Pith. sign in

REVIEW 2 major objections 3 minor 2 cited by

Coupling a $^{73}$Ge nuclear spin to an electrostatically defined quantum dot

T0 review · 2 major / 3 minor · reviewed 2026-08-04 · deepseek-v4-flash

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

Pith's one-line read A single 73Ge nuclear spin couples to a silicon quantum dot electron, with hyperfine coupling tunable from 180 to 350 kHz via gate voltages.

desk verdict First clean ESR spectrum of a single 73Ge nucleus in a SiMOS dot; worthy of refereeing, with two fixable gaps and a small overclaim. read the letter →

arxiv 2510.03981 v1 pith:WXEJ6KMM submitted 2025-10-05 cond-mat.mes-hall quant-ph

Paul Steinacker , Gauri Goenka , Rocky Yue Su , Tuomo Tanttu , Wee Han Lim , Santiago Serrano , Tim Botzem , Jesus D. Cifuentes
show 12 more authors
Shao Qi Lim Jeffrey C. McCallum Brett C. Johnson Fay E. Hudson Kok Wai Chan Christopher C. Escott Andre Saraiva Chih Hwan Yang Vincent Mourik Andrea Morello Andrew S. Dzurak Arne Laucht
This is my paper · ORCID
classification cond-mat.mes-hallquant-ph
keywords 73Genuclearspinsiliconquantumdothyperfineinteractionspin-9/2quditelectronresonanceionimplantationSiMOSreadout
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

The paper sets out to show that a single 73Ge nucleus — a spin-9/2 system with ten accessible states — can be hyperfine-coupled to the electron of a gate-defined quantum dot in silicon. Using isotope-selective implantation of 73Ge near the Si/SiO2 interface, the authors observe ten equally spaced electron spin resonance lines, the fingerprint of a single spin-9/2 nucleus, with a spacing A = 353(1) kHz. They then show that A is electrically tunable from about 180 to 350 kHz by changing the lateral gate voltages, which moves and re-confines the electron wavefunction. The paper presents this as a viable ten-level qudit for silicon quantum computing, with the advantage that, being isoelectronic, it adds no charge and the electron can be shuttled away without destroying the nuclear state.

What carries the argument

The Fermi-contact hyperfine interaction, A = (2/3)ℏ² μ0 γe γGe |Ψ(0)|², is the central coupling. It links the electron spin to the 73Ge nuclear spin (I=9/2) and splits each electron spin resonance into 2I+1 = 10 equally spaced lines separated by A. The electron wavefunction density at the nucleus, |Ψ(0)|², is what the gate electrodes alter; moving and confining the electron changes |Ψ(0)|² and hence A, yielding the observed tunability from 180 to 350 kHz. The ten-line spectrum is the direct experimental signature of a single spin-9/2 nucleus.

What would settle it

Run the identical experiment on a device fabricated without any 73Ge implantation; if the same ten-line pattern appears, or if a double-resonance measurement shows a nuclear Larmor frequency different from 73Ge's expected gyromagnetic ratio of 1.49 MHz per tesla, the central claim is wrong.

Watch

Extended reading notes

Core claim

In a SiMOS device, a single 73Ge nuclear spin is coupled to a quantum-dot electron through the Fermi-contact hyperfine interaction. The electron spin resonance spectrum shows ten equally spaced peaks with spacing A = 353(1) kHz, matching a spin-9/2 nucleus. The coupling strength is tuned between 179(1) and 357(2) kHz by adjusting the confinement gate voltage, which shifts and squeezes the electron wavefunction, changing its density at the nucleus. This is the first demonstration of a 73Ge nucleus coupled to a gate-defined quantum dot, extending the family of isoelectronic nuclear spins in silicon beyond 29Si to a high-spin qudit.

Load-bearing premise

The claim assumes that the ten equally spaced lines in the electron spin resonance spectrum come from a single 73Ge nucleus in the quantum dot and not from some other impurity or a set of nuclei.

Editorial extensions

If this is right

  • The ten-dimensional Hilbert space of a single 73Ge nucleus is now addressable in a gate-defined dot, enabling future qudit control and readout experiments.
  • Because 73Ge is isoelectronic, the quantum-dot electron can be shuttled away and back without destroying the nuclear spin coherence, a key requirement for scalable architectures that move electrons between dots.
  • The gate-voltage tunability of the hyperfine coupling provides a control knob for adjusting the electron-nuclear interaction strength during device operation.
  • With improved electrostatic control (e.g., a more effective J-gate), deterministic initialization via ENDOR and coherent nuclear spin manipulation should become possible, as the authors note.
  • In the longer term, this could support entanglement distribution between distant nuclear spins and repeated weak measurements of a nuclear spin, as the authors suggest.

