1. What electron spin is — a tiny magnet's direction

First, an everyday picture

Think of a compass needle. The needle is a small magnet that points north or south. An electron has a similar property: it behaves like a tiny magnet that points “up” or “down.” This property is called spin.

Why does this make a qubit? A qubit needs two states that stand for 0 and 1. When a magnetic field is applied, an electron spin separates cleanly into two states: along the field and against it. Assign 0 and 1 to these two, and you have a qubit.

Matching it to the qubit arrow

In this series a qubit state is drawn as an arrow from the centre of a sphere to its surface. Pointing at the north pole means 0, at the south pole means 1, and anywhere in between is a superposition of 0 and 1. For an electron spin, you can lay this arrow directly on “the direction of the electron's tiny magnet.” When the arrow is tilted, a measurement gives 0 or 1, and the probability depends on the tilt. After the measurement, the original arrow is not recovered.

Why is electron spin a good qubit candidate?

The review by Burkard and colleagues describes spin as a natural two-level system that is insensitive to electric fields, and says this is why long coherence (the time a quantum state survives) can be obtained Sourced [Ref. 3]. Chips are full of electrical jitter (fluctuating electric fields). Spin is a magnet direction, so it is less sensitive to such electrical jitter. But “less sensitive” does not mean not sensitive. As we will see, the real limits of today's qubits are set by electrical jitter (charge noise) and by nearby nuclear spins.

History in one line

The idea of confining an electron in a quantum dot and using its spin as a qubit was proposed by Loss and DiVincenzo in 1998 Sourced [Ref. 1]. In the same year, Kane proposed a quantum computer that uses the spin of the nucleus of phosphorus atoms in silicon Sourced [Ref. 2]. This article deals mainly with the former (electron spin) and touches the latter (phosphorus atoms, or “donors”) briefly.

2. Magnetic field, energy and temperature — why extreme cold is needed (our calculation)

In a magnetic field, the energy of an electron spin splits in two (Fig. 2). The gap ΔE is the “energy difference between 0 and 1” of the qubit. Here we check how big it is with real numbers.

Step 1: express the energy gap as a frequency

For a free electron spin the frequency per tesla (T) of magnetic field is about 28.02 GHz. The NIST table of physical constants gives the electron gyromagnetic ratio divided by 2π as 28 024.951 MHz/T Sourced [Ref. 4]. For an electron in silicon, the value can shift a little because of valley and interface effects (the review by Burkard and colleagues mentions corrections from the mixing of valley states [Ref. 3]). For example, in the device of Steinacker and colleagues (arXiv version) the field is 0.666 T, the Zeeman energy is about 77 µeV, and the microwave (local oscillator) frequency is 18.610 GHz Sourced [Ref. 19]. Using the free-electron value, 28.025 GHz/T × 0.666 T = about 18.7 GHz, which matches the paper closely Our calculation. A frequency in the 18 GHz range is far above that of a microwave oven (about 2.45 GHz).

Step 2: convert that to temperature

The energy of a frequency f is h × f (h is Planck's constant). Converted this way, ΔE at 0.666 T is about 77 µeV (micro-electronvolts), which corresponds to a temperature of about 0.90 K (kelvin) Our calculation (Planck's and Boltzmann's constants from NIST [Ref. 4]). In other words, at about 0.9 K (−272 °C), the energy of the surrounding thermal jitter is about the same as the up-down energy gap of the spin.

Step 3: heat scrambles the directions

When the thermal jitter is large, spins scatter randomly between up and down. The degree to which they favor the lower-energy direction (the polarization P) can be computed, with thermal energy k_BT, as P = tanh(ΔE / 2k_BT) (our explanation; this is the standard formula for a two-level system in thermal equilibrium). It means: the larger ΔE is compared with the thermal energy, the closer P gets to 1 (almost all spins in the lower direction). Let us look at numbers.

