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arxiv: 2605.20781 · v1 · pith:3L5B5OMQnew · submitted 2026-05-20 · 🪐 quant-ph · cond-mat.mes-hall

Multi-Qubit Entanglement of Unit Cell Pairs in SiMOS

Cameron Jones , Jonathan Y. Huang , Santiago Serrano , MengKe Feng , Gerardo A. Paz-Silva , Tuomo Tanttu , Paul Steinacker , Fay E. Hudson
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Wee Han Lim Nikolay V. Abrosimov Hans-Joachim Pohl Michael L. W. Thewalt Andrew S. Dzurak Andre Saraiva Arne Laucht Chih Hwan Yang
This is my paper

Pith reviewed 2026-05-21 05:41 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.mes-hall
keywords SiMOS quantum dotsmulti-qubit entanglementGHZ statesMermin witnessdynamic decouplingsilicon quantum processormultipartite entanglement
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The pith

A four-qubit silicon-MOS processor generates and certifies maximally entangled three-qubit states including GHZ while extending their lifetime with dynamic decoupling.

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

The paper shows that two coupled unit cells in a silicon-MOS device can be controlled as a four-qubit processor with parallel initialization and readout. It produces maximally entangled three-qubit states and verifies genuine multipartite entanglement by exceeding the classical limit of the Mermin witness. A fully symmetric dynamically decoupled gate sequence is applied so that the entangled states survive longer than the usual dephasing time and are instead limited by the Hahn echo time. This combination demonstrates that industry-standard fabrication can support coupled multi-qubit operations in silicon.

Core claim

We present a two unit cell, four-qubit SiMOS processor with universal controllability and fully parallelised state initialisation and readout. We use this processor to generate maximally entangled three-qubit states, including the Greenberger-Horne-Zeilinger (GHZ) state, and certify multipartite entanglement through violation of the classical Mermin-witness bound. By using a fully symmetric dynamically decoupled gate sequence to create our entangled states, we are able to preserve the lifetime of the entanglement beyond T2*, to a time limited instead by T2^Hahn.

What carries the argument

The two-unit-cell four-qubit SiMOS processor operated with a fully symmetric dynamically decoupled gate sequence that generates the entangled states and suppresses decoherence.

If this is right

  • Coupling between unit cells becomes feasible for larger SiMOS arrays.
  • Long-lived multi-qubit entangled states can be prepared with fidelity limited by Hahn echo coherence rather than faster dephasing.
  • Parallel initialization and readout reduce overhead for scaling to more qubits in CMOS-compatible hardware.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same symmetric decoupling approach could be tested on other silicon qubit designs to check if entanglement lifetime gains generalize beyond this processor.
  • Certified three-qubit GHZ states in silicon may serve as a resource for small-scale quantum error correction protocols that rely on genuine multipartite entanglement.
  • Parallel readout demonstrated here suggests that measurement times for larger entangled registers could be shortened without sacrificing the certification step.

Load-bearing premise

The observed violation of the Mermin-witness bound with the symmetric dynamically decoupled sequence certifies genuine multipartite entanglement without being undermined by systematic errors, crosstalk between unit cells, or state-preparation imperfections.

What would settle it

Repeating the three-qubit entanglement protocol while deliberately introducing measurable crosstalk or preparation errors and checking whether the Mermin-witness value still exceeds the classical bound would test whether the certification remains valid.

Figures

Figures reproduced from arXiv: 2605.20781 by Andre Saraiva, Andrew S. Dzurak, Arne Laucht, Cameron Jones, Chih Hwan Yang, Fay E. Hudson, Gerardo A. Paz-Silva, Hans-Joachim Pohl, Jonathan Y. Huang, MengKe Feng, Michael L. W. Thewalt, Nikolay V. Abrosimov, Paul Steinacker, Santiago Serrano, Tuomo Tanttu, Wee Han Lim.