Reading between the lines

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

  • If the identification holds, the same fabrication approach could place multiple 73Ge nuclei at known positions, each serving as a ten-level qudit, with electron shuttling providing a scalable coupling mechanism between them — a step the paper leaves implicit.
  • The demonstrated range of A (roughly 180–350 kHz) is small compared with donor hyperfine couplings (~100 MHz), implying that nuclear readout via the electron will be slower; quantifying this trade-off experimentally would be a natural next step.
  • Because no control device without 73Ge is shown, a direct comparison with an unimplanted but otherwise identical device would test whether the ten-line pattern is specific to 73Ge, ruling out alternative spin-9/2 defects.
  • The linear dependence of A on the simulated wavefunction shift suggests that A could serve as a sensitive, in-situ probe of the electron wavefunction position and confinement in such devices.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 3 minor

Summary. The manuscript reports the observation of hyperfine coupling between a single 73Ge nuclear spin (I=9/2) and an electron spin in a gate-defined SiMOS quantum dot. The ESR spectrum exhibits ten equally spaced peaks, assigned to the ten nuclear spin projections, with a hyperfine constant A ≈ 353 kHz. The authors further demonstrate electrical tuning of A from ~180 to ~350 kHz via confinement gate voltages. The work is positioned as a step toward using 73Ge as a spin-9/2 qudit in silicon quantum dots, exploiting the isoelectronic nature of Ge for electron shuttling.

Significance. If the identification holds, this is the first demonstration of a single 73Ge nuclear spin hyperfine-coupled to an electrostatically defined quantum dot, extending the toolkit of nuclear qudits in silicon to isoelectronic group-IV impurities. The direct extraction of A from the peak spacing is model-independent, and the repeated measurements showing stability (353–357 kHz) are a strength. The gate-voltage tunability is a useful feature for future shuttling-based architectures. However, the evidence for the nuclear species assignment is incomplete, which tempers the significance until the ambiguity is resolved.

major comments (2)
  1. [Nuclear spin signature, Fig. 2] The assignment of the ten equally spaced ESR peaks to a single 73Ge nucleus relies solely on the peak count and the implantation dose. The paper does not report the fitted Lorentzian amplitudes, which would discriminate between a single thermal I=9/2 nucleus (near-equal intensities) and an alternative of nine equivalent 29Si nuclei (I=1/2) producing the same number of equally spaced lines with binomial intensities (1:9:36:84:126:126:84:36:9:1). Given the 800 ppm residual 29Si and the fact that Ref. 14 observed hyperfine-coupled 29Si nuclei in a similar device, this alternative is not implausible. The authors should provide the measured peak amplitudes (or a control device without 73Ge) and compare to the expected intensity patterns. Without this, the central claim that the coupled nucleus is 73Ge is not fully established.
  2. [Data Availability (Appendix)] The manuscript states that the data supporting this work are available in a Zenodo repository, but gives no URL, DOI, or accession code. Because the central claims rest on fitting ten-peak spectra and the tuning curve, the absence of a retrievable dataset prevents independent verification of the peak amplitudes and the extracted A values. Please provide the repository link in the final version.
minor comments (3)
  1. [Fig. 3(b)] There is a numerical inconsistency between the text and the figure: the text says the linear fit slope is m = 473 kHz/V, while the equation in the figure is A(VCB) = 437 kHz/V · VCB + 227 kHz. One of these is a typo and should be corrected.
  2. [Eq. (2) and f_ESR] The Hamiltonian in Eq. (2) uses γe and γGe as positive constants, while the ESR frequency is written as f_ESR = |γe|B0 + m_I A. Please clarify the sign convention for the electron gyromagnetic ratio and define the ordering of m_s levels.
  3. [Eq. (3) reference] The sentence 'In Eq. 3, we assume...' refers to the Fermi-contact expression labeled (3). Ensure the equation numbering is clear in the final typeset version, as the current text might be ambiguous.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: hyperfine coupling A is extracted from measured ESR peak spacings, and the gate-voltage dependence is a direct fit to data.