Calculation: ΔE = h × 28.025 GHz/T × B, P = tanh(ΔE / 2k_BT) (Our calculation). Constants from the NIST physical constants table; the free-electron value is used (it can shift slightly in silicon).

3. Trapping exactly one electron — two ways to build a quantum dot

An everyday picture: put exactly one marble in a small dent

To use an electron spin as a qubit, you have to place exactly one electron at a chosen spot. Imagine pressing a small dent into a flat board and dropping in a single marble. On a semiconductor chip, the dent is made with “voltage.” Thin metal electrodes (gates) are laid on the surface, and applying voltages pulls electrons together or pushes them away just beneath each gate. A small region that traps electrons this way is called a quantum dot (the materials side of quantum dots is covered in our explainer on quantum dots; here the word simply means “a small room that holds one electron at a time”).

The review by Burkard and colleagues also treats the gate-defined quantum dot, in which gate voltages confine the electron, as the basic form of the electron-spin qubit Sourced [Ref. 3].

Two main ways to build it

Silicon quantum dots fall into two main types according to where the electron is held. In a MOS-type dot, the electron sits at the boundary (interface) between silicon and its oxide (SiO₂). In a Si/SiGe-type dot, layers of silicon and silicon-germanium alloy (SiGe) are stacked, and the electron sits in a thin silicon layer (a quantum well).

The table is our own organization (Our calculation). Numbers are as stated in each paper or review. It does not argue which type is better.

4. Control and readout — rotate with microwaves, read by turning spin into charge

To use an electron spin as a qubit you need three things: prepare it, rotate it, and read it. Each is explained below with methods used in actual experiments.

1. Prepare — align the direction and start

First, the qubit is prepared in state 0. In silicon spin qubits, the device is cooled so that the electron tends to point in the lower-energy direction (the calculation in Chapter 2). In the experiment of Steinacker and colleagues, the quantum dots were disconnected from the electron reservoir and loaded with four electrons (as described in the arXiv version) [Ref. 19].

2. Control — rotate the arrow with microwaves

When a microwave magnetic field at the frequency that matches the up-down energy gap ΔE is applied, the arrow rotates (the principle of magnetic resonance; Fig. 2 in Chapter 1). The length of the pulse sets the rotation angle. This is a single-qubit gate.

There are two ways to deliver the microwaves, depending on the experiment. Steinacker and colleagues drive a current through an aluminium line (a stripline) near the device to make the microwave magnetic field Sourced [Ref. 19]. Noiri and colleagues use the gradient of the magnetic field made by a small magnet (a Ti/Co micromagnet) on top of the device, and rotate the spin by shaking the electron very slightly with gate voltages Sourced [Ref. 13]. The latter has the advantage that the spin can be driven with electrical signals alone.

For a two-qubit gate, the barrier between two neighboring electrons is lowered with the voltage on a gate electrode (J in Fig. 4). The two electrons then interact slightly (the exchange interaction), so that the direction of one spin affects the other. Petit and colleagues reported that the strength of this coupling could be tuned with gate voltage from 0.5 to 18 MHz Sourced [Ref. 23].

3. Read out — turn the spin direction into presence or absence of charge

The direction of a spin is hard to measure directly. So the spin direction is first turned into the presence or absence of charge, and that is measured. In 2004, Elzerman and colleagues read out the spin direction of a single electron in a quantum dot electrically in a single measurement (spin-to-charge conversion, with detection by a nearby charge detector) Sourced [Ref. 27]. In today's silicon devices, a method based on the Pauli spin blockade is used: whether an electron can hop to the neighboring dot depends on whether two spins point the same way or differently. The review by Burkard and colleagues explains that this maps the spin state onto the charge configuration Sourced [Ref. 3]. The difference in charge configuration is detected as a change in current by a nearby charge sensor (such as a single-electron transistor) [Ref. 19].

5. Why silicon, and why 28Si — the nuisance of nuclear spins

The question: what disturbs an electron spin?

