mathrm{Hz}}$ at 1 Hz across different locations and device sizes, about two to five times lower than earlier Ge/SiGe stacks grown on silicon. Using the spin qubit itself as a noise sensor with dynamical-decoupling pulse sequences, the paper separates electrical charge noise from magnetic hyperfine noise and identifies the two nuclear baths that limit coherence: $^{73}$Ge in the quantum well and $^{29}$Si in the surrounding SiGe barriers. If correct, the result says that the main remaining path to long coherence is isotopic purification of both germanium and silicon, and that scaling to larger arrays does not by itself reintroduce the noise that shortens qubit lifetimes.

What carries the argument

The load-bearing object is the epitaxial stack: a strained 16 nm Ge quantum well in a SiGe barrier grown on a Ge wafer with a low threading-dislocation density, whose reduced lattice mismatch suppresses disorder. The load-bearing instrument is the qubit used as a local spectrometer: Carr-Purcell-Meiboom-Gill trains of $N$ refocusing pulses ($N=1,\dots,64$) act as tunable frequency filters, and the decay of each echo sequence as a function of wait time $\tau$ maps the power spectral density $S_{f_L}(f)$ of Larmor-frequency noise. That noise is described by the model $$S_{f_L}(f)=\frac{S_0}{f}+S_{0,\mathrm{hf}}\,$e^{{-(f-f_{^{73}}$\mathrm{Ge}})^2/(2\sigma_{^{73}\mathrm{Ge}}^2)}$$ (with a second Gaussian for $^{29}$Si), where the $S_0/f$ term is interpreted as charge noise coupling through the spin-orbit interaction and the Gaussian peaks are hyperfine noise from spinful nuclei; fitting the echo data against this model yields the paper's central numbers.

What would settle it

Repeat the CPMG-64 experiment on the same device geometry with an isotopically purified stack ($^{70}$Ge quantum well and $^{28}$Si$^{70}$Ge barriers, residual $^{73}$Ge and $^{29}$Si below 0.01%). If the attribution is right, the collapse-and-revival dips at $\gamma_{{}^{73}\mathrm{Ge}}B$ and $\gamma_{{}^{29}\mathrm{Si}}B$ should disappear while the $S_0/f$ term stays at about $0.17\times 10^9\ \mathrm{Hz}^2/\mathrm{Hz}$; if the $1/f$ term also drops or reshapes, slow nuclear-spin diffusion was contributing to the low-frequency noise all along.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that a Ge/SiGe heterostructure grown on a Ge wafer combines the two properties a scalable spin-qubit platform needs: low electrical noise and measurable, countable magnetic noise sources. Charge-noise spectroscopy on devices containing up to ten quantum dots and four radio-frequency charge sensors returns $\sqrt{S_0}=0.3(1)\ \mu\mathrm{eV}/\sqrt{\mathrm{Hz}}$ at 1 Hz, and Coulomb-peak tracking at 10 mHz gives comparable noise that is uniform across a 1.5 $\mu$m array. The paper then establishes hole-spin qubit control in the same material and, through CPMG-N noise spectroscopy, shows that the qubit frequency noise is a $1/f$ component plus Gaussian peaks at the Larmor precession frequencies of $^{73}$Ge and $^{29}$Si nuclei. From those peaks it extracts integrated hyperfine noise amplitudes $\sigma_f = 180(8)$ kHz for $^{73}$Ge and $\sigma_f = 47(5)$ kHz for $^{29}$Si, so that the coherence of natural-germanium qubits is set by nuclear spins, while the $1/f$ component is attributed to charge noise and sets a much weaker limit once the nuclei are removed.

Load-bearing premise

The qubit-noise model attributes the slow, 1/f part of the measured frequency wobble to charge noise in the device; if slow nuclear-spin diffusion is actually producing that part, the extracted voltage-noise levels and the charge-noise-limited coherence times would need to be revised.

Editorial extensions

If this is right

  • Charge noise stays low as devices grow: the ten-dot, four-sensor array shows comparable noise to small linear arrays across a 1.5 $\mu$m distance, so the platform does not obviously degrade when scaled to dense, micron-scale circuits.
  • At magnetic fields below roughly 150 mT, $^{73}$Ge hyperfine noise dominates qubit decoherence; above it, charge noise through spin-orbit coupling takes over, so operating-field choice and material purity are both controllable levers.
  • The demonstrated $^{29}$Si coherence modulation means the hole wavefunction reaches into the SiGe barrier, so isotopic purification must include the barrier layers, not only the germanium quantum well.
  • With both nuclear baths removed, the paper projects Hahn-echo times near 0.4 ms at 10 mT (versus tens of microseconds measured in natural material), quantifying the coherence gain available from purification.
  • The spin-echo-derived voltage noise of $12(1)\ \mu\mathrm{V}/\sqrt{\mathrm{Hz}}$ at 1 Hz is a factor of two better than the comparable silicon-substrate device in the reference it builds on, consistent with the directly measured charge-noise improvement.

