An Addressable and Tunable Module for Donor-based Scalable Silicon Quantum Computing

Peihao Huang; Shihang Zhang; Yu He

REVIEW 2 major objections 5 minor 91 references

An Addressable and Tunable Module for Donor-based Scalable Silicon Quantum Computing

T0 review · 2 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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

Pith's one-line read A single off-center ancilla donor in silicon provides both addressable single-qubit gates and tunable two-qubit coupling, with simulated fidelities above 99%.

desk verdict A genuinely new asymmetric ancilla-donor module resolves a known donor-qubit tension, but the 'surface-code-compatible' fidelities rest on unmodeled nuclear spin polarization that needs to be addressed before the claim fully lands. read the letter →

arxiv 2412.20055 v1 pith:J3HFEUJY submitted 2024-12-28 cond-mat.mes-hall quant-ph

Shihang Zhang , Yu He , Peihao Huang This is my paper · ORCID

classification cond-mat.mes-hallquant-ph

keywords silicondonor-basedspinqubitssuperexchangecouplingqubitaddressabilitytunabletwo-qubitgatessurfacecodearchitecturevalleyoscillationtoleranceSchrieffer-Wolfftransformationelectronresonance

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 proposes a three-donor module for a silicon spin-qubit processor in which one extra 'ancilla' donor is placed closer to one computing donor than to the other. The asymmetry is the key: the strong tunnel coupling gives the near qubit a hyperfine-shifted frequency that makes it individually addressable, while the weak coupling to the far qubit lets the two-qubit superexchange be switched off during single-qubit gates. The central claim is that this resolves a contradiction in symmetric designs, where the large tunneling needed for addressability leaves a residual two-qubit coupling that spoils single-qubit fidelity. With realistic charge noise and hyperfine dephasing, the paper reports single-qubit fidelities above 99.5% and SWAP/CZ fidelities above 99%, meeting the roughly 99% surface-code fault-tolerance threshold. If correct, the module is a building block for a scalable, globally controlled donor array that avoids micromagnets and relaxes donor placement precision to a few nanometers.

What carries the argument

The machinery is a three-site generalized Fermi-Hubbard Hamiltonian for two electrons on two computing donors (CDL, CDR) and one ancilla donor (ADM), with tunnel couplings $t_{c1}=t_{L,M}$ and $t_{c2}=t_{M,R}$ and detunings $\epsilon_1,\epsilon_2$. The addressability mechanism is the hyperfine ZZ coupling of Eq. (3): with the ancilla nuclear spin in $\left|\Uparrow\right\rangle$ and the computing-donor nuclei in $\left|\Downarrow\right\rangle$, shifting the electron wavefunction toward the ancilla changes its Larmor frequency by up to about $A\approx117$ MHz, enough for a $\sim14$ MHz frequency separation that suppresses crosstalk. The two-qubit mechanism is superexchange through the ancilla, an effective coupling mediated by virtual tunneling through the intermediate donor, obtained by a fourth-order Schrieffer-Wolff transformation (a perturbative elimination of the excited charge states), with $J_{\mathrm{SE}}\propto t_{c1}^2 t_{c2}^2 \beta(\epsilon_1,\epsilon_2)$, tunable by detunings and switchable by choosing $\epsilon_2$ in the off region. The resonance condition $(\epsilon_1-\epsilon_0)/(\epsilon_2-\epsilon_0)=t_{c1}/t_{c2}$ locates the high-fidelity SWAP window, while the CZ gate is best at detunings away from resonance where the superexchange is stronger than the qubit frequency detuning.

What would settle it

An experiment would measure the residual superexchange $J_{\mathrm{off}}$ between the two qubits while one qubit is being driven; if $J_{\mathrm{off}}$ cannot be reduced below about 0.07 MHz with $t_{c1}\approx80$ GHz and a reasonable $t_{c2}$, the predicted single-qubit fidelity above 99% would fail. A second direct check is to monitor the ancilla donor's nuclear spin polarization after many gate operations, since the addressability mechanism disappears if it flips.

Watch

Extended reading notes

Core claim

The paper's central discovery is that addressability and tunability can coexist in one donor module if the ancilla donor is placed asymmetrically between the two computing donors. With the computing-donor nuclear spins polarized down and the ancilla nuclear spin up, the electron qubit frequency is shifted by the hyperfine interaction when the electron is detuned toward the ancilla; this frequency shift is used to address one qubit without locally generated microwaves. The same ancilla mediates a fourth-order superexchange $J_{\mathrm{SE}} = t_{c1}^2 t_{c2}^2 \beta(\epsilon_1,\epsilon_2)$ between the two qubits, tunable through detunings $\epsilon_1$ and $\epsilon_2$. The asymmetry ($t_{c1} > t_{c2}$) is what lets the coupling be turned off, with residual $J_{\mathrm{off}} \lesssim 0.07$ MHz, while the addressed qubit still sees the large tunneling it needs for charge-noise resilience. The result is fault-tolerant single-qubit and two-qubit gates in the plotted operating windows and, because valley-induced tunneling oscillation is weaker along the [110] direction, a relaxed fabrication tolerance of roughly 5 nm.

Load-bearing premise

The load-bearing premise is that the ancilla donor's nuclear spin remains polarized upward and both computing donors' nuclear spins remain downward for the whole computation; if the ancilla's nucleus flips during repeated ESR pulses or over an error-correction cycle, the hyperfine frequency shift that provides addressability disappears and the crosstalk and fidelity estimates no longer hold.