Electron spins were insensitive to electrical jitter. So what does damage a qubit? One major cause is the nuclei of the surrounding atoms. Some atomic nuclei have a tiny-magnet property of their own (nuclear spin). When many such nuclear magnets sit near an electron, the electron feels the faint magnetic field they produce. That field fluctuates as the nuclear magnets slowly change direction, and the electron spin's arrow gradually blurs.

The review by Burkard and colleagues says that in GaAs (gallium arsenide) quantum dots, the fluctuating nuclear field limits the dephasing time T₂* to about 10 ns Sourced [Ref. 3]. In GaAs every atom has a magnetic nucleus. Silicon is different.

Silicon isotopes — some carry a magnet, some do not

Even within one element, there are varieties with different nuclear masses, called isotopes. Natural silicon contains 92.223% 28Si, 4.685% 29Si and 3.092% 30Si (NIST) Sourced [Ref. 5]. Of these, only 29Si has a nuclear spin (a magnet property); 28Si and 30Si do not (our explanation; Tyryshkin and colleagues describe 28Si as a form of silicon with no magnetic nuclei [Ref. 6]). So silicon made only of 28Si is a “quiet container” with no disturbing magnets around.

How quiet does it get? — numbers from experiments

Using 28Si greatly extends how long spin coherence lasts. Here are some results using donors (phosphorus atoms).

• Tyryshkin et al. (2012): in high-purity 28Si with less than 50 ppm residual 29Si, the coherence time T₂ of donor electron spins reached up to 2 seconds. Suppressing interactions between electrons gave an extrapolated 10 seconds at 1.8 K Sourced [Ref. 6]. (ppm means parts per million. This was a measurement on an ensemble of many spins.)
• Muhonen et al. (2014): in a gated device on a 28Si substrate, the coherence of the nuclear spin of a single phosphorus atom exceeded 30 seconds (using a pulse sequence called CPMG), with control fidelity above 99.99%. The CPMG coherence time of the electron spin exceeded 0.5 seconds Sourced [Ref. 7].

For the electron spin in a quantum dot, on the other hand, Yoneda and colleagues (2018) reported, in a 28Si/SiGe device, a dephasing time (T₂*) of 20 µs, an average single-qubit gate fidelity above 99.9%, and charge noise as the main cause of the fluctuations Sourced [Ref. 12]. Note that the quantum-dot electron (tens of µs) is far shorter than the donor nuclear spin (seconds). This is because a quantum-dot electron is easy to drive electrically but is therefore also sensitive to electrical jitter (charge noise) (our explanation).

How many 29Si atoms remain? (our calculation)

“800 ppm of 29Si remains” is hard to feel, so let us convert it to a count. The lattice constant of the silicon crystal is 0.5431 nm (NIST), and one cubic unit cell holds 8 atoms. So the number of silicon atoms per cm³ is 8 / (0.5431 nm)³ = about 5.0 × 10²² Our calculation [Ref. 4].

Suppose the electron occupies a region of 20 nm × 20 nm × 5 nm (a made-up size for explanation, not the size of any real device). That volume is 2.0 × 10⁻¹⁸ cm³ and holds about 100,000 silicon atoms. The number of 29Si among them is about 4,700 in natural silicon, about 80 at 800 ppm, about 40 at 400 ppm, and about 5 at 50 ppm Our calculation.

How is 28Si made?

Isotopes behave almost identically in chemistry, so ordinary chemical purification cannot separate them (our explanation). They are separated by their difference in mass instead.