Reading between the lines

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

  • If threading dislocations are the dominant charge-noise source, then pushing dislocation density further down in Ge-wafer growth should directly lower $\sqrt{S_0}$; this is an extension of the paper's speculation, not one of its measurements.
  • The $^{29}$Si signature could be used as a routine wafer-screening metric: the CPMG intensity of the $^{29}$Si dip at a few sites should correlate with interface abruptness, giving a quick quality flag before full qubit fabrication.
  • Local spin-echo mapping across the 2D array (three qubit sites here) could be extended to every dot in the array to produce a noise map that directly guides which dots are most suitable as logical qubits.
  • The same CPMG-plus-model protocol can be run on other spin-qubit materials to build comparable noise budgets, since it yields separate numbers for charge and hyperfine noise without needing a second device.
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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

4 major / 7 minor

Summary. The manuscript characterizes charge and magnetic noise in Ge/SiGe heterostructures grown on Ge wafers. Using flank and Coulomb-peak-tracking methods on small linear arrays and on a 3-4-3 ten-dot array with four rf sensors, the authors report an average charge noise of sqrt(S0) = 0.3(1) ueV/sqrt(Hz) at 1 Hz and comparable noise at 10 mHz across a 1.5 um scale. They then demonstrate EDSR control of hole spin qubits and use CPMG-N sequences to fit a noise model comprising a 1/f term and a Gaussian peak at the 73Ge Larmor frequency, extracting S0, S0,hf, and sigma_Ge-73. From these fitted parameters they derive an effective voltage noise of 12(1) uV/sqrt(Hz) at 1 Hz and charge-noise-limited T2* estimates of 3.7(3) us at 117.5 mT and 44(4) us at 10 mT. They also observe a coherence dip in CPMG-64 data, attribute it to 29Si in the SiGe barriers, and extract a gyromagnetic ratio of 8.6(9) MHz/T and an integrated 29Si hyperfine noise amplitude of 47(5) kHz. The paper concludes with predictions for coherence improvements under isotopic purification.

Significance. If the extracted parameters hold, this work provides a valuable benchmark for hole spin qubits in strained Ge: a low and spatially uniform charge noise at the micron scale, a quantitative decomposition of electrical versus hyperfine noise, and a falsifiable 29Si signature. The open data repository, the use of two independent electrical noise methods, and the gyromagnetic-ratio check for 29Si are notable strengths that enhance reproducibility. The main caveat is that the spin-echo-derived low-frequency component is assigned to charge noise on plausibility grounds; however, the direct electrical charge-noise measurements are model-independent and constitute the core benchmark. The quantitative noise budget and the prediction of coherence gains from isotopic purification are of clear interest to the semiconductor spin qubit community.