Editorial extensions

If this is right

A single added ancilla donor per pair supplies both addressable single-qubit gates and tunable two-qubit gates, so the module avoids micromagnets, local field gradients, or two extra donors.
Single-qubit gate fidelities exceed 99.5% and SWAP/CZ fidelities exceed 99% in the modeled operating windows, meeting the roughly 99% surface-code fault-tolerance threshold.
The residual superexchange during single-qubit operations can be suppressed below $J_{\mathrm{off}}<0.07$ MHz without optimal control, and the allowed range of $t_{c2}$ is wide enough that donor placement precision relaxes to about 5 nm.
Tiling the modules into a two-dimensional array with global ESR/NMR pulses yields a surface-code-compatible processor in which the ancilla donor needs no readout.
With lower charge noise ($\sigma_\epsilon \approx 0.2$ $\mu$eV) and a hyperfine dephasing rate of 0.5 kHz, the paper projects single-qubit fidelities above 99.9%.

Reading between the lines

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

A natural next test, not reported in the paper, would be to fabricate a three-donor device with $t_{c1}\approx80$ GHz and $t_{c2}\approx20$ GHz and measure whether the residual coupling $J_{\mathrm{off}}$ during single-qubit operation drops below the 0.07 MHz threshold; that measurement would also probe the assumed nuclear-spin polarization lifetime.
The same frequency-modulator role of the ancilla could in principle be reused for selective readout or qubit reset, since the ancilla shifts the electron spin frequency without requiring a local magnetic field.
If the nuclear-spin polarization assumption holds, the module generalizes to different donor spacings and donor species, because the superexchange strength depends only on the two tunnel couplings and detunings rather than on identical donor placements.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

First thing to know: this is a real proposal paper, not a salami-slice claim. The new idea—using one ancilla donor asymmetrically placed between two computing donors, strongly coupled to one for addressability and weakly to the other for coupling turn-off—is a clean resolution of a known tension in donor-based spin qubits, and it is not in the cited literature. Second thing: the headline 'surface-code-compatible' fidelities are simulation outputs under chosen operating parameters, and the whole addressability mechanism silently depends on nuclear spin polarization staying fixed for many error-correction cycles. That assumption is stated but never modeled, and it is the paper's real soft spot.

What it does well: The paper lays out the contradiction clearly, shows why the symmetric scheme fails, and gives a simple geometric fix. The superexchange scaling J ∝ tc1^2 tc2^2 is standard fourth-order perturbation theory, and the paper checks it against numerical diagonalization away from charge transitions. The noise model includes charge noise and hyperfine-induced dephasing, and the parameter scans in Figs. 4–6 give a useful picture of where the fidelities exceed 99%. The discussion of valley oscillations and placement precision, with specific donor separations from the literature, is concrete and honest. The authors also compare briefly with micromagnet and two-ancilla alternatives, which is good context.

Where it is soft: The biggest issue is exactly what the stress test says. The addressability scheme relies on the CD nuclear spins staying down and the AD nuclear spin staying up. The paper justifies dropping the transverse hyperfine terms by saying flip-flops are off-resonant and the drive field can be oriented to suppress them, but it never quantifies the nuclear flip probability under a 1 µs ESR pulse, over a surface-code cycle, or with finite drive amplitude. A single ancilla flip shifts the qubit frequency by roughly the full hyperfine constant A (~117 MHz), not the 14 MHz discrimination they engineered, so the addressing breaks. This is a load-bearing resource, not a minor parameter. The authors should either model the depolarization dynamics or propose a repolarization protocol; as written, the surface-code claim is premature.

Two smaller issues. First, the operating parameters (tc1=80 GHz, tc2=20 GHz, detunings, frequency separation) are chosen to satisfy the target fidelities; that is legitimate engineering design, but it means the quoted numbers are not predictions in a strong sense. Second, the full error formulas and the fourth-order SW derivation are in a supplementary file that the arXiv version points to with a publisher-inserted URL; I could not check them. No simulation code is shipped, so the numerical results are not independently reproducible from the paper alone.

Bottom line: this is a paper for people working on donor-based qubit architectures, especially STM-patterned devices. It deserves a serious referee: the central asymmetric-module idea is worth engaging with, and the nuclear-polarization gap is addressable in revision. I would send it to peer review, with a referee request that the authors either model nuclear depolarization or clearly scope the claim away from 'surface-code-compatible.'

Referee Report

2 major / 5 minor

Summary. The paper proposes an asymmetric three-donor module for silicon-based electron spin qubits, in which a single ancilla donor (AD) is strongly tunnel-coupled to one computing donor (CDL) and weakly coupled to the other (CDR). The AD serves both as a frequency-modulating element that enables addressable single-qubit ESR control of CDL and as a mediator of a tunable superexchange interaction for two-qubit gates. Using a generalized Fermi-Hubbard model, a fourth-order Schrieffer-Wolff treatment for the superexchange, and numerical diagonalization, the authors map out operating regions in detuning and tunneling parameter space where single-qubit fidelities exceed 99.5% and SWAP/CZ fidelities exceed 99%. They further argue that the asymmetric tunnel couplings relax donor-placement precision to about 5 nm and propose a 2D surface-code-compatible processor layout.