full rationale

The central observable in this paper is the hyperfine constant A, obtained by fitting the spacing of the observed ESR lines in Fig. 2(b) to the Larmor relation f_ESR = |γ_e|B0 + m_I A. This is a parameter extraction from data, not a prediction generated by the model: Eq. (2) defines the Hamiltonian containing A as a free parameter, and Eq. (3) is introduced only after the fact to interpret the measured A as a Fermi-contact interaction. No value of A is predicted from |Ψ(0)|^2 and then used to claim agreement. Similarly, the gate-voltage tuning in Fig. 3(b) is presented as a linear fit to measured A values; the simulation provides the shift of the electron-density center as an explanatory coordinate, but the paper does not use the simulation to produce A values that are then compared with the fit. The identification of the ten ESR peaks as the signature of a single spin-9/2 73Ge nucleus relies on the line count, the implantation conditions, and the expected spectrum of a spin-9/2 system. Imposing equal spacing in the Lorentzian fit is a standard spectral parameterization and does not by itself manufacture the central claim; the existence of ten resolvable resonances and the extracted A values are data-driven. The only notable self-citation is Ref. [14] (Hensen et al.), used to motivate the choice of 800 ppm implantation dose. That prior work is an externally reported experimental result, not an unverified internal premise, and it is not load-bearing for the present identification of 73Ge. Possible concerns about the absence of a no-73Ge control device or about alternative multinuclear 29Si explanations are matters of experimental control and interpretation, not circularity of the derivation chain.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the standard hyperfine Hamiltonian and Fermi-contact theory, plus the experimental assumption that a single implanted 73Ge nucleus is the source of the 10-line spectrum. No new physical entities are introduced. The only fitted parameters are descriptive linear-fit coefficients for the tuning curve; the hyperfine constant itself is a directly measured spectral splitting.

free parameters (2)
  • Linear fit slope of A vs VCB = 473 kHz/V (0.437 kHz/mV)
    Fit to measured hyperfine values as a function of confinement voltage in Fig. 3(b); descriptive of the tuning data, not used as an input to a prediction.
  • Linear fit intercept of A vs VCB = 227 kHz
    Fit to measured A at the reference confinement voltage; descriptive of the tuning curve, not load-bearing for the central claim.
assumptions (4)
  • domain assumption The electron-nuclear spin system is described by H = B0(γe Sz + γGe Iz) + A S·I (Eq. 1-2), with no quadrupole or anisotropic terms.
    Used to derive f_ESR = γe B0 + mI A and to interpret the equal peak spacing; the authors state anisotropic terms are negligible after tuning to maximize HFI.
  • standard math The hyperfine coupling is given by the Fermi-contact expression A = (2/3)ℏ²μ0γeγGe|Ψ(0)|² (Eq. 3).
    Standard result for s-wave electron-nucleus contact interaction, invoked to connect A to the electron density at the nucleus.
  • domain assumption The implanted 73Ge dose produces on average one 73Ge nucleus in the active dot region (800 ppm target).
    The experiment relies on a single 73Ge being present and coupled; the 10-peak spectrum is consistent with one I=9/2 nucleus.
  • domain assumption Electrostatic simulations of the electron wavefunction (Fig. 3) correctly capture the dot position and confinement as a function of gate voltages.
    Used to explain the gate-voltage tuning of A as a shift of wavefunction overlap; simulation details are not fully presented in the paper.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Coupling a $^{73}$Ge nuclear spin to an electrostatically defined quantum dot." pith.science (2026). https://pith.science/paper/WXEJ6KMM

@misc{pith2026251003981,
  author       = {Pith},
  title        = {Pith review of: Coupling a $^73$Ge nuclear spin to an electrostatically defined quantum dot},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WXEJ6KMM}},
  note         = {Machine review of arXiv:2510.03981}
}
abstract

Single nuclear spins in silicon are a promising resource for quantum technologies due to their long coherence times and excellent control fidelities. Qubits and qudits have been encoded on donor nuclei, with successful demonstrations of Bell states and quantum memories on the spin-1/2 $^{31}$P and cat-qubits on the spin-7/2 $^{123}$Sb nuclei. Isoelectronic nuclear spins coupled to gate-defined quantum dots, such as the naturally occurring $^{29}$Si isotope, possess no additional charge and allow for the coupled electron to be shuttled without destroying the nuclear spin coherence. Here, we demonstrate the coupling and readout of a spin-9/2 $^{73}$Ge nuclear spin to a gate-defined quantum dot in SiMOS. The $^{73}$Ge nucleus was implanted by isotope-selective ion-implantation. We observe the hyperfine interaction (HFI) to the coupled quantum dot electron and are able to tune it from 180 kHz to 350 kHz, through the voltages applied to the lateral gate electrodes. This work lays the foundation for future spin control experiments on the spin-9/2 qudit as well as more advanced experiments such as entanglement distribution between distant nuclear spins or repeated weak measurements.