major comments (4)
  1. [Charge and hyperfine noise in hole spin qubits (Eq. 9 and Methods, 'Charge noise-limited T2*')] The low-frequency term S0/f in Eq. (9) is assigned to charge noise, and this assignment is load-bearing for the voltage-noise conversion in Eq. (1), the claimed two-fold improvement over Ref. [29], and the charge-noise-limited T2* predictions in the Methods. The paper explicitly acknowledges that slow nuclear diffusion could contribute to this term, and the supporting consistency check (120(10) versus 80(60) uV/sqrt(Hz) at 10 mHz) compares different devices and dots with large scatter. I request either a control fit of the CPMG data with an alternative low-frequency spectral shape (e.g., f^-2 or a zero-frequency Lorentzian) showing that S0 and the derived voltage noise are stable, or a direct measurement that isolates charge noise (e.g., simultaneous qubit and sensor noise correlation), or a clear qualification that the voltage-noise and T2* numbers are conditional on this assumption. Without one of these, the spin-echo-derived voltage-noise claim is not fully supported.
  2. [Methods, 'Estimation of the hyperfine coupling constants', Eq. (11)] The integrated hyperfine noise sigma_f = 180(8) kHz and T2* = 1.25(5) us are computed from the Gaussian parameters S0,hf and sigma_Ge-73 that were fitted to the same CPMG traces used to build the model. These numbers are therefore model outputs rather than independent determinations, and the quoted uncertainties omit systematic contributions from the model form and the filter-function implementation. To make the estimates falsifiable, please report Ramsey free-induction decay measurements on the same qubits (or an independent measurement of the Overhauser field distribution) and/or state the sensitivity of sigma_f to the fitting range and to the choice of filter function.
  3. [Eq. (1) and surrounding text in 'Charge and hyperfine noise in hole spin qubits'] The conversion from S0 to voltage noise via Eq. (1) uses the g-factor susceptibility Delta_g/Delta_V = 6.7e-4 mV^-1 taken from Ref. [54] (a preprint) without an uncertainty, and assumes spatially homogeneous, uncorrelated traps under the gates. The propagation of only the statistical uncertainty in S0 leads to the quoted sqrt(S_V) = 12(1) uV/sqrt(Hz), which is misleading given the systematic uncertainty in the susceptibility and the correlation assumption. Please provide the source and uncertainty of Delta_g/Delta_V and discuss how correlated fluctuations would modify the result, or present this value with a clear caveat.
  4. [Hyperfine interaction with 29Si nuclei, Fig. 4] The identification of the 29Si hyperfine signature rests on the harmonic choice n=2 in f_dip = (2n-1)/(2 t_dip) and on a two-stage fit of Eq. (10) in which the 73Ge parameters are fixed. The extracted gyromagnetic ratio 8.6(9) MHz/T is consistent with 29Si, but only three field points and one dip are used, and the quoted sigma_Si-29 = 99(20) kHz likely depends on the fitting range and on the fixed 73Ge parameters. Please justify the harmonic assignment, report the stability of the 29Si parameters to these choices, and provide residuals or a goodness-of-fit metric for the fits in Fig. 4a.
minor comments (7)
  1. [Page 5, first sentence of the CPMG-1 paragraph] The phrase 'an CPMG-1 experiment' should be 'a CPMG-1 experiment'.
  2. [Eq. (1)] The displayed formula appears to show S_V = S0 (Delta_fL/Delta_V)^2, but the correct relation by unit analysis and by the numerical result 140 uV^2/Hz is S_V = S0 / (Delta_fL/Delta_V)^2; please correct the typo.
  3. [Supplementary Fig. S10(d) caption] The caption states 'S0=0.17(3) Hz2/Hz', which is missing the factor 10^9 that appears in the main text (S0=0.17(3)x10^9 Hz^2/Hz); please fix the units or the prefactor.
  4. [Abstract and 'Hyperfine interaction with 29Si nuclei'] The phrase 'identify coherence modulations associated with the interaction with the 29Si nuclear spin bath' is stronger than the evidence supports, given the single dip and the harmonic-assignment caveat; suggest 'attribute coherence modulations to' or similar.
  5. [Fig. 1e] Please state the number of spectra per gate and clarify whether the uncertainty on the average charge noise is the standard deviation of the distribution or the standard error of the mean.
  6. [Methods, 'Qubit noise model'] The fitting procedure follows Ref. [29] via reference only; since the filter-function treatment is central to the extraction, please include at least a brief description of the filter functions and the fitting procedure in the main text or Methods.
  7. [Eq. (14) and surrounding Methods text] The choice of frequency cutoffs f_L = 1 mHz and f_H = 1 MHz is not justified; please provide the reasoning or cite a reference for these values.

Circularity Check

1 steps flagged · score 6.0 of 10

The charge-noise-limited T2* values are closed-form restatements of the S0 fitted to the same CPMG data, so the 'predictions' are forced by the fit; the material charge-noise benchmark itself is independent.

  1. fitted input called prediction [Results section 'Charge and hyperfine noise in hole spin qubits' and Methods 'Charge noise-limited T2*' (Eqs. 12-14)]
    "Performing a similar analysis on the low-frequency component, we predict a charge noise-limited dephasing time of T∗2 = 3.7(3) µs at 117.5 mT, and 44(4) µs at 10 mT (Methods). ... We evaluate the charge noise-limited T∗2 using the extracted voltage noise amplitude of √SV = 12(1) µV/√Hz at 1 Hz and the effective g-factor susceptibility of ∆g/∆V = 6.7·10−4 mV−1."