Significance. If the underlying assumptions hold, the scheme is a genuinely useful design idea: it resolves a real tension between the large tunnel coupling needed for addressability and the small residual coupling needed for turning off two-qubit interactions. The paper is careful to compare analytical and numerical results for the superexchange, to identify high-fidelity operating windows, and to provide concrete parameter sets (tc1 = 80 GHz, tc2 = 20 GHz, B0 = 0.3 T, 1 microsecond gate time). The proposed asymmetry also has practical appeal for mitigating valley oscillations. The main risk is that the fidelity estimates depend on static nuclear spin polarization and on a simplified hyperfine Hamiltonian, and the paper does not quantify the lifetime of that polarization resource under operation. The claim of surface-code compatibility is therefore stronger than what the module-level simulations establish.

major comments (2)

[Sec. II, Eq. (3) and Sec. III.A] The addressability protocol assumes that the CD nuclear spins remain |down> and the AD nuclear spin remains |up> for the duration of operation. The Hamiltonian in Eq. (3) drops the transverse hyperfine terms, with the justification that flip-flop transitions are off-resonant and that nuclear coherence is long. The paper does not quantify the nuclear spin-flip probability under the proposed 1 microsecond ESR pulses, over a full error-correction cycle, or in the presence of finite drive amplitude and nuclear-spin noise. A single flip of the ancilla nuclear spin changes the electron spin resonance frequency by about A = 117 MHz and removes the frequency discrimination on which the entire scheme relies. This is a load-bearing resource, not a parameter tweak; the authors should estimate the flip rate quantitatively (including drive-induced flip-flop contributions) or provide a repolarization protocol, and state what nuclear polarization lifetime is required for the quoted fidelities.
[Sec. III.A, Sec. III.C, and Figs. 5-6] The single-qubit gate analysis is performed only for the left computing donor CDL, which is strongly coupled to the AD. The text states that the AD provides addressability only for CDL, so the mechanism by which CDR is addressed within a module is not established by the presented simulations. If CDR is meant to be addressed by an AD from an adjacent module, the paper should say so explicitly and estimate the resulting inter-module crosstalk and its effect on the CDL-CDR two-qubit gate, since the processor layout in Fig. 7 is part of the surface-code-compatibility claim. As written, the module-level claim that each pair of donors supports addressable single-qubit gates on both qubits is incomplete.

minor comments (5)

[Sec. II, basis states] The example state |(up,0,down)> is described as 'one electron with spin-up at CDL and one electron with spin-down at CDL'; the second site should be CDR, not CDL.
[Sec. III.A] The sentence 'the AD provides addressability only to the its nearest qubit' contains a grammatical error, and the surrounding text should clarify whether CDR is addressed by the same AD or by a different AD.
[Sec. III and Abstract] The threshold terminology is inconsistent: the introduction quotes the surface-code threshold as 99%, Section III sets an error threshold of 0.5%, and the abstract highlights single-qubit fidelities above 99.5%. Please state explicitly which threshold is used for single-qubit gates and which for two-qubit gates.
[Sec. III.A/B] The statement that the 'sweet line' (epsilon1 = epsilon2) can still be used for the CZ gate should be reconciled with Fig. 4(c), where the high-fidelity CZ region appears away from the qubit resonance condition; a brief explanation of the asymmetric sweet-line condition would help.
[Fig. 4(a)] The color scale is labeled log10(J) without units; please state the units of J (e.g., MHz) in the caption.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the gate fidelities are computed outputs of an explicit Fermi-Hubbard model with literature noise parameters, and the few self-citations are supporting rather than load-bearing.

full rationale

The central derivation is self-contained. The authors start from an explicit Fermi-Hubbard Hamiltonian (Eq. 2) with literature values for U, V, gamma_e, gamma_n, A, and noise parameters, then numerically diagonalize and use fourth-order Schrieffer-Wolff perturbation theory to obtain the superexchange coupling JSE (Eq. 4) and gate fidelities. The claimed fidelities are outputs of this model, not inputs: the operating points (tc1=80 GHz, tc2=20 GHz, detunings near resonance/sweet line, 14 MHz frequency discrimination) are chosen by scanning the parameter space and checking where the computed fidelity exceeds the 0.5% threshold. This is engineering design/optimization, not circular derivation. The few self-citations (e.g., Refs. [41] and [56] by co-authors) are used only as supporting references alongside independent sources (Refs. [46], [48], [60]) for established concepts such as superexchange scaling and hyperfine-frequency addressability; the key equations are derived in the paper and supplementary material rather than imported by citation. The nuclear-spin-polarization assumption (CD |down>, AD |up>) is a stated physical assumption, not a result derived from the target fidelities; whether it holds dynamically is a correctness/robustness question, not circularity. No 'prediction' in the paper is fixed by construction, and no load-bearing claim is a renamed fit.

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

The central results rest on a three-site Hubbard model with literature-derived parameters and selected operating points. No new physical entity is introduced; the ancilla donor is a standard phosphorus donor. The main non-standard assumptions are the truncation of the hyperfine interaction to ZZ coupling, the stability of initialized nuclear polarizations under operation, and the quantitative noise model.

free parameters (6)

tc1 (CDL-ADM tunneling) = 80 GHz nominal; threshold tc1 > 80 GHz for >99.5% single-qubit fidelity
Chosen large to suppress charge-noise dephasing and enable addressability; not fixed by experimental data.
tc2 (CDR-ADM tunneling) = 20 GHz nominal; upper bound ~30-40 GHz depending on tc1
Chosen small so residual superexchange Joff < 0.07 MHz during single-qubit gates; lower bound set by two-qubit gate speed.
B0 static magnetic field = 0.3 T
Sets Zeeman and hyperfine energy scales; chosen as a representative operating field.
Single-qubit gate time = 1 micro-second
Used to translate residual coupling and dephasing rates into error budgets; changing the gate time shifts the Joff threshold.
Error budget for gates = 0.5%
The authors set 0.5% as the fault-tolerance threshold; this drives the chosen frequency separation and the Joff < 0.07 MHz requirement.
Qubit frequency detuning for addressability = 10*sqrt(2) = approx 14 MHz
Chosen so off-resonant driving of idling qubits contributes less than 0.5% error for 1 micro-second pulses.