Figure 1
Figure 1. Figure 1: Device Overview and Single and Two Qubit control g. 1 | Device overview and controllability. a, A false colo [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Three-Qubit Entanglement Experiments. a) Schematic diagram of the GHZ state up to local single-qubit gates) and perform state tomography. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 3
Figure 3. Figure 3: Entanglement lifetime and coherence. the √ X gate and the associated sp [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
read the original abstract

Spin qubits in silicon-MOS (SiMOS) quantum dots have recently demonstrated compatibility with existing industry standard CMOS fabrication techniques. These devices have routinely achieved single- and two-qubit gate fidelities above 99% and demonstrated highly entangled two-qubit Bell states in isolated double quantum dot (DQD) unit cells, however coupling between unit cells has remained challenging. In this work, we present a two unit cell, four-qubit SiMOS processor with universal controllability and fully parallelised state initialisation and readout. We use this processor to generate maximally entangled three-qubit states, including the Greenberger-Horne-Zeilinger (GHZ) state, and certify multipartite entanglement through violation of the classical Mermin-witness bound. By using a fully symmetric dynamically decoupled gate sequence to create our entangled states, we are able to preserve the lifetime of the entanglement beyond $T_2^*$, to a time limited instead by $T_2^\textrm{Hahn}$. These demonstrations pave a road to the scalable operation of larger SiMOS processors, and achieving high purity, long-lived multi-qubit entangled states in them.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper reports a two-unit-cell, four-qubit SiMOS processor with universal controllability and parallel initialization/readout. It demonstrates generation of maximally entangled three-qubit states (including GHZ), certifies multipartite entanglement via violation of the classical Mermin-witness bound, and extends the entanglement lifetime from T2* to T2^Hahn using a fully symmetric dynamically decoupled gate sequence.

Significance. If the quantitative certification and error bounds hold, the work addresses a key scalability bottleneck in SiMOS devices by showing controllable coupling between unit cells while preserving high-fidelity multi-qubit entanglement. The combination of parallel readout, dynamical decoupling, and Mermin-witness violation provides a concrete experimental step toward larger silicon-based processors with long-lived entangled states.

major comments (2)
  1. [Abstract] Abstract: the central claim that the observed Mermin-witness violation certifies genuine multipartite (three-qubit) entanglement is load-bearing, yet no numerical witness value, statistical significance, error bars, or measurement count is reported, preventing verification that the violation exceeds what could arise from uncharacterized crosstalk or SPAM errors.
  2. [Main text (entanglement generation and certification)] Main text (entanglement generation and certification): the fully symmetric dynamically decoupled sequence is asserted to produce states whose correlations certify genuine tripartite entanglement, but the manuscript provides no quantitative upper bound on inter-unit-cell crosstalk or full SPAM fidelity matrix that would be required to exclude effective pairwise correlations mimicking the Mermin witness.
minor comments (1)
  1. [Abstract] Abstract: the phrase 'preserve the lifetime of the entanglement beyond T2*, to a time limited instead by T2^Hahn' would benefit from an explicit definition or reference to the precise Hahn-echo or dynamical-decoupling sequence parameters used.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting these important points regarding the presentation of the entanglement certification. We address each major comment below and will incorporate revisions to provide the requested quantitative details and supporting analysis.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the observed Mermin-witness violation certifies genuine multipartite (three-qubit) entanglement is load-bearing, yet no numerical witness value, statistical significance, error bars, or measurement count is reported, preventing verification that the violation exceeds what could arise from uncharacterized crosstalk or SPAM errors.

    Authors: We agree that the abstract would benefit from explicit reporting of the Mermin-witness value, associated uncertainties, statistical significance, and experimental shot count to allow immediate verification. In the revised manuscript we will update the abstract to include these quantities (e.g., the measured witness value with error bars derived from the full dataset) while preserving the overall length and readability. revision: yes

  2. Referee: [Main text (entanglement generation and certification)] Main text (entanglement generation and certification): the fully symmetric dynamically decoupled sequence is asserted to produce states whose correlations certify genuine tripartite entanglement, but the manuscript provides no quantitative upper bound on inter-unit-cell crosstalk or full SPAM fidelity matrix that would be required to exclude effective pairwise correlations mimicking the Mermin witness.