Figures

Figures reproduced from arXiv: 2510.03981 by the authors.

Figure 1
Figure 1. FIG. 1: Device and electron-nucleus coupled system. (a) Scanning electron micrograph of a nominally identical device. The [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Nuclear spin signature in ESR. (a) Normalized even electron spin probability [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Hyperfine interaction tuning. (a) Simulated electron [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

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

  1. Noise-resilient and Scalable Quantum Error Correction for Nuclear Spin Qubits in Silicon with Electron Shuttling

    quant-ph 2026-07 conditional novelty 6.0 of 10

    A protocol called electron pair interferometry transfers the parity of nuclear spin qubits to the measurable singlet/triplet state of a shuttled electron pair, enabling CSS quantum error correction.

  2. Maximizing the nondemolition nature of a quantum measurement via an adaptive readout protocol

    quant-ph 2025-11 conditional novelty 6.0 of 10

    An adaptive readout protocol that switches to non-perturbing negative-result measurements after one positive outcome improves nuclear-qudit QND readout fidelity to 99.61% with a 3x speedup.

Reference graph

Works this paper leans on

47 extracted references · 6 canonical work pages · cited by 2 Pith papers

  1. [1]

    T.et al.Storing quantum information for 30 seconds in a nanoelectronic device.Nature Nanotech- nology9, 986–991 (2014)

    Muhonen, J. T.et al.Storing quantum information for 30 seconds in a nanoelectronic device.Nature Nanotech- nology9, 986–991 (2014). URLhttps://www.nature. com/articles/nnano.2014.211

    2014

  2. [2]

    T.et al.Precision tomography of a three-qubit donor quantum processor in silicon.Nature 601, 348–353 (2022)

    Mądzik, M. T.et al.Precision tomography of a three-qubit donor quantum processor in silicon.Nature 601, 348–353 (2022). URLhttps://www.nature.com/ articles/s41586-021-04292-7

    2022

  3. [3]

    URLhttps: //www.nature.com/articles/s41565-024-01853-5

    Thorvaldson, I.et al.Grover’s algorithm in a four-qubit silicon processor above the fault-tolerant threshold.Na- ture Nanotechnology20, 472–477 (2025). URLhttps: //www.nature.com/articles/s41565-024-01853-5

    2025

  4. [4]

    URL 5 https://arxiv.org/abs/2509.24766

    Zhang, C.et al.Demonstration of quantum error de- tection in a silicon quantum processor (2025). URL 5 https://arxiv.org/abs/2509.24766. 2509.24766

    arXiv 2025

  5. [5]

    J.et al.High-fidelity readout and control of a nuclearspinqubitinsilicon.Nature496, 334–338(2013)

    Pla, J. J.et al.High-fidelity readout and control of a nuclearspinqubitinsilicon.Nature496, 334–338(2013). URLhttps://www.nature.com/articles/nature12011

    2013

  6. [6]

    URLhttps: //www.science.org/doi/10.1126/science.1189075

    Neumann, P.et al.Single-Shot Readout of a Single Nu- clear Spin.Science329, 542–544 (2010). URLhttps: //www.science.org/doi/10.1126/science.1189075

    doi:10.1126/science.1189075 2010

  7. [7]

    URLhttps://www.science.org/doi/ 10.1126/science.1131871

    Childress, L.et al.Coherent Dynamics of Coupled Elec- tron and Nuclear Spin Qubits in Diamond.Science314, 281–285 (2006). URLhttps://www.science.org/doi/ 10.1126/science.1131871

    doi:10.1126/science.1131871 2006

  8. [8]

    J.et al.Coherent Control of a Single Si 29 Nuclear Spin Qubit.Physical Review Letters113, 246801 (2014)