assumptions (6)

domain assumption The three-site Fermi-Hubbard model with on-site U, nearest-neighbor V, and nearest-neighbor tunneling captures the relevant physics of two electrons in three phosphorus donors.
Invoked in Sec. II, Eq. (2); all fidelity estimates follow from this Hamiltonian.
domain assumption The hyperfine interaction can be truncated to ZZ coupling, with electron-nuclear flip-flop terms neglected.
Sec. II after Eq. (3); this truncation is needed for the simple frequency-shift picture of addressability.
domain assumption Nuclear spin polarizations are initialized to CD down, AD up and remain stable during operations.
Sec. II and Sec. IIIA; the hyperfine shift used for addressability depends on these polarizations.
domain assumption Charge noise acts as a Gaussian quasi-static fluctuation of detunings with sigma_epsilon = 2 micro-eV, and hyperfine-induced dephasing is 1 kHz.
Sec. IIIB; gate fidelities are computed relative to these noise strengths, which are taken from specific experimental references.
domain assumption Surface-code compatibility can be assessed from per-gate fidelities above the assumed 0.5% error threshold without full error-correction simulation.
Secs. III and VI; the 'fault-tolerant threshold' claim is tied to this assumed error budget, not to a full surface-code cycle simulation.
domain assumption Tunneling magnitudes and valley-oscillation envelopes from effective-mass and tight-binding calculations in Refs. [36,37,82] apply to the proposed donor spacings.
Sec. IV; used to translate tunnel-coupling tolerances into the claimed ~5 nm donor placement precision.

how reviews work

0 comments

Cite this review

Pith. "Pith review of An Addressable and Tunable Module for Donor-based Scalable Silicon Quantum Computing." pith.science (2026). https://pith.science/paper/J3HFEUJY

@misc{pith2026241220055,
  author       = {Pith},
  title        = {Pith review of: An Addressable and Tunable Module for Donor-based Scalable Silicon Quantum Computing},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/J3HFEUJY}},
  note         = {Machine review of arXiv:2412.20055}
}

read the original abstract

Donor-based spin qubit offers a promising silicon quantum computing route for building large-scale qubit arrays, attributed to its long coherence time and advancements in nanoscale donor placement. However, the state-of-the-art device designs face scalability challenges, notably in achieving tunable two-qubit coupling and ensuring qubit addressability. Here, we propose a surface-code-compatible architecture, where each module has both tunable two-qubit gates and addressable single-qubit gates by introducing only a single extra donor in a pair of donors. We found that to compromise between the requirement of tunability and that of addressability, an asymmetric scheme is necessary. In this scheme, the introduced extra donor is strongly tunnel-coupled to one of the donor spin qubits for addressable single-qubit operation, while being more weakly coupled to the other to ensure the turning on and off of the two-qubit operation. The fidelity of single-qubit and two-qubit gates can exceed the fault-tolerant threshold in our design. Additionally, the asymmetric scheme effectively mitigates valley oscillations, allowing for engineering precision tolerances up to a few nanometers. Thus, our proposed scheme presents a promising prototype for large-scale, fault-tolerant, donor-based spin quantum processors.

Figures

Figures reproduced from arXiv: 2412.20055 by the authors.

**Figure 2.** FIG. 2. Schematic diagrams of configurations for implementing idling, addressable single-qubit operations, and tunable two [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** FIG. 3. The addressability of computing qubits for small tunneling [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: FIG. 4. Two-qubit coupling and gate fidelities for the asymmetric scheme, when [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: FIG. 5. The tunability of the superexchange in the asymmet [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 6.** Figure 6: FIG. 6. The tolerance for the tunneling in the asymmetric scheme. (a) The fidelity of single-qubit gates [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 7.** Figure 7: FIG. 7. The schematic of the scalable donor quantum computing device based on the asymmetric scheme. (a) 2D donor array [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

91 extracted references · 71 canonical work pages

[1]

B. E. Kane, Nature393, 133 (1998)

1998
[2]

J. J. L. Morton, A. M. Tyryshkin, R. M. Brown, S. Shankar, B. W. Lovett, A. Ardavan, T. Schenkel, E. E. Haller, J. W. Ager, and S. A. Lyon, Nature455, 1085 (2008)

2008
[3]

Fuechsle, S

M. Fuechsle, S. Mahapatra, F. A. Zwanenburg, M. Friesen, M. A. Eriksson, and M. Y. Simmons, Nat. Nanotechnol. 5, 502 (2010)

2010
[4]

A. M. Tyryshkin, S. Tojo, J. J. Morton, H. Riemann, N. V. Abrosimov, P. Becker, H. J. Pohl, T. Schenkel, M. L. Thewalt, K. M. Itoh, and S. A. Lyon, Nat. Mater. 11, 143 (2011)

2011
[5]

Fuechsle, J

M. Fuechsle, J. A. Miwa, S. Mahapatra, H. Ryu, S. Lee, O. Warschkow, L. C. L. Hollenberg, G. Klimeck, and M. Y. Simmons, Nat. Nanotechnol.7, 242 (2012)

2012
[6]

J. J. Pla, K. Y. Tan, J. P. Dehollain, W. H. Lim, J. J. Morton, D. N. Jamieson, A. S. Dzurak, and A. Morello, Nature 489, 541 (2012)

2012
[7]

Saeedi, S

K. Saeedi, S. Simmons, J. Z. Salvail, P. Dluhy, H. Rie- mann, N. V. Abrosimov, P. Becker, H.-J. Pohl, J. J. L. Morton, and M. L. W. Thewalt, Science342, 830 (2013)

2013
[8]

J. T. Muhonen, J. P. Dehollain, A. Laucht, F. E. Hud- son, R. Kalra, T. Sekiguchi, K. M. Itoh, D. N. Jamieson, J. C. McCallum, A. S. Dzurak, and A. Morello, Nat. Nan- otechnol. 9, 986 (2014)