• Industrial methods such as gas centrifuges: Dwyer and colleagues called this approach “industrial gas centrifuges” and studied an alternative [Ref. 8].
• Mass selection of ions: Dwyer et al. (2014) made silicon ions from commercial silane (SiH₄), sorted them by mass in a magnetic field and deposited them on a Si(100) substrate, obtaining films in which the fractions of both 29Si and 30Si are below 1 × 10⁻⁶ Sourced [Ref. 8]. Tang et al. (2020) used a similar ion-beam deposition to grow 28Si films with controlled enrichment from the natural ratio up to 99.99987% (0.832 × 10⁻⁶ of 29Si) Sourced [Ref. 9]. Both are laboratory-scale.
• Growth from purified silane: Yoneda and colleagues grew a strained 28Si well by gas-source molecular beam epitaxy from isotope-purified silane (about 800 ppm of 29Si) [Ref. 12]. Mazzocchi and colleagues report a CVD-grown 28Si epitaxial film (99.992%) on 300 mm substrates (as given in the title) Sourced [Ref. 10].

An overview of isotope-controlled materials (silicon and diamond) is given in the review by Itoh and Watanabe [Ref. 11].

6. Interfaces and valleys — material uniformity becomes qubit performance

Charge noise — the other wall

Even after nuclear spins are removed with 28Si, another wall remains: charge noise. An electron spin is insensitive to electric fields, but in a quantum dot the spin is driven with the help of electric fields. As a result, it also picks up the jitter of the electric field (charge noise). Yoneda and colleagues showed that the dephasing was caused not by magnetic noise but by charge noise (of the 1/f type, whose power is inversely proportional to frequency), and that this 1/f spectrum extends over seven decades of frequency Sourced [Ref. 12]. In the device of Steinacker and colleagues, charge noise measured with a single-electron transistor was about 0.8 µeV/√Hz at 1 Hz, similar to the low values of earlier similar devices (arXiv version) Sourced [Ref. 19].

The cause of charge noise is thought to be defects and impurities in the oxide and at the interface that capture and release electrons (general understanding; our explanation). This is where materials engineers come in. Interface quality, defects in films and control of metal impurities decide qubit performance.

Valleys — a nuisance unique to silicon

Silicon has one more problem of its own: valleys. An electron in a crystal spreads out as a wave. In silicon there are six different “wave shapes” with the lowest energy (the review by Burkard and colleagues: the conduction-band minimum is six-fold degenerate) Sourced [Ref. 3]. The electron may be in any of these six “valley bottoms,” and these are the six valleys (this concerns the wavelength of the electron's wave, not a real hill or valley).

In a quantum dot, only the two valleys along the confinement direction (vertical) matter. In MOS devices the vertical electric field, and in Si/SiGe devices the strain, lifts the other four valleys. The energy difference between the two remaining valleys is called the valley splitting Sourced [Ref. 3].

What goes wrong if valley splitting is small?

If the valley splitting is close to, or smaller than, the spin's energy gap (the Zeeman energy), the spin state mixes with the valley state and the qubit becomes hard to use (our explanation; the review says that mixing of valley states affects the g-factor and spin relaxation [Ref. 3]). Yoneda and colleagues write that they confirmed by magneto-spectroscopy that the valley splitting was much larger than the Zeeman splitting [Ref. 12]. As the lower half of Fig. 7 shows, against 77 µeV at 0.666 T, the lower end of the reported MOS range (50 µeV) is below it. So the size of the valley splitting has to be checked device by device (our reading).

Si/SiGe devices have another problem. Paquelet Wuetz and colleagues explained that concentration fluctuations of Si and Ge atoms at each three-dimensional spot of the interface make valley splitting vary widely across many devices Sourced [Ref. 28]. Against prevailing belief, they propose adding some Ge to the well to increase these fluctuations and so raise the valley splitting statistically [Ref. 28]. The key point is that a flat and uniform interface translates directly into uniform qubits.

7. Building in a chip factory — where 300 mm wafers stand, and the open problems

Why does “can be made in a factory” matter?

