{"id":"673b57fb-1144-4b98-af05-488ea8d64ceb","arxiv_id":"2411.11526","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"Epitaxial germanium quantum wells on germanium wafers show 0.3 μeV/√Hz charge noise at 1 Hz and coherence limited by 73Ge and 29Si nuclear spins, motivating isotopic purification.","lead":"Researchers measured noise in germanium spin qubit devices grown on germanium wafers, finding low electrical noise and identifying magnetic noise from two nuclear isotopes. The work supports a route toward larger, more coherent spin qubit arrays by pinpointing material improvements and isotopic purification targets.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The low-frequency S0 term in Eq. (9) is assigned to charge noise rather than nuclear diffusion, and both the CPMG fit and the voltage-noise conversion assume that assignment; an alternative spectral-shape fit would settle it.","rationale":"The reader's verdict is CONDITIONAL with medium risk, and the identified weakest assumption matches the concern raised here: the low-frequency S0 component in Eq. (9) is attributed to charge noise, but the supporting evidence for that attribution is not independent. The direct charge-noise measurements via the flank and Coulomb-peak-tracking methods are credible and open, so the material benchmark sqrt(S0) = 0.3(1) ueV/sqrt(Hz) is not the primary risk. The spin-qubit noise extraction, however, depends on a model where S0/f is assumed to be charge noise; the subsequent conversion to voltage noise uses a computed g-factor susceptibility and a specific trap distribution, making the comparison with direct voltage noise partly circular. The CPMG filter functions are insensitive to very low frequencies, so the N-dependence of the fits is the main constraint, and an alternative nuclear-diffusion spectral shape could plausibly fit the same envelopes. This does not warrant rejection: the 29Si assignment is independently supported by the extracted gyromagnetic ratio of 8.6(9) MHz/T, and the direct charge-noise measurements stand on their own. The concern is addressable by a concrete re-analysis of the open data with an alternative low-frequency noise model. Since the reader already conditioned the verdict on essentially this issue, the verdict should remain CONDITIONAL, with no change needed.","tokens_in":21351,"tokens_out":8970,"duration_ms":91811,"concrete_test":"Using the open data repository, re-fit the full CPMG-N dataset (N=1,2,4,8,16,32 at B=117.5 and 138.2 mT for Q1/Q4/Q7, plus the CPMG-1 B-sweep) with an alternative noise model in which the S0/f term is replaced by a nuclear-diffusion term S0'/f^2 or a zero-frequency Lorentzian, keeping the 73Ge and 29Si Gaussian peaks fixed in form. Compare reduced chi-square or BIC; if the alternative fits equally well or better, the charge-noise attribution is not established and the T2* predictions should be labeled model-dependent. If the 1/f model is significantly preferred, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is the identification of the extracted low-frequency term S0 in Eq. (9) with charge noise. The paper acknowledges the ambiguity: 'While nuclear spin effects could in principle also contribute to the low-frequency noise spectrum due to slow nuclear diffusion... we find it more plausible to associate the low frequency component S0/f to charge noise in the device.' The support offered is a conversion of S0 into an effective voltage noise of 12(1) uV/sqrt(Hz) at 1 Hz using a computed g-factor susceptibility Delta g/Delta V = 6.7e-4 mV^-1, obtained under the assumption of spatially homogeneous, uncorrelated traps under the gates. This is circular in structure: the CPMG-N data are fit with a model that already contains a 1/f charge-noise term, and the extracted S0 is then interpreted through a conversion that assumes charge-noise coupling. The CPMG filter functions suppress low-frequency noise, so the constraint on S0 comes from the N-dependence of the envelopes and from the assumed Gaussian peak shape; a slow nuclear-diffusion component (e.g., f^-2 or a zero-frequency Lorentzian) could partially absorb the same decay and shift S0. If the attribution is wrong, the voltage-noise comparison, the charge-noise-limited T2* predictions (3.7(3) us at 117.5 mT, 44(4) us at 10 mT), and the claimed two-fold improvement over Ref [29] would all require revision. The measured free-induction T2* values of 1-2 us are consistent with hyperfine domination under either interpretation and do not discriminate.