2014

Show all 91 references

[9]

Harvey-Collard, N

P. Harvey-Collard, N. T. Jacobson, M. Rudolph, J. Dominguez, G. A. Ten Eyck, J. R. Wendt, T. Pluym, J. K. Gamble, M. P. Lilly, M. Pioro-Ladrière, and M. S. Carroll, Nat. Commun.8, 1029 (2017)

2017
[10]

Y. He, S. K. Gorman, D. Keith, L. Kranz, J. G. Keizer, and M. Y. Simmons, Nature571, 371 (2019)

2019
[11]

M. T. M¸ adzik, S. Asaad, A. Youssry, B. Joecker, K. M. Rudinger, E. Nielsen, K. C. Young, T. J. Proctor, A. D. Baczewski, A. Laucht, V. Schmitt, F. E. Hudson, K. M. Itoh, A. M. Jakob, B. C. Johnson, D. N. Jamieson, A. S. Dzurak, C. Ferrie, R. Blume-Kohout, and A. Morello, Nat...

2022
[12]

J. L. Pacheco, M. Singh, D. L. Perry, J. R. Wendt, G. Ten Eyck, R. P. Manginell, T. Pluym, D. R. Luh- man, M. P. Lilly, M. S. Carroll, and E. Bielejec, Rev. Sci. Instrum. 88, 123301 (2017)

2017
[13]

D.N.Jamieson, W.I.Lawrie, S.G.Robson, A.M.Jakob, B. C. Johnson, and J. C. McCallum, Mater. Sci. Semi- cond. Process.62, 23 (2017)

2017
[14]

Holmes, W

D. Holmes, W. I. L. Lawrie, B. C. Johnson, A. Asadpo- ordarvish, J. C. McCallum, D. R. McCamey, and D. N. Jamieson, Phys. Rev. Mater.3, 083403 (2019)

2019
[15]

A. M. Jakob, S. G. Robson, V. Schmitt, V. Mourik, M. Posselt, D. Spemann, B. C. Johnson, H. R. Fir- gau, E. Mayes, J. C. McCallum, A. Morello, and D. N. Jamieson, Adv. Mater.34, 2103235 (2022)

2022
[16]

Holmes, B

D. Holmes, B. Wilhelm, A. M. Jakob, X. Yu, F. E. Hud- son, K. M. Itoh, A. S. Dzurak, D. N. Jamieson, and A. Morello, Adv. Quantum Technol.7, 2300316 (2024)

2024
[17]

D. R. Ward, M. T. Marshall, D. M. Campbell, T. M. Lu, J. C. Koepke, D. A. Scrymgeour, E. Bussmann, and S. Misra, Appl. Phys. Lett.111, 193101 (2017)

2017
[18]

X. Wang, J. Wyrick, R. V. Kashid, P. Namboodiri, S. W. Schmucker, A. Murphy, M. D. Stewart, and R. M. Silver, Commun. Phys.3, 82 (2020)

2020
[19]

Bussmann, R

E. Bussmann, R. Butera, J. Owen, J. Randall, S. Rinaldi, A. Baczewski, and S. Misra, MRS Bull.46, 607 (2021)

2021
[20]

Kiczynski, S

M. Kiczynski, S. K. Gorman, H. Geng, M. B. Donnelly, Y. Chung, Y. He, J. G. Keizer, and M. Y. Simmons, Nature 606, 694 (2022)

2022
[21]

While referring to the theoretical results of tunneling magnitude based on tight-bind modeling, the distance can be around 7-12 (13-20) nm [39, 82]

nm [37]. While referring to the theoretical results of tunneling magnitude based on tight-bind modeling, the distance can be around 7-12 (13-20) nm [39, 82]. Within these ranges of distances, the oscillation on tunneling is within one order of magnitude [36]. Consequently, the...
[22]

H. G. Stemp, S. Asaad, M. R. v. Blankenstein, A. Vaart- jes, M. A. I. Johnson, M. T. Mądzik, A. J. A. Heskes, H. R. Firgau, R. Y. Su, C. H. Yang, A. Laucht, C. I. Ostrove, K. M. Rudinger, K. Young, R. Blume-Kohout, F. E. Hudson, A. S. Dzurak, K. M. Itoh, A. M. Jakob, B. C. Joh...

2024
[23]

Thorvaldson, D

I. Thorvaldson, D. Poulos, C. M. Moehle, S. H. Misha, H. Edlbauer, J. Reiner, H. Geng, B. Voisin, M. T. Jones, M. B. Donnelly, L. F. Pena, C. D. Hill, C. R. Myers, J. G. Keizer, Y. Chung, S. K. Gorman, L. Kranz, and M. Y. Simmons, arXiv preprint arXiv:2404.08741 (2024)

2024 arXiv
[24]

Loss and D

D. Loss and D. P. DiVincenzo, Phys. Rev. A57, 120 (1998)

1998
[25]

D. P. DiVincenzo, Fortschritte der Physik48, 771 (2000)

2000
[26]

D. S. Wang, A. G. Fowler, and L. C. L. Hollenberg, Phys. Rev. A83, 020302 (2011)

2011
[27]

A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Phys. Rev. A86, 032324 (2012)

2012
[28]

X. Xue, M. Russ, N. Samkharadze, B. Undseth, A. Sam- mak, G. Scappucci, and L. M. K. Vandersypen, Nature 601, 343 (2022)

2022
[29]

Scappucci, and S

A.Noiri, K.Takeda, T.Nakajima, T.Kobayashi, A.Sam- mak, G. Scappucci, and S. Tarucha, Nature 601, 338 (2022)

2022
[30]

A. R. Mills, C. R. Guinn, M. J. Gullans, A. J. Sigillito, M. M. Feldman, E. Nielsen, and J. R. Petta, Sci. Adv.8, eabn5130 (2022)

2022
[31]

J. Y. Huang, R. Y. Su, W. H. Lim, M. Feng, B. van Straaten, B. Severin, W. Gilbert, N. Dumoulin Stuyck, T. Tanttu, S. Serrano, J. D. Cifuentes, I. Hansen, A. E. Seedhouse, E. Vahapoglu, R. C. C. Leon, N. V. Abrosi- mov, H.-J. Pohl, M. L. W. Thewalt, F. E. Hudson, C. C. Escott,...