A practical quantum computer is expected to need a very large number of qubits in order to correct errors. Neyens and colleagues state that putting millions of qubits on one processor with solid-state devices will require device fabrication on a scale comparable to the modern CMOS industry Sourced [Ref. 22]. That is why the existing mass-production infrastructure of semiconductor factories is attractive for making qubits, and it is the main motivation behind silicon spin qubits.

But whether a high-performance device made in a research lab can also be made the same way in a factory was a separate question. At the start of their paper, Steinacker and colleagues write that it had not been clear whether the excellent fidelities and long coherence shown by devices made in a lab could be reproduced by devices made in a semiconductor foundry (a contract manufacturing plant) Sourced [Ref. 20].

The flow of building in a factory

Steinacker and colleagues write that the device was designed by Diraq and fabricated in a 300 mm spin-qubit process at imec. The gate pitch is below 100 nm, and optical lithography and electron-beam lithography (EBL) are combined to allow fast cycles and design flexibility (arXiv version) Sourced [Ref. 19]. In other words, even in a “300 mm factory,” the finest parts of the qubit include patterns drawn with an electron beam. Intel, by comparison, says it made Tunnel Falls on 300 mm wafers in its most advanced transistor fabrication facility, including extreme ultraviolet (EUV) lithography (company claim) [Ref. 26].

Main results so far (checked 16 October 2026)

Numbers are as stated in each paper or announcement. Checked 16 October 2026. We could not find gate-fidelity numbers for the eight-qubit work (none in the abstract). The table is our own organization (Our calculation).

8. Reading the results — how to take a fidelity number

How impressive is “99.5%”?

The fidelity of a quantum gate expresses “how closely the ideal operation was carried out” (see our explainer on coherence and fidelity). At a fidelity of 99.5%, the error is 0.5%, so on average one operation in 200 fails Our calculation. At 99.9% it is one in 1,000, and at 99.99% one in 10,000.

A useful yardstick is the threshold of an error-correcting code. Fowler and colleagues showed that for the surface code, error correction starts to work when the error rate is about 1% or lower Sourced [Ref. 36] (see our explainer on quantum error correction and the surface code). Noiri and colleagues reported that two-qubit gate fidelity of electron-spin qubits had been limited to 98%, and that they now obtained 99.5% (and 99.8% for single-qubit gates) Sourced [Ref. 13].

Number of qubits, and performance achieved at the same time

In 2022, Philips and colleagues built a six-qubit processor in silicon and reported running operations, state preparation and measurement together at respectable fidelities Sourced [Ref. 17]. The authors write that increasing the number of qubits and keeping high fidelity are usually conflicting requirements. As seen above, factory-made devices have been confirmed up to eight qubits (preprint) [Ref. 21].

In other words, the strength of silicon spin qubits lies in the performance of each individual qubit (long coherence and high fidelity) and in the way they are made, while the number of qubits is something still to be increased (our summary; checked 16 October 2026).

In addition, Mills and colleagues of Princeton reported a two-qubit silicon quantum processor with operation fidelity exceeding 99% (as given in the title) Sourced [Ref. 15]. Mądzik and colleagues, using the donor type with the nuclear spins of phosphorus atoms, reported a single-qubit gate fidelity of up to 99.95% and a two-qubit gate fidelity of 99.37% (evaluated with gate set tomography) Sourced [Ref. 18].

9. Running at higher temperatures, and a summary of strengths and weaknesses

Why raise the temperature?

As the calculation in Chapter 2 showed, low temperatures favor running a qubit in a good state. But the cooling power of a refrigerator is smaller the colder it runs. Yang and colleagues point out that for solid-state qubits, each additional qubit adds heat, while the cooling power of dilution refrigerators is extremely limited below 100 mK Sourced [Ref. 24]. So researchers are looking for qubits that work at higher temperatures (above 1 K).