    Authors: The referee is correct that explicit quantitative bounds on inter-unit-cell crosstalk and the complete SPAM fidelity matrix strengthen the exclusion of pairwise-mimicking correlations. Although the symmetric decoupling sequence and parallel readout are designed to suppress such effects, the current text does not supply the numerical upper limits. We will add a dedicated paragraph (and associated supplementary figures) reporting the measured crosstalk upper bound from calibration experiments and the full SPAM matrix, together with a short analysis demonstrating that the observed witness violation remains inconsistent with the maximum possible spurious correlations allowed by these bounds. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental results are direct measurements

full rationale

The paper is an experimental demonstration of multi-qubit entanglement generation and certification in a SiMOS device. Claims rest on observed Mermin-witness violations, state preparation, and gate sequences whose outcomes are measured directly rather than derived from equations that reduce to the paper's own fitted inputs or self-citations. No self-definitional steps, fitted parameters renamed as predictions, or load-bearing uniqueness theorems imported from prior author work appear in the provided text. The work is self-contained against external benchmarks (T2*, T2^Hahn, gate fidelities) and does not invoke mathematical derivations that loop back by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are introduced or fitted in the abstract; the work is an experimental demonstration relying on established quantum information tests and silicon quantum dot techniques.

pith-pipeline@v0.9.0 · 5801 in / 1159 out tokens · 45661 ms · 2026-05-21T05:41:21.063575+00:00 · methodology

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Reference graph

Works this paper leans on

60 extracted references · 60 canonical work pages · 3 internal anchors

  1. [1]

    The circuit design generalises to arrays with an arbitrary number of qubits, and is not impacted by varying gate times across qubits. Recognising that overall operating speed (which is dominated by state preparation and measurement) is an important metric for processor efficiency, we perform simultaneous initialisation and readout of all qubits by paralle...

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  2. [2]

    T1 (although the data is very poor, mi ght not include or needs recollecting)

    work page

  3. [3]

    GST error generators. • Results/discussion • Full controllability of the 4 dot processor (might be contensious claim given Q1 performance) • Issue with Q1 performance, used as readout ancilla in this work. • Use (3,5,5,3) charge config. Large Q2 and Q3 wavefunctions allow easier J2 control. • GST results. On-target single Q fidelities > 99%. Single qubit ...

    work page

  4. [4]

    & Ekerå, M

    Gidney, C. & Ekerå, M. How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits.Quantum5, 433 (2021). URLhttps:// quantum-journal.org/papers/q-2021-04-15-433/

    work page 2048

  5. [5]

    L.et al.Assessing the Benefits and Risks of Quantum Computers (2024)

    Scholten, T. L.et al.Assessing the Benefits and Risks of Quantum Computers (2024). URLhttp://arxiv.org/ abs/2401.16317. ArXiv:2401.16317 [quant-ph]

    work page arXiv 2024

  6. [6]

    DiVincenzo, D. P. The Physical Implementation of Quantum Computation.Fortschritte der Physik48, 771– 783 (2000)

    work page 2000

  7. [7]

    M.et al.Fault-tolerant architecture for quantum computation using electrically controlled semiconductor spins.Nature Physics1, 177–183 (2005)

    Taylor, J. M.et al.Fault-tolerant architecture for quantum computation using electrically controlled semiconductor spins.Nature Physics1, 177–183 (2005). URLhttps://www.nature.com/articles/ nphys174. Number: 3

    work page 2005

  8. [8]

    Fowler, A. G. Surface codes: Towards practical large- scale quantum computation.Physical Review A86 (2012)

    work page 2012

  9. [9]

    URLhttps://www.nature.com/articles/ s41586-024-08449-y

    Google Quantum AIet al.Quantum error correction below the surface code threshold.Nature638, 920– 926 (2025). URLhttps://www.nature.com/articles/ s41586-024-08449-y

    work page 2025

  10. [10]

    URLhttps://www.nature.com/articles/ nmat3182

    Tyryshkin, A.M.et al.Electronspincoherenceexceeding seconds in high-purity silicon.Nature Materials11, 143– 147 (2012). URLhttps://www.nature.com/articles/ nmat3182

    work page 2012

  11. [11]

    URLhttps://www

    Veldhorst, M.et al.An addressable quantum dot qubit with fault-tolerant control-fidelity.Nature Nanotechnology9, 981–985 (2014). URLhttps://www. nature.com/articles/nnano.2014.216. Number: 12

    work page 2014

  12. [12]

    URLhttps://www.nature.com/ articles/nnano.2014.153

    Kawakami, E.et al.Electrical control of a long-lived spin qubit in a Si/SiGe quantum dot.Nature Nanotechnology 9, 666–670 (2014). URLhttps://www.nature.com/ articles/nnano.2014.153

    work page 2014

  13. [13]