2024
[32]

C.-A. Wang, V. John, H. Tidjani, C. X. Yu, A. S. 13 Ivlev, C.Déprez, F.vanRiggelen-Doelman, B.D.Woods, N. W. Hendrickx, W. I. L. Lawrie, L. E. A. Stehouwer, S. D. Oosterhout, A. Sammak, M. Friesen, G. Scappucci, S. L. de Snoo, M. Rimbach-Russ, F. Borsoi, and M. Veld- horst, Sc...

2024
[33]

Kalra, A

R. Kalra, A. Laucht, C. D. Hill, and A. Morello, Phys. Rev. X4, 021044 (2014)

2014
[34]

Koiller, X

B. Koiller, X. Hu, and S. Das Sarma, Phys. Rev. Lett. 88, 027903 (2001)

2001
[35]

J. K. Gamble, N. T. Jacobson, E. Nielsen, A. D. Baczewski, J. E. Moussa, I. Montaño, and R. P. Muller, Phys. Rev. B91, 235318 (2015)

2015
[36]

Salfi, B

J. Salfi, B. Voisin, A. Tankasala, J. Bocquel, M. Usman, M. Y. Simmons, L. C. L. Hollenberg, R. Rahman, and S. Rogge, Phys. Rev. X8, 031049 (2018)

2018
[37]

Voisin, J

B. Voisin, J. Bocquel, A. Tankasala, M. Usman, J. Salfi, R. Rahman, M. Y. Simmons, L. C. L. Hollenberg, and S. Rogge, Nat. Commun.11, 6124 (2020)

2020
[38]

Joecker, A

B. Joecker, A. D. Baczewski, J. K. Gamble, J. J. Pla, A. Saraiva, and A. Morello, New J. Phys. 23, 073007 (2021)

2021
[39]

Hsueh, H

Y.-L. Hsueh, H. Büch, Y. Tan, Y. Wang, L. C. L. Hol- lenberg, G. Klimeck, M. Y. Simmons, and R. Rahman, Phys. Rev. Lett.113, 246406 (2014)

2014
[40]

Y. Wang, A. Tankasala, L. C. L. Hollenberg, G. Klimeck, M. Y. Simmons, and R. Rahman, npj Quantum Inf.2, 16008 (2016)

2016
[41]

H. Buch, S. Mahapatra, R. Rahman, A. Morello, and M. Y. Simmons, Nat. Commun.4, 2017 (2013)

2013
[42]

F. N. Krauth, S. K. Gorman, Y. He, M. T. Jones, P. Macha, S. Kocsis, C. Chua, B. Voisin, S. Rogge, R. Rahman, Y. Chung, and M. Y. Simmons, Phys. Rev. Appl. 17, 054006 (2022)

2022
[43]

Sarkar, J

A. Sarkar, J. Hochstetter, A. Kha, X. Hu, M. Y. Sim- mons, R. Rahman, and D. Culcer, npj Quantum Inf.8, 127 (2022)

2022
[44]

Kranz, S

L. Kranz, S. Roche, S. K. Gorman, J. G. Keizer, and M. Y. Simmons, Phys. Rev. Appl.19, 024068 (2023)

2023
[45]

M. T. Jones, M. S. Monir, F. N. Krauth, P. Macha, Y.-L. Hsueh, A. Worrall, J. G. Keizer, L. Kranz, S. K. Gorman, Y. Chung, R. Rahman, and M. Y. Simmons, ACS Nano 17, 22601 (2023)

2023
[46]

S. Mehl, H. Bluhm, and D. P. DiVincenzo, Phys. Rev. B 90, 045404 (2014)

2014
[47]

Srinivasa, H

V. Srinivasa, H. Xu, and J. M. Taylor, Phys. Rev. Lett. 114, 226803 (2015)

2015
[48]

T. A. Baart, T. Fujita, C. Reichl, W. Wegscheider, and L. M. Vandersypen, Nat. Nanotechnol.12, 26 (2017)

2017
[49]

M. J. Rančić and G. Burkard, Phys. Rev. B96, 201304 (2017)

2017
[50]

Martins, F

F. Martins, F. K. Malinowski, P. D. Nissen, S. Fal- lahi, G. C. Gardner, M. J. Manfra, C. M. Marcus, and F. Kuemmeth, Phys. Rev. Lett.119, 227701 (2017)

2017
[51]

Croot, S

X. Croot, S. Pauka, J. Watson, G. Gardner, S. Fallahi, M. Manfra, and D. Reilly, Phys. Rev. Appl.10, 044058 (2018)

2018
[52]

F. K. Malinowski, F. Martins, T. B. Smith, S. D. Bartlett, A. C. Doherty, P. D. Nissen, S. Fallahi, G. C. Gardner, M. J. Manfra, C. M. Marcus, and F. Kuem- meth, Phys. Rev. X8, 011045 (2018)

2018
[53]

F. K. Malinowski, F. Martins, T. B. Smith, S. D. Bartlett, A. C. Doherty, P. D. Nissen, S. Fallahi, G. C. Gardner, M. J. Manfra, C. M. Marcus, and F. Kuem- meth, Nat. Commun.10, 1196 (2019)