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":21764,"tokens_out":12136,"duration_ms":113455,"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":[{"comment":"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.","section":"Charge and hyperfine noise in hole spin qubits (Eq. 9 and Methods, 'Charge noise-limited T2*')"},{"comment":"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.","section":"Methods, 'Estimation of the hyperfine coupling constants', Eq. (11)"},{"comment":"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.","section":"Eq. (1) and surrounding text in 'Charge and hyperfine noise in hole spin qubits'"},{"comment":"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.","section":"Hyperfine interaction with 29Si nuclei, Fig. 4"}],"minor_comments":[{"comment":"The phrase 'an CPMG-1 experiment' should be 'a CPMG-1 experiment'.","section":"Page 5, first sentence of the CPMG-1 paragraph"},{"comment":"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.","section":"Eq. (1)"},{"comment":"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.","section":"Supplementary Fig. S10(d) caption"},{"comment":"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.","section":"Abstract and 'Hyperfine interaction with 29Si nuclei'"},{"comment":"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.","section":"Fig. 1e"},{"comment":"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.","section":"Methods, 'Qubit noise model'"},{"comment":"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.","section":"Eq. (14) and surrounding Methods text"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The genuinely new and useful results here are the uniform charge-noise benchmark on the Ge-wafer platform — 0.3(1) μeV/√Hz at 1 Hz across six dots and two devices, plus the 10-dot array — and the first detection of 29Si coherence modulation in a Ge/SiGe qubit, backed by a gyromagnetic-ratio fit of 8.6(9) vs 8.465 MHz/T. The CPMG noise decomposition into 73Ge hyperfine and low-frequency 1/f terms is plausible but rests on an attribution of that 1/f term to charge noise that the authors themselves flag as an assumption.\n\nThe paper does several things well. Data are open; the charge noise is characterized by two independent methods (flank and Coulomb peak tracking) that agree; the statistics across devices and locations are real; and the uniformity across a 1.5-micron array is a useful data point for the scaling argument. The 29Si identification is cross-checked against the known gyromagnetic ratio and is a solid new observation.\n\nSoft spots, in proportion. The low-frequency S0 attribution is the one I'd push on. The stress-test note is right that CPMG filter functions suppress low frequencies, so the constraint on S0 comes mainly from the N-dependence and the assumed Gaussian peak shape; a slow nuclear-diffusion component (e.g. a zero-frequency Lorentzian) could partially absorb the same decay. The authors acknowledge this ambiguity in the text. Their supporting check is the conversion of S0 to a voltage noise of 12(1) μV/√Hz at 1 Hz and comparison with the direct dot measurements at 10 mHz, which lands in the same range. That is suggestive but not a proof. A cleaner test would be a fit with an alternative spectral shape or a measurement at lower magnetic field where the 73Ge peak moves away.\n\nThe T2* “predictions” for isotopically purified material are extrapolations from parameters fitted on the same coherence traces using the model inherited from Ref [29]; they are not independent forecasts. The authors should label them as such. The harmonic index for the 29Si dip (n=2) is chosen without justification; a simultaneous fit of n with the peak parameters would strengthen the claim, though the gyromagnetic agreement already helps. The two-fold improvement over Ref [29] in voltage noise is based on differently computed g-factor susceptibilities, so I would not hang too much weight on that comparison.\n\nWho this is for: the Ge/SiGe spin-qubit community, materials growers, and people doing noise spectroscopy. It deserves serious peer review. I would send it out, asking for the alternative spectral-shape check on S0 and a clearer statement of what is fitted versus predicted. I'd cite the charge-noise benchmark and the 29Si result in my own work.","headline":"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.","tokens_in":22364,"tokens_out":2414,"would_cite":true,"duration_ms":25794,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["charge noise","spin qubits","germanium quantum wells","Ge/SiGe heterostructures","hyperfine noise","dynamical decoupling","hole spin qubits","isotopic purification"],"falsifier":"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.","tokens_in":21181,"feed_emoji":"⚛️","tokens_out":8081,"duration_ms":77029,"temperature":0.7,"pith_summary":"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.","feed_headline":"Germanium spin qubits reach low-noise benchmark","feed_subtitle":"A Ge/SiGe stack on a Ge wafer cuts qubit frequency jitter and pinpoints the nuclear spins still limiting coherence.