    The predicted T∗2 is computed by substituting S0, extracted from fits to the CPMG-N coherence traces with the Eq. 9 model, into the closed-form quasi-static formulas T∗2 = 1/(√(2π)∆f) and ∆f = (∆g/∆V)∆VRMS, with ∆VRMS derived from SV = S0/(∆fL/∆V)2. No free-induction decay or low-field coherence data enter at this stage; the result is a deterministic rearrangement of the fitted S0 together with the assumed 1/f charge-noise attribution and the same-group g-factor susceptibility from Ref. [54]. The 'prediction' therefore reduces by construction to the fitted amplitude, although the underlying charge-noise benchmark is measured independently.

full rationale

The material-level charge noise benchmark (√S0 = 0.3(1) µeV/√Hz from flank and CPT measurements) is an independent electrical characterization and is not circular. The spin-echo noise analysis is largely honest data analysis: S0, S0,hf, and σGe−73 are fit to CPMG-N data using an empirical model (Eq. 9) inherited from Ref. [29], and the integrated σf values are summaries of those fitted parameters rather than independent predictions. The circular step is the subsequent 'prediction' of charge-noise-limited T2*: Eqs. 12-14 are closed-form rearrangements of the already-fitted S0, converted through a same-group g-factor susceptibility [54] and the assumed 1/f charge-noise attribution. The quoted 3.7(3) µs and 44(4) µs values are therefore forced by the fit and add no new information, even though they are framed as predictions. The hyperfine-derived T2* = 1.25(5) µs is compared with measured 1-2 µs values from same-group Ref. [54]; this is a broad consistency check, not circular, because those measured values were not used in the fit. The authors' explicit acknowledgment that slow nuclear diffusion could also contribute to S0 is a correctness risk rather than circularity. Because the core material benchmark is independent but one set of 'predictions' reduces by construction to fitted inputs, the circularity score is 6.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central claims rest on the noise model from Ref [29], on the attribution of the 1/f component to charge noise, and on the g-factor susceptibility from the authors' own preprint. The measured noise values themselves are direct data, but the derived predictions (T2*, T2^H) depend on these assumptions and on several fitted parameters.

free parameters (7)
  • S0 (charge noise amplitude at 1 Hz) = 0.17(3) x 10^9 Hz^2/Hz (average from qubits Q1, Q4, Q7)
    Fitted to CPMG coherence decays using Eq. (9); used to derive voltage noise and charge-noise-limited T2*.
  • S0,hf (73Ge hyperfine peak amplitude) = 1.1(3) x 10^6 Hz^2/Hz (average)
    Fitted parameter in the Gaussian peak of Eq. (9); determines σf = 180(8) kHz.
  • σ_Ge-73 (73Ge frequency spread) = 12(1) kHz
    Fitted Gaussian width; enters σf and T2* estimate.
  • S0,Si-29 (29Si hyperfine peak amplitude) = 9.0(8) x 10^3 Hz^2/Hz
    Fitted from the expanded model Eq. (10) in the two-stage 29Si analysis.
  • σ_Si-29 (29Si frequency spread) = 99(20) kHz
    Fitted Gaussian width for 29Si peak; yields σf = 47(5) kHz for 29Si.
  • α (spectral exponent) = 0.9(2) flank average, 1.64(5) CPT, 1.0(3) Q4/Q7
    Exponent in S0/f^α fits of charge noise spectra; varies across methods and conditions.
  • harmonic index n for 29Si dip conversion = 2
    Chosen to map observed dip time to frequency; n=2 is required for agreement with the known 29Si gyromagnetic ratio.
assumptions (5)
  • domain assumption The qubit frequency noise PSD is S_fL = S0/f + S0,hf exp(-(f-f_Ge-73)^2/(2σ^2)), Eq. (9), from Ref [29].
    Adopted without re-derivation; the Gaussian peak shape and 1/f component structure are assumed. Entered in Methods 'Qubit noise model'.
  • domain assumption The low-frequency 1/f component is attributed to charge noise rather than nuclear spin diffusion.
    The authors state this is 'more plausible' but acknowledge nuclear diffusion could contribute. This attribution underpins the voltage-noise conversion and charge-noise-limited T2* predictions.
  • domain assumption The 29Si coherence modulation is modeled by adding a Gaussian peak with fixed precession frequency f_Si-29 = 8.465 MHz/T × B.
    The second Gaussian peak in Eq. (10) is assumed; the gyromagnetic ratio is taken from known nuclear physics, but the presence of the peak in the qubit spectrum is a modeling assumption.
  • domain assumption g-factor susceptibility Δg/ΔV = 6.7x10^-4 mV^-1 from simulation (Ref [54]).
    Used to convert fitted frequency noise S0 to voltage noise. Ref [54] is the authors' own preprint; not independently verified here.
  • domain assumption In-plane and out-of-plane g-tensor components (gx=-gy=0.04, gz=11) for angle estimation.
    Taken from Refs [6] and [29]; used to estimate the magnetic field misalignment angle of 3 degrees.