2019
[54]

H. Qiao, Y. P. Kandel, S. Fallahi, G. C. Gardner, M. J. Manfra, X. Hu, and J. M. Nichol, Phys. Rev. Lett.126, 017701 (2021)

2021
[55]

K.DengandE.Barnes,Phys.Rev.B 102,035427(2020)

2020
[56]

G. X. Chan and X. Wang, Phys. Rev. A106, 022420 (2022)

2022
[57]

G. X. Chan, P. Huang, and X. Wang, Phys. Rev. B108, 035402 (2023)

2023
[58]

M. M. Munia, S. Monir, E. N. Osika, M. Y. Simmons, and R. Rahman, Phys. Rev. Appl.21, 014038 (2024)

2024
[59]

V. N. Golovach, M. Borhani, and D. Loss, Phys. Rev. B 74, 165319 (2006)

2006
[60]

Tokura, W

Y. Tokura, W. G. van der Wiel, T. Obata, and S. Tarucha, Phys. Rev. Lett.96, 047202 (2006)

2006
[61]

G. Tosi, F. A. Mohiyaddin, V. Schmitt, S. Tenberg, R. Rahman, G. Klimeck, and A. Morello, Nat. Commun. 8, 450 (2017)

2017
[62]

Yoneda, K

J. Yoneda, K. Takeda, T. Otsuka, T. Nakajima, M. R. Delbecq, G. Allison, T. Honda, T. Kodera, S. Oda, Y. Hoshi, N. Usami, K. M. Itoh, and S. Tarucha, Nat. Nanotechnol. 13, 102 (2018)

2018
[63]

Struck, A

T. Struck, A. Hollmann, F. Schauer, O. Fedorets, A. Schmidbauer, K. Sawano, H. Riemann, N. V. Abrosi- mov, L. Cywiński, D. Bougeard, and L. R. Schreiber, npj Quantum Inf.6, 40 (2020)

2020
[64]

Takeda, A

K. Takeda, A. Noiri, T. Nakajima, J. Yoneda, T. Kobayashi, and S. Tarucha, Nat. Nanotechnol. 16, 965 (2021)

2021
[65]

Reiner, Y

J. Reiner, Y. Chung, S. H. Misha, C. Lehner, C. Moehle, D. Poulos, S. Monir, K. J. Charde, P. Macha, L. Kranz, I. Thorvaldson, B. Thorgrimsson, D. Keith, Y. L. Hsueh, R. Rahman, S. K. Gorman, J. G. Keizer, and M. Y. Sim- mons, Nat. Nanotechnol.19, 605 (2024)

2024
[66]

Savytskyy, T

R. Savytskyy, T. Botzem, I. F. de Fuentes, B. Joecker, J. J. Pla, F. E. Hudson, K. M. Itoh, A. M. Jakob, B. C. Johnson, D. N. Jamieson, A. S. Dzurak, and A. Morello, Sci. Adv.9, eadd9408 (2023)

2023
[67]

C. D. Hill, E. Peretz, S. J. Hile, M. G. House, M. Fuech- sle, S. Rogge, M. Y. Simmons, and L. C. L. Hollenberg, Sci. Adv.1, e1500707 (2015)

2015
[68]

Veldhorst, H

M. Veldhorst, H. G. J. Eenink, C. H. Yang, and A. S. Dzurak, Nat. Commun.8, 1766 (2017)

2017
[69]

Hansen, A

I. Hansen, A. E. Seedhouse, K. W. Chan, F. E. Hudson, K. M. Itoh, A. Laucht, A. Saraiva, C. H. Yang, and A. S. Dzurak, Appl. Phys. Rev.9, 031409 (2022)

2022
[70]

S. J. Hile, L. Fricke, M. G. House, E. Peretz, C. Y. Chen, Y. Wang, M. Broome, S. K. Gorman, J. G. Keizer, R. Rahman, and M. Y. Simmons, Sci. Adv.4, eaaq1459 (2018)

2018
[71]

Fricke, S

L. Fricke, S. J. Hile, L. Kranz, Y. Chung, Y. He, P. Pakkiam, M. G. House, J. G. Keizer, and M. Y. Sim- mons, Nat. Commun.12, 3323 (2021)

2021
[72]

C. D. Hill, M. Usman, and L. C. L. Hollenberg, arXiv preprint arXiv:2107.11981 (2021)

2021 arXiv
[73]

Morello, J

A. Morello, J. J. Pla, P. Bertet, and D. N. Jamieson, Adv. Quantum Technol.3, 2000005 (2020)

2020
[74]

The resonance condition for qubit frequency is also discussed

See the supplemental material at [url will be inserted by publisher], which provides descriptions of the hyper- fine interaction between the electron spin and nuclear spin, superexchange-based two-qubit gate, and address- able single-qubit gate. The resonance condition for qub...
[75]

R. M. Jock, N. T. Jacobson, P. Harvey-Collard, A. M. Mounce, V. Srinivasa, D. R. Ward, J. Anderson, R. Manginell, J. R. Wendt, M. Rudolph, T. Pluym, J. K. Gamble, A. D. Baczewski, W. M. Witzel, and M. S. Car- roll, Nat. Commun.9, 1768 (2018)

2018
[76]

Kranz, S

L. Kranz, S. K. Gorman, B. Thorgrimsson, Y. He, D. Keith, J. G. Keizer, and M. Y. Simmons, Adv. Mater. 32, 2003361 (2020)

2020
[77]

L. M. K. Vandersypen and I. L. Chuang, Rev. Mod. Phys. 76, 1037 (2005)

2005
[78]