• Petit et al. (2020): reported that silicon quantum dots can execute a universal gate set (single- and two-qubit gates) above 1 K. Single-qubit gate fidelity was up to 99.3%, and the exchange interaction could be tuned from 0.5 to 18 MHz Sourced [Ref. 23].
• Yang et al. (2020): operated a two-qubit unit cell in 28Si at about 1.5 K, with single-qubit gate fidelity of 98.6% and a coherence time of 2 µs, comparable to spin qubits in natural silicon measured at millikelvin temperatures. The field could be lowered to 0.1 T. Initialization and readout used only tunneling of electrons between quantum dots, with the dots isolated from the reservoir Sourced [Ref. 24].
• Camenzind et al. (2022): made a qubit from the spin of a hole (a missing electron) in a silicon FinFET (fin-shaped transistor) and operated it above 4 K, with a drive frequency up to 150 MHz and single-qubit gate fidelity at the fault-tolerance threshold Sourced [Ref. 25].

Strengths and weaknesses (no ranking against other platforms)

The table is our own organization (Our calculation). It is not a judgment of which is better. For comparison with other platforms (superconducting, ion, neutral atom, photonic), see the explainer for each platform in this series. Devices differ in conditions from paper to paper.

10. What we could not confirm, and a summary

What we could not confirm

• The full text of the Nature version of Steinacker et al.: we checked the abstract, but details such as the residual 29Si level (400 ppm) were checked in the arXiv version (October 2024, second version). The numbers in the Nature full text may differ (the Nature version has four devices and the arXiv version one, and values such as T₂* also differ).
• The journal for the eight-qubit paper: we checked the preprint, but could not confirm publication in Nature Communications (as press reports say) on a journal page. The abstract does not give gate-fidelity numbers.
• Intel's situation from 2024 onward: we have not checked the current state of Intel's silicon spin-qubit work after Tunnel Falls (2023) and Neyens et al. (2024).
• Secondary reports that logical operations were demonstrated with silicon spin qubits in 2026: we saw them, but could not confirm the primary paper, so we do not include them.
• Supply volume and price of 28Si feedstock, and the purity each company uses: not confirmed.
• Standards specific to silicon spin qubits: not confirmed (Chapter 11).
• Materials other than silicon, such as germanium hole spins: only touched on.

11. How to read evaluations and standards

The progress of silicon spin qubits is measured with several “yardsticks”: fidelity (how correct operations are), coherence time (how long the state is kept), accuracy of readout and state preparation, number of qubits, and uniformity of manufacturing. No single one tells the whole story. The number of qubits alone does not show performance, and a fidelity can mean different things depending on how it was measured (randomized benchmarking or gate set tomography) and on temperature and conditions. On the standards side, terminology standards are taking shape, but we could not confirm any evaluation standard specific to silicon spin qubits (checked 16 October 2026).

The table is our own organization (Our calculation). Numbers in brackets are reference numbers. ISO and IEEE numbers, titles and status were checked on the official pages (16 October 2026). Standards texts are paywalled, so we limit ourselves to titles and scope.

Cautions in reading (for materials engineers)

• “How many qubits” alone does not show performance: for silicon spin qubits, which have two to eight qubits, fidelity and coherence numbers are ahead of qubit count. Comparing them naively with platforms that have more qubits is meaningless. Always check whether qubits are physical or logical (all numbers in this article are physical qubits)
• A laboratory best value and a factory “uniform value” are different things: Yoneda et al. (single-qubit above 99.9%) and Steinacker et al. (above 99% on all four devices) are both important, but they mean different things. The latter shows reproducibility (whether devices come out alike)
• A company announcement and independent verification are different: Intel's 95% yield, Diraq's random selection and future qubit targets are company claims. Read them apart from what peer-reviewed papers confirm
• Standards are mostly recommendations, not requirements: ISO/IEC 4879 is a terminology standard and does not decide pass or fail on performance (our explanation). Treat plans and targets (qubit counts, years) as Not yet confirmed, not as achieved facts

12. Glossary

13. References (primary sources)

1. Loss D., DiVincenzo D. P. "Quantum computation