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Cite this review

Pith. "Pith review of Exploiting epitaxial strained germanium for scaling low noise spin qubits at the micron-scale." pith.science (2026). https://pith.science/paper/SLXDME6P

@misc{pith2026241111526,
  author       = {Pith},
  title        = {Pith review of: Exploiting epitaxial strained germanium for scaling low noise spin qubits at the micron-scale},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SLXDME6P}},
  note         = {Machine review of arXiv:2411.11526}
}
abstract

Disorder in the heterogeneous material stack of semiconductor spin qubit systems introduces noise that compromises quantum information processing, posing a challenge to coherently control large-scale quantum devices. Here, we exploit low-disorder epitaxial strained quantum wells in Ge/SiGe heterostructures grown on Ge wafers to comprehensively probe the noise properties of complex micron-scale devices comprising of up to ten quantum dots and four rf-charge sensors arranged in a two-dimensional array. We demonstrate an average charge noise of $\sqrt{S_{0}}=0.3(1)$ $\mu\mathrm{eV}/\sqrt{\mathrm{Hz}}$ at 1 Hz across different locations on the wafer, providing a benchmark for quantum confined holes. We then establish hole-spin qubit control in these heterostructures and extend our investigation from electrical to magnetic noise through spin echo measurements. Exploiting dynamical decoupling sequences, we quantify the power spectral density components arising from the hyperfine interaction with $^{73}$Ge spinful isotopes and identify coherence modulations associated with the interaction with the $^{29}$Si nuclear spin bath near the Ge quantum well. We estimate an integrated hyperfine noise amplitude $\sigma_f$ of 180(8) kHz from $^{73}$Ge and of 47(5) kHz from $^{29}$Si, underscoring the need for full isotopic purification of the qubit host environment.

Figures

Figures reproduced from arXiv: 2411.11526 by the authors.

Figure 1
Figure 1. Charge noise in minimal quantum dot linear arrays. (a) False-coloured atomic force microscopy image (top panel) of a device lithographically identical to the measured ones. The device consists of two sensor (dark blue) and two plunger gates (light blue) to define up to four quantum dots, barrier gates (red/green), screening gates (purple), and platinum germanosilicide ohmic contacts (orange). The scale bar is 100 nm… view at source ↗
Figure 2
Figure 2. Charge noise in a micron-scale 2D quantum dot array. (a) Schematic of the gate layout of the quantum dot array, hosting 10 quantum dot qubits under plunger gates P1-P10 arranged in a 3-4-3 configuration. Quantum dots are read out by nearby charge sensors NS, ES, SS, WS. Scale bar represents 1 µm. The inter-connectivity of the array is shown below. The quantum dots investigated are shown as circles with a thick black… view at source ↗
Figure 3
Figure 3. Charge and hyperfine noise characterisation using spin echo measurement protocols. (a) Charge stability diagram for qubit pair Q1-Q4. Labels I, M, and R indicate approximate virtual plunger gate voltages associated with the initialisation, manipulation and read-out stages, respectively. (b) Exemplary Q1 EDSR spectroscopy (top panel) and Rabi oscillations (bottom panel) at B = 117.5 mT. Larmor (fLQ1 ) and Rabi freque… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Influence of 29Si nuclear spin on qubit co￾herence. (a) Collapse and revival of the qubit Q7 spin state during a CPMG-64 measurement protocol for a magnetic field of 138 (blue), 152 (orange), and 166 (green) mT. The dashed black line shows the best fit when taking into…

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Forward citations

Cited by 2 Pith papers

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    A room-temperature permanent magnet outside the cryostat aligns the magnetic field in-plane for a germanium hole spin qubit, yielding T2* = 13 us, T2H = 88 us, and single-qubit gate fidelities above 99.9%.

  2. Modular Autonomous Virtualization System for Two-Dimensional Semiconductor Quantum Dot Arrays

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    MAViS autonomously builds a five-layer stack of virtual plunger and barrier gates for a ten-dot Ge/SiGe array, keeping charge states fixed while tuning couplings.

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