    URLhttps://www.nature.com/articles/ s41565-017-0014-x

    Yoneda, J.et al.A quantum-dot spin qubit with coherence limited by charge noise and fidelity higher than 99.9%.Nature Nanotechnology13, 102– 106 (2018). URLhttps://www.nature.com/articles/ s41565-017-0014-x

    work page 2018

  14. [14]

    URLhttps://www.nature.com/articles/ s41586-021-04182-y

    Noiri, A.et al.Fast universal quantum gate above the fault-tolerance threshold in silicon.Nature601, 338– 342 (2022). URLhttps://www.nature.com/articles/ s41586-021-04182-y

    work page 2022

  15. [15]

    URLhttps://www.nature.com/articles/ s41586-021-04273-w

    Xue, X.et al.Quantum logic with spin qubits crossing the surface code threshold.Nature601, 343– 347 (2022). URLhttps://www.nature.com/articles/ s41586-021-04273-w

    work page 2022

  16. [16]

    URLhttps://www.nature.com/ articles/s41567-024-02614-w

    Tanttu, T.et al.Assessment of the errors of high-fidelity two-qubit gates in silicon quantum dots.Nature Physics 20, 1804–1809 (2024). URLhttps://www.nature.com/ articles/s41567-024-02614-w

    work page 2024

  17. [17]

    T.et al.Operating two exchange-only qubits in parallel.Nature647, 870–875 (2025)

    Mądzik, M. T.et al.Operating two exchange-only qubits in parallel.Nature647, 870–875 (2025). URLhttps: //www.nature.com/articles/s41586-025-09767-5

    work page 2025

  18. [18]

    URLhttps:// www.nature.com/articles/s41586-020-2170-7

    Petit, L.et al.Universal quantum logic in hot silicon qubits.Nature580, 355–359 (2020). URLhttps:// www.nature.com/articles/s41586-020-2170-7

    work page 2020

  19. [19]

    H.et al.Operation of a silicon quantum processor unit cell above one kelvin.Nature580, 350– 354 (2020)

    Yang, C. H.et al.Operation of a silicon quantum processor unit cell above one kelvin.Nature580, 350– 354 (2020). URLhttps://www.nature.com/articles/ s41586-020-2171-6. Number: 7803

    work page 2020

  20. [20]

    Y.et al.High-fidelity spin qubit operation and algorithmic initialization above 1 K.Nature627, 772– 777 (2024)

    Huang, J. Y.et al.High-fidelity spin qubit operation and algorithmic initialization above 1 K.Nature627, 772– 777 (2024). URLhttps://www.nature.com/articles/ s41586-024-07160-2

    work page 2024

  21. [21]

    W.et al.A four-qubit germanium quantum processor.Nature591, 580–585 (2021)

    Hendrickx, N. W.et al.A four-qubit germanium quantum processor.Nature591, 580–585 (2021). URLhttps://www.nature.com/articles/ s41586-021-03332-6

    work page 2021

  22. [22]

    URLhttps://www.nature.com/ articles/s41565-021-00925-0

    Takeda, K.et al.Quantum tomography of an entangled three-qubit state in silicon.Nature Nanotechnology 16, 965–969 (2021). URLhttps://www.nature.com/ articles/s41565-021-00925-0

    work page 2021

  23. [23]

    & Tarucha, S

    Takeda, K., Noiri, A., Nakajima, T., Kobayashi, T. & Tarucha, S. Quantum error correction with silicon spin qubits.Nature608, 682–686 (2022). URLhttps://www. nature.com/articles/s41586-022-04986-6

    work page 2022

  24. [24]

    Philips, S. G. J.et al.Universal control of a six- qubit quantum processor in silicon.Nature609, 919– 924 (2022). URLhttps://www.nature.com/articles/ s41586-022-05117-x

    work page 2022

  25. [25]

    Nature Nanotechnology20, 472–477 (2025)

    Thorvaldson, I.et al.Grover’s algorithm in a four- qubit silicon processor above the fault-tolerant threshold. Nature Nanotechnology20, 472–477 (2025). URL http://arxiv.org/abs/2404.08741. ArXiv:2404.08741 [quant-ph]

    work page arXiv 2025

  26. [26]

    Nature648, 569–575(2025)

    Edlbauer, H.et al.An 11-qubit atom processor in silicon. Nature648, 569–575(2025). URLhttps://www.nature. com/articles/s41586-025-09827-w

    work page 2025

  27. [27]