    Pla, J. J.et al.Coherent Control of a Single Si 29 Nuclear Spin Qubit.Physical Review Letters113, 246801 (2014). URLhttps://link.aps.org/doi/10. 1103/PhysRevLett.113.246801

    2014

Show all 47 references
  1. [9]

    URLhttps://pubs.aip

    Laucht, A.et al.High-fidelity adiabatic inversion of a31P electron spin qubit in natural silicon.Applied Physics Letters104, 092115 (2014). URLhttps://pubs.aip. org/aip/apl/article/132507

    2014

  2. [10]

    A.et al.Quantum dots in Si/SiGe 2DEGs with Schottky top-gated leads.New Journal of Physics 7, 246–246 (2005)

    Slinker, K. A.et al.Quantum dots in Si/SiGe 2DEGs with Schottky top-gated leads.New Journal of Physics 7, 246–246 (2005). URLhttps://iopscience.iop.org/ article/10.1088/1367-2630/7/1/246

    2005 doi

  3. [11]

    Assali, L. V. C.et al.Hyperfine interactions in sil- icon quantum dots.Physical Review B83, 165301 (2011). URLhttps://link.aps.org/doi/10.1103/ PhysRevB.83.165301

    2011

  4. [12]

    URLhttps://www.nature.com/articles/ s41467-019-13416-7

    Zhao, R.et al.Single-spin qubits in isotopically enriched siliconatlowmagneticfield.Nature Communications10, 5500 (2019). URLhttps://www.nature.com/articles/ s41467-019-13416-7

    2019

  5. [13]

    Lawrie, W. I. L.et al.Quantum dot arrays in silicon and germanium.Applied Physics Letters116, 080501 (2020). URLhttps: //pubs.aip.org/apl/article/116/8/080501/38569/ Quantum-dot-arrays-in-silicon-and-germanium

    2020

  6. [14]

    URLhttps://www.nature.com/articles/ s41565-019-0587-7

    Hensen, B.et al.A silicon quantum-dot-coupled nu- clear spin qubit.Nature Nanotechnology15, 13– 17 (2020). URLhttps://www.nature.com/articles/ s41565-019-0587-7

    2020

  7. [15]

    M., Lutz, J

    Witzel, W. M., Lutz, J. J. & Luhman, D. R. Remark- able Prospect for Quantum-Dot-Coupled Tin Qubits in Silicon.PRX Quantum3, 040320 (2022). URLhttps: //link.aps.org/doi/10.1103/PRXQuantum.3.040320

    2022 doi

  8. [16]

    Isotopeengineeringofsilicon and diamond for quantum computing and sensing appli- cations.MRS Communications4, 143–157 (2014)

    Itoh, K.M.&Watanabe, H. Isotopeengineeringofsilicon and diamond for quantum computing and sensing appli- cations.MRS Communications4, 143–157 (2014). URL http://link.springer.com/10.1557/mrc.2014.32

    2014 doi

  9. [17]

    URLhttps://www.nature.com/ articles/nnano.2014.216

    Veldhorst, M.et al.An addressable quantum dot qubit with fault-tolerant control-fidelity.Nature Nanotechnol- ogy9, 981–985 (2014). URLhttps://www.nature.com/ articles/nnano.2014.216

    2014

  10. [18]

    W., Bhatt, R

    Pica, G., Lovett, B. W., Bhatt, R. N., Schenkel, T. & Lyon, S. A. Surface code architecture for donors and dots in silicon with imprecise and nonuniform qubit couplings. Physical Review B93, 035306 (2016). URLhttps:// link.aps.org/doi/10.1103/PhysRevB.93.035306

    2016 doi

  11. [19]

    Veldhorst, M., Eenink, H. G. J., Yang, C. H. & Dzu- rak, A. S. Silicon CMOS architecture for a spin- based quantum computer.Nature Communications8, 1766 (2017). URLhttps://www.nature.com/articles/ s41467-017-01905-6

    2017

  12. [20]

    URLhttps://www.science.org/doi/10.1126/sciadv

    Li, R.et al.A crossbar network for silicon quan- tum dot qubits.Science Advances4, eaar3960 (2018). URLhttps://www.science.org/doi/10.1126/sciadv. aar3960

    2018 doi

  13. [21]