Khaneja, T

N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbrüggen, and S. J. Glaser, J. Magn. Reson.172, 296 (2005)

2005
[79]

X. Wang, F. A. Calderon-Vargas, M. S. Rana, J. P. Kest- ner, E. Barnes, and S. Das Sarma, Phys. Rev. B 90, 155306 (2014)

2014
[80]

J. Zeng, C. H. Yang, A. S. Dzurak, and E. Barnes, Phys. Rev. A99, 052321 (2019)

2019
[81]

C. H. Yang, K. W. Chan, R. Harper, W. Huang, T. Evans, J. C. C. Hwang, B. Hensen, A. Laucht, T. Tanttu, F. E. Hudson, S. T. Flammia, K. M. Itoh, A. Morello, S. D. Bartlett, and A. S. Dzurak, Nat. Elec- tron. 2, 151 (2019)

2019
[82]

Heinz, A

I. Heinz, A. R. Mills, J. R. Petta, and G. Burkard, Phys. Rev. Res.6, 013153 (2024)

2024
[83]

Tankasala, B

A. Tankasala, B. Voisin, Z. Kembrey, J. Salfi, Y.-L. Hsueh, E. N. Osika, S. Rogge, and R. Rahman, Phys. Rev. B105, 155158 (2022)

2022
[84]

L. C. L. Hollenberg, A. D. Greentree, A. G. Fowler, and C. J. Wellard, Phys. Rev. B74, 045311 (2006)

2006
[85]

Schenkel, C

T. Schenkel, C. C. Lo, C. D. Weis, J. Bokor, A. M. Tyryshkin, and S. A. Lyon, arXiv preprint arXiv:1110.2228 (2011)

2011 arXiv
[86]

O’Gorman, N

J. O’Gorman, N. H. Nickerson, P. Ross, J. J. L. Morton, and S. C. Benjamin, npj Quantum Inf.2, 15019 (2016)

2016
[87]

R. Li, L. Petit, D. P. Franke, J. P. Dehollain, J. Helsen, M. Steudtner, N. K. Thomas, Z. R. Yoscovits, K. J. Singh, S. Wehner, L. M. K. Vandersypen, J. S. Clarke, and M. Veldhorst, Sci. Adv.4, eaar3960 (2018)

2018
[88]

J. M. Boter, J. P. Dehollain, J. P. van Dijk, Y. Xu, T. Hensgens, R. Versluis, H. W. Naus, J. S. Clarke, M. Veldhorst, F. Sebastiano, and L. M. Vandersypen, Phys. Rev. Appl.18, 024053 (2022)

2022
[89]

F. K. Unseld, M. Meyer, M. T. Mądzik, F. Borsoi, S. L. de Snoo, S. V. Amitonov, A. Sammak, G. Scappucci, M. Veldhorst, and L. M. K. Vandersypen, Appl. Phys. Lett. 123, 084002 (2023)

2023
[90]

Yoneda, T

J. Yoneda, T. Otsuka, T. Takakura, M. Pioro-Ladrière, R. Brunner, H. Lu, T. Nakajima, T. Obata, A. Noiri, C. J. Palmstrøm, A. C. Gossard, and S. Tarucha, Appl. Phys. Express8, 084401 (2015)

2015
[91]

S. G. J. Philips, M. T. Mądzik, S. V. Amitonov, S. L. de Snoo, M. Russ, N. Kalhor, C. Volk, W. I. L. Lawrie, D. Brousse, L. Tryputen, B. P. Wuetz, A. Sammak, M. Veldhorst, G. Scappucci, and L. M. K. Vandersypen, Nature 609, 919 (2022)

2022

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

B. E. Kane, Nature393, 133 (1998)

1998

[2] [2]

J. J. L. Morton, A. M. Tyryshkin, R. M. Brown, S. Shankar, B. W. Lovett, A. Ardavan, T. Schenkel, E. E. Haller, J. W. Ager, and S. A. Lyon, Nature455, 1085 (2008)

2008

[3] [3]

Fuechsle, S

M. Fuechsle, S. Mahapatra, F. A. Zwanenburg, M. Friesen, M. A. Eriksson, and M. Y. Simmons, Nat. Nanotechnol. 5, 502 (2010)

2010

[4] [4]

A. M. Tyryshkin, S. Tojo, J. J. Morton, H. Riemann, N. V. Abrosimov, P. Becker, H. J. Pohl, T. Schenkel, M. L. Thewalt, K. M. Itoh, and S. A. Lyon, Nat. Mater. 11, 143 (2011)

2011

[5] [5]

Fuechsle, J

M. Fuechsle, J. A. Miwa, S. Mahapatra, H. Ryu, S. Lee, O. Warschkow, L. C. L. Hollenberg, G. Klimeck, and M. Y. Simmons, Nat. Nanotechnol.7, 242 (2012)

2012

[6] [6]

J. J. Pla, K. Y. Tan, J. P. Dehollain, W. H. Lim, J. J. Morton, D. N. Jamieson, A. S. Dzurak, and A. Morello, Nature 489, 541 (2012)

2012

[7] [7]

Saeedi, S

K. Saeedi, S. Simmons, J. Z. Salvail, P. Dluhy, H. Rie- mann, N. V. Abrosimov, P. Becker, H.-J. Pohl, J. J. L. Morton, and M. L. W. Thewalt, Science342, 830 (2013)

2013

[8] [8]

J. T. Muhonen, J. P. Dehollain, A. Laucht, F. E. Hud- son, R. Kalra, T. Sekiguchi, K. M. Itoh, D. N. Jamieson, J. C. McCallum, A. S. Dzurak, and A. Morello, Nat. Nan- otechnol. 9, 986 (2014)

2014