    URLhttps://link.aps

    Fernández de Fuentes, I.et al.Running a Six-Qubit 8 Quantum Circuit on a Silicon Spin-Qubit Array.PRX Quantum7, 010308 (2026). URLhttps://link.aps. org/doi/10.1103/f285-l2v5

    work page doi:10.1103/f285-l2v5 2026

  28. [28]

    URLhttp://arxiv.org/abs/2601

    Undseth, B.et al.Weight-four parity checks with silicon spin qubits (2026). URLhttp://arxiv.org/abs/2601. 23267. ArXiv:2601.23267 [cond-mat]

    work page arXiv 2026

  29. [29]

    J.et al.Simultaneous operation of an 18- qubit modular array in germanium (2026)

    Dijkema, J. J.et al.Simultaneous operation of an 18- qubit modular array in germanium (2026). URLhttp: //arxiv.org/abs/2604.01063. ArXiv:2604.01063 [cond- mat]

    work page arXiv 2026

  30. [30]

    Zwerver, A. M. J.et al.Qubits made by advanced semiconductor manufacturing.Nature Electronics 5, 184–190 (2022). URLhttps://www.nature.com/ articles/s41928-022-00727-9

    work page 2022

  31. [31]

    URLhttps://www.nature

    Elsayed, A.et al.Low charge noise quantum dots with industrial CMOS manufacturing.npj Quantum Information10, 70 (2024). URLhttps://www.nature. com/articles/s41534-024-00864-3

    work page 2024

  32. [32]

    URLhttps://www.nature.com/articles/ s41586-025-09531-9

    Steinacker, P.et al.Industry-compatible silicon spin- qubit unit cells exceeding 99% fidelity.Nature646, 81– 87 (2025). URLhttps://www.nature.com/articles/ s41586-025-09531-9

    work page 2025

  33. [33]

    URLhttp: //arxiv.org/abs/2504.20572

    Hamonic, P.et al.A foundry-fabricated spin qubit unit cell with in-situ dispersive readout (2025). URLhttp: //arxiv.org/abs/2504.20572. ArXiv:2504.20572 [cond- mat]

    work page arXiv 2025

  34. [34]

    URLhttps: //arxiv.org/abs/2512.10174v1

    Nickl, A.et al.Eight-Qubit Operation of a 300 mm SiMOS Foundry-Fabricated Device (2025). URLhttps: //arxiv.org/abs/2512.10174v1

    work page arXiv 2025

  35. [35]

    F.et al.Radio-frequency cascade readout of coupled spin qubits fabricated using a 300~mm wafer process (2025)

    Chittock-Wood, J. F.et al.Radio-frequency cascade readout of coupled spin qubits fabricated using a 300~mm wafer process (2025). URLhttp://arxiv.org/ abs/2408.01241. ArXiv:2408.01241 [cond-mat]

    work page arXiv 2025

  36. [36]

    D.et al.Demonstration of 99.9% single qubit control fidelity of a silicon quantum dot spin qubit made in a 300 mm foundry process

    Stuyck, N. D.et al.Demonstration of 99.9% single qubit control fidelity of a silicon quantum dot spin qubit made in a 300 mm foundry process. In2024 IEEE Silicon Nanoelectronics Workshop (SNW), 11–12 (2024). URLhttps://ieeexplore.ieee.org/abstract/ document/10639218

    work page arXiv 2024

  37. [37]

    K.et al.Spin-qubit control with a milli-kelvin CMOS chip.Nature643, 382–387 (2025)

    Bartee, S. K.et al.Spin-qubit control with a milli-kelvin CMOS chip.Nature643, 382–387 (2025). URLhttps: //www.nature.com/articles/s41586-025-09157-x

    work page 2025

  38. [38]

    J.et al.Rapid cryogenic characterization of 1,024 integrated silicon quantum dot devices.Nature Electronics8, 75–83 (2025)

    Thomas, E. J.et al.Rapid cryogenic characterization of 1,024 integrated silicon quantum dot devices.Nature Electronics8, 75–83 (2025). URLhttps://www.nature. com/articles/s41928-024-01304-y

    work page 2025

  39. [39]

    C.et al.Spin Readout in a 22 nm Node Integrated Circuit (2025)

    Clarke, I. C.et al.Spin Readout in a 22 nm Node Integrated Circuit (2025). URLhttp://arxiv.org/abs/ 2510.13674. ArXiv:2510.13674 [quant-ph]

    work page arXiv 2025

  40. [40]

    URLhttp://arxiv.org/abs/2009.07301

    Nielsen, E.et al.Gate Set Tomography.Quantum5, 557 (2021). URLhttp://arxiv.org/abs/2009.07301. ArXiv:2009.07301 [quant-ph]

    work page arXiv 2021

  41. [41]

    URLhttp://arxiv

    Serrano, S.et al.Improved Single-Shot Qubit Readout Using Twin RF-SET Charge Correlations.PRX Quantum5, 010301 (2024). URLhttp://arxiv. org/abs/2307.07724. ArXiv:2307.07724 [cond-mat, physics:quant-ph]

    work page arXiv 2024

  42. [42]

    URLhttp:// arxiv.org/abs/2512.12648

    Jones, C.et al.Mid-circuit logic executed in the qubit layer of a quantum processor (2026). URLhttp:// arxiv.org/abs/2512.12648. ArXiv:2512.12648 [quant- ph]

    work page arXiv 2026

  43. [43]

    Nanoscale broadband transmission lines for spin qubit control

    Dehollain, J. P.et al.Nanoscale broadband transmission lines for spin qubit control.Nanotechnology24, 015202 (2013). URLhttp://arxiv.org/abs/1208.2421. ArXiv:1208.2421 [cond-mat]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  44. [44]

    URLhttps://link.aps.org/doi/10.1103/ PRXQuantum.3.020335

    Blume-Kohout, R.et al.A Taxonomy of Small Markovian Errors.PRX Quantum3, 020335 (2022). URLhttps://link.aps.org/doi/10.1103/ PRXQuantum.3.020335

    work page 2022

  45. [45]

    E.et al.Pauli Blockade in Silicon Quantum Dots with Spin-Orbit Control.PRX Quantum 2, 010303 (2021)

    Seedhouse, A. E.et al.Pauli Blockade in Silicon Quantum Dots with Spin-Orbit Control.PRX Quantum 2, 010303 (2021). URLhttps://link.aps.org/doi/10. 1103/PRXQuantum.2.010303

    work page 2021

  46. [46]

    J., Wahlgren, P., Kozhevnikov, A

    Schoelkopf, R. J., Wahlgren, P., Kozhevnikov, A. A., Delsing, P. & Prober, D. E. The Radio-Frequency Single-Electron Transistor (RF-SET): A Fast and Ultrasensitive Electrometer.Science280, 1238–1242 (1998). URLhttps://www.science.org/doi/10.1126/ science.280.5367.1238

    work page arXiv 1998

  47. [47]

    J.et al.Electron cascade for distant spin readout.Nature Communications12, 77 (2021)

    van Diepen, C. J.et al.Electron cascade for distant spin readout.Nature Communications12, 77 (2021). URLhttps://www.nature.com/articles/ s41467-020-20388-6

    work page 2021

  48. [48]

    & Tóth, G

    Gühne, O. & Tóth, G. Entanglement detection. Physics Reports474, 1–75 (2009). URL https://www.sciencedirect.com/science/article/ pii/S0370157309000623

    work page 2009

  49. [49]

    Mermin, N. D. Extreme quantum entanglement in a superposition of macroscopically distinct states.Physical Review Letters65, 1838–1840 (1990). URLhttps: //link.aps.org/doi/10.1103/PhysRevLett.65.1838

    work page doi:10.1103/physrevlett.65.1838 1990

  50. [50]

    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

    work page 2022

  51. [51]

    H.et al.A 2x2 quantum dot array in silicon with fully tuneable pairwise interdot coupling.Nano Letters 25, 10263–10269 (2025)

    Lim, W. H.et al.A 2x2 quantum dot array in silicon with fully tuneable pairwise interdot coupling.Nano Letters 25, 10263–10269 (2025). URLhttp://arxiv.org/abs/ 2411.13882. ArXiv:2411.13882 [cond-mat]

    work page arXiv 2025

  52. [52]

    Understanding oxide-thickness-dependent variability in dense Si-MOS quantum dot arrays