    J., Bertet, P

    Morello, A., Pla, J. J., Bertet, P. & Jamieson, D. N. Donor Spins in Silicon for Quantum Tech- nologies.Advanced Quantum Technologies3, 2000005 (2020). URLhttps://onlinelibrary.wiley.com/doi/ 10.1002/qute.202000005

    2020 doi

  14. [22]

    F.et al.Scaling silicon-based quan- tum computing using CMOS technology.Nature Elec- tronics4, 872–884 (2021)

    Gonzalez-Zalba, M. F.et al.Scaling silicon-based quan- tum computing using CMOS technology.Nature Elec- tronics4, 872–884 (2021). URLhttps://www.nature. com/articles/s41928-021-00681-y

    2021

  15. [23]

    URLhttps://www.nature.com/ articles/s41467-024-49182-4

    Künne, M.et al.The SpinBus architecture for scaling spin qubits with electron shuttling.Nature Communica- tions15, 4977 (2024). URLhttps://www.nature.com/ articles/s41467-024-49182-4

    2024

  16. [24]

    & Fogarty, M

    Siegel, A., Strikis, A. & Fogarty, M. Towards Early Fault Tolerance on a 2×N Array of Qubits Equipped with Shuttling.PRX Quantum5, 040328 (2024). URLhttps: //link.aps.org/doi/10.1103/PRXQuantum.5.040328

    2024 doi

  17. [25]

    Nature Communications12, 4114 (2021)

    Yoneda, J.et al.Coherent spin qubit transport in silicon. Nature Communications12, 4114 (2021). URLhttps: //www.nature.com/articles/s41467-021-24371-7

    2021

  18. [26]

    URLhttps://www

    Noiri, A.et al.A shuttling-based two-qubit logic gate for linking distant silicon quantum processors.Nature Communications13, 5740 (2022). URLhttps://www. nature.com/articles/s41467-022-33453-z

    2022

  19. [27]

    URLhttps://www.nature.com/articles/ s41534-022-00615-2

    Seidler, I.et al.Conveyor-mode single-electron shuttling in Si/SiGe for a scalable quantum com- puting architecture.npj Quantum Information8, 100 (2022). URLhttps://www.nature.com/articles/ s41534-022-00615-2

    2022

  20. [28]

    URLhttps://link.aps.org/doi/10

    Zwerver, A.et al.Shuttling an Electron Spin through a Silicon Quantum Dot Array.PRX Quantum4, 030303 (2023). URLhttps://link.aps.org/doi/10. 1103/PRXQuantum.4.030303

    2023

  21. [29]

    URLhttps://www.nature.com/articles/ s41467-024-46519-x

    Xue, R.et al.Si/SiGe QuBus for single electron information-processing devices with memory and micron- scale connectivity function.Nature Communications15, 2296 (2024). URLhttps://www.nature.com/articles/ s41467-024-46519-x

    2024

  22. [30]

    URLhttps://www.nature.com/articles/ s41565-025-01920-5

    De Smet, M.et al.High-fidelity single-spin shut- tling in silicon.Nature Nanotechnology20, 866– 872 (2025). URLhttps://www.nature.com/articles/ s41565-025-01920-5

    2025

  23. [31]

    URL https://arxiv.org/abs/2507.15554

    Lin, S.-C.et al.Interplay of Zeeman Splitting and Tunnel Coupling in Coherent Spin Qubit Shuttling (2025). URL https://arxiv.org/abs/2507.15554. Version Number: 2

    2025

  24. [32]

    D.et al.A surface code quantum com- puter in silicon.Science Advances1, e1500707 (2015)

    Hill, C. D.et al.A surface code quantum com- puter in silicon.Science Advances1, e1500707 (2015). URLhttps://www.science.org/doi/full/10. 1126/sciadv.1500707

    2015

  25. [33]

    G.et al.Tomography of entangling two-qubit logic operations in exchange-coupled donor electron spin qubits.Nature Communications15, 8415 (2024)

    Stemp, H. G.et al.Tomography of entangling two-qubit logic operations in exchange-coupled donor electron spin qubits.Nature Communications15, 8415 (2024). URLhttps://www.nature.com/articles/ s41467-024-52795-4

    2024

  26. [34]

    G.et al.Scalable entanglement of nuclear spins mediated by electron exchange.Science389, 1234–1238 (2025)

    Stemp, H. G.et al.Scalable entanglement of nuclear spins mediated by electron exchange.Science389, 1234–1238 (2025). URLhttps://www.science.org/ doi/full/10.1126/science.ady3799