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the heterostructure itself: growth of the low-dislocation Ge/SiGe stack on a Ge wafer, with the mobility and threading-dislocation metrics used throughout.","marker":"[24]"},{"why":"Supplies the qubit noise model (Eq. 9), its fitting procedure, and the single-qubit-on-Si-substrate comparison against which the voltage-noise improvement is measured.","marker":"[29]"},{"why":"Provides the similar-depth Ge/SiGe-on-Si charge-noise benchmark ($\\sqrt{S_0}=0.6\\ \\mu\\mathrm{eV}/\\sqrt{\\mathrm{Hz}}$) used to quantify the improvement.","marker":"[16]"},{"why":"Provides the shallow Ge/SiGe-on-Si charge-noise benchmark ($\\sqrt{S_0}=1.4\\ \\mu\\mathrm{eV}/\\sqrt{\\mathrm{Hz}}$) used in the comparison.","marker":"[30]"},{"why":"Provides the silicon-substrate Coulomb-peak-tracking noise value (about 20 $\\mu\\mathrm{eV}/\\sqrt{\\mathrm{Hz}}$ at 10 mHz) that the 2D array measurement is compared with.","marker":"[20]"},{"why":"Supplies the 3-4-3 dot array design and operating procedures adapted here for dense occupancy and qubit control.","marker":"[6]"},{"why":"Supplies the flank and Coulomb-peak-tracking methods used for the direct charge-noise spectra.","marker":"[15]"},{"why":"Supplies the analysis relation converting current noise to charge-noise energy (Eq. 2) and the link between charge noise and electrically active dislocations.","marker":"[18]"},{"why":"Supplies the gate-by-gate g-factor susceptibility calculation and the experimentally observed $T_2^*$ range used to convert spin-echo-derived $S_0$ into voltage noise and to check hyperfine-limited dephasing.","marker":"[54]"}],"fun_headline_variants":["Ge qubits hit low-noise mark, reveal nuclear culprits","Strained germanium cuts spin-qubit noise to record low","Micron-scale Ge qubit arrays: quiet, then nuclear-limited","Low-noise Ge hole qubits pinpoint nuclear spin noise","Germanium qubit array: charge noise tamed, nuclei remain"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Ge qubits hit low-noise mark, reveal nuclear culprits","Strained germanium cuts spin-qubit noise to record low","Micron-scale Ge qubit arrays: quiet, then nuclear-limited","Low-noise Ge hole qubits pinpoint nuclear spin noise","Germanium qubit array: charge noise tamed, nuclei remain"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000199,"raw_usage":{"total_tokens":1433,"prompt_tokens":1067,"completion_tokens":366,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":683,"completion_tokens_details":{"reasoning_tokens":280}},"tokens_in":683,"tokens_out":366,"duration_ms":3886,"temperature":1.0,"reasoning_tokens":280,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T18:24:50.037083+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Hendrickx, L","cited_arxiv_id":null,"evidence_quote":"Supplies the qubit noise model (Eq. 9), its fitting procedure, and the single-qubit-on-Si-substrate comparison against which the voltage-noise improvement is measured."},{"cited_title":"Lodari, N","cited_arxiv_id":null,"evidence_quote":"Provides the similar-depth Ge/SiGe-on-Si charge-noise benchmark ($\\sqrt{S_0}=0.6\\ \\mu\\mathrm{eV}/\\sqrt{\\mathrm{Hz}}$) used to quantify the improvement."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the shallow Ge/SiGe-on-Si charge-noise benchmark ($\\sqrt{S_0}=1.4\\ \\mu\\mathrm{eV}/\\sqrt{\\mathrm{Hz}}$) used in the comparison."},{"cited_title":"Massai, B","cited_arxiv_id":null,"evidence_quote":"Provides the silicon-substrate Coulomb-peak-tracking noise value (about 20 $\\mu\\mathrm{eV}/\\sqrt{\\mathrm{Hz}}$ at 10 mHz) that the 2D array measurement is compared with."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the 3-4-3 dot array design and operating procedures adapted here for dense occupancy and qubit control."},{"cited_title":"Kranz, S","cited_arxiv_id":null,"evidence_quote":"Supplies the flank and Coulomb-peak-tracking methods used for the direct charge-noise spectra."},{"cited_title":"Paquelet Wuetz, D","cited_arxiv_id":null,"evidence_quote":"Supplies the analysis relation converting current noise to charge-noise energy (Eq. 2) and the link between charge noise and electrically active dislocations."}],"review_version":1}