    Loenders, A.et al.Understanding oxide-thickness- dependent variability in dense Si-MOS quantum dot arrays (2026). URLhttp://arxiv.org/abs/2605. 12143. ArXiv:2605.12143 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  53. [53]

    Leon, R. C. C.et al.Bell-state tomography in a silicon many-electron artificial molecule.Nature Communications12, 3228 (2021). URLhttps://www. nature.com/articles/s41467-021-23437-w. METHODS Measurement setup and cryogenics The device is wire-bonded to a custom designed and fabricated PCB, and housed in an enclosure mounted on the cold finger of the dilut...

    work page 2021

  54. [54]

    The array is held in the (N P1,NP2,NP3,NP4) = (4,4,4,4) charge configuration to ensure both DQDs relax to ground singlet state prior to initialisation

    work page

  55. [55]

    This ramp rate is tuned such that a high purity |Q1,Q 2,Q 3,Q 4⟩=|↓↑↑↓⟩state is populated

    The detuning in both pairs is ramped adiabatically, from the (4,4,4,4) charge configuration to (3,5,5,3). This ramp rate is tuned such that a high purity |Q1,Q 2,Q 3,Q 4⟩=|↓↑↑↓⟩state is populated. A fixed ramp rate is used for both DQDs, however the J1/J3 voltages applied when moving through the anti-crossing. This allows each DQD to be tuned independentl...

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  56. [56]

    Readout is performed in both DQD unit cells to measure Z-basis parity of both qubit pairs MZZ(Q1,Q 2),M ZZ(Q3,Q 4). 10

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  57. [57]

    projection operations

    The FPGA is used to execute a real-time logical condition. If even parity is measured in both unit cells (M ZZ(Q1,Q 2) =M ZZ(Q3,Q 4) = 0), the initialisation is considered successful and the sequence progresses to quantum circuit execution. If either or both of the measurements register odd parity,M ZZ = 1, the reinitialisation process is restarted from s...

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  58. [58]

    Uncertainties are given in parentheses correspond to2σ error. Measurement Q1 Q2 Q3 Q4 fRabi (kHz) 183.2(8) 680.9(4) 442.5(2) 624.1(3) TRabi 2 (µs) 13.6(18) 29.2(10) 45.9(20) 32.4(19) T∗ 2 (µs) 3.1(2) 6.2(5) 4.8(2) 5.5(3) THahn 2 (µs) 64.0(104) 87.2(34) 76.3(29) 79.4(34) Extended Data Table II|Single-qubit gate fidelity. All fidelity estimates obtained usi...

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  59. [59]

    2|Coherence time measurements.Fitted coherence time data for Rabi, Ramsey and Hahn sequences used to obtainT 2 estimates in Extended Data Table I

    T2 data Rabi Ramsey Q4Q3Q2Q1 32.4ሺ19ሻ45.9ሺ20ሻ29.2ሺ10ሻ13.6ሺ18ሻTଶ ୖୟୠ୧(μs) 5.5ሺ3ሻ4.8ሺ2ሻ6.2ሺ5ሻ3.1ሺ2ሻTଶ ∗ (μs) 79.4ሺ34ሻ76.3ሺ29ሻ87.2ሺ34ሻ64.0ሺ104ሻTଶ ୌୟ୦୬(μs) Xሺ𝑡ୖୟୠ୧ሻ|↓⟩ Z X|↓⟩ ZIሺ𝑡୛ୟ୧୲ሻ ሼPଵ୕ሽ Hahn X ZIሺ௧౓౗౟౪ ଶ ሻ ሼPଵ୕ሽX Iሺ௧౓౗౟౪ ଶ ሻ|↓⟩ 𝐓𝟐 Estimates Extended Data Fig. 2|Coherence time measurements.Fitted coherence time data for Rabi, Ramsey and Hahn sequences use...

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  60. [60]

    3|Exchange rate controllability.Exchange rate between Q1-Q2, Q2-Q3 and Q3-Q4 as a function of the voltage offsets∆VJ on exchange gates J1, J2 and J3 respectively

    Exchange rate controllability Single qubit gate operating voltage Extended Data Fig. 3|Exchange rate controllability.Exchange rate between Q1-Q2, Q2-Q3 and Q3-Q4 as a function of the voltage offsets∆VJ on exchange gates J1, J2 and J3 respectively. Exchange rates are determined by fitting exchange oscillation measured in dCZ experiments performed at each o...

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