    2025 doi

  27. [35]

    URLhttps://www.nature.com/articles/ 6 s41586-020-2057-7

    Asaad, S.et al.Coherent electrical control of a sin- gle high-spin nucleus in silicon.Nature579, 205– 209 (2020). URLhttps://www.nature.com/articles/ 6 s41586-020-2057-7

    2020

  28. [36]

    URLhttps://www.nature.com/articles/ s41467-024-45368-y

    Fernández De Fuentes, I.et al.Navigating the 16- dimensional Hilbert space of a high-spin donor qudit with electric and magnetic fields.Nature Communications15, 1380 (2024). URLhttps://www.nature.com/articles/ s41467-024-45368-y

    2024

  29. [37]

    URLhttps://www.nature.com/articles/ s41567-024-02745-0

    Yu, X.et al.Schrödinger cat states of a nu- clear spin qudit in silicon.Nature Physics21, 362– 367 (2025). URLhttps://www.nature.com/articles/ s41567-024-02745-0

    2025

  30. [38]

    URLhttps://linkinghub.elsevier

    Vaartjes, A.et al.Certifying the quantumness of a nu- clear spin qudit through its uniform precession.Newton 1, 100017 (2025). URLhttps://linkinghub.elsevier. com/retrieve/pii/S295063602500009X

    2025

  31. [39]

    URLhttps://www.nature.com/ articles/s41467-017-00378-x

    Tosi, G.et al.Silicon quantum processor with ro- bust long-distance qubit couplings.Nature Communi- cations8, 450 (2017). URLhttps://www.nature.com/ articles/s41467-017-00378-x

    2017

  32. [40]

    J., Ferguson, A

    Angus, S. J., Ferguson, A. J., Dzurak, A. S. & Clark, R. G. Gate-Defined Quantum Dots in Intrinsic Silicon. Nano Letters7, 2051–2055 (2007). URLhttps://pubs. acs.org/doi/10.1021/nl070949k

    doi

  33. [41]

    URLhttps://link.aps.org/doi/10

    Veldhorst, M.et al.Spin-orbit coupling and opera- tion of multivalley spin qubits.Physical Review B92, 201401 (2015). URLhttps://link.aps.org/doi/10. 1103/PhysRevB.92.201401

    2015

  34. [42]

    Leon, R. C. C.et al.Coherent spin control of s-, p-, d- and f-electrons in a silicon quantum dot.Nature Com- munications11, 797 (2020). URLhttps://www.nature. com/articles/s41467-019-14053-w

    2020

  35. [43]

    J., Ferguson, A

    Angus, S. J., Ferguson, A. J., Dzurak, A. S. & Clark, R. G. A silicon radio-frequency single electron transistor. Applied Physics Letters92, 112103 (2008). URLhttps: //pubs.aip.org/apl/article/92/11/112103/326252/ A-silicon-radio-frequency-single-electron

    2008

  36. [44]

    E.et al.Pauli Blockade in Silicon Quan- tum Dots with Spin-Orbit Control.PRX Quantum2, 010303 (2021)

    Seedhouse, A. E.et al.Pauli Blockade in Silicon Quan- tum Dots with Spin-Orbit Control.PRX Quantum2, 010303 (2021). URLhttps://link.aps.org/doi/10. 1103/PRXQuantum.2.010303

    2021

  37. [45]

    Van De Walle, C. G. & Blöchl, P. E. First-principles calculations of hyperfine parameters.Physical Review B47, 4244–4255 (1993). URLhttps://link.aps.org/ doi/10.1103/PhysRevB.47.4244

    1993 doi

  38. [46]

    Gross, J. A. Designing Codes around Interactions: The Case of a Spin.Physical Review Letters127, 010504 (2021). URLhttps://link.aps.org/doi/10. 1103/PhysRevLett.127.010504

    2021

  39. [47]

    A., Godfrin, C., Blais, A

    Gross, J. A., Godfrin, C., Blais, A. & Dupont-Ferrier, E. Hardware-efficient error-correcting codes for large nuclear spins.Physical Review Applied22, 014006 (2024). URLhttps://link.aps.org/doi/10.1103/ PhysRevApplied.22.014006. APPENDIX EXPERIMENT AL DEVICE The device studied...

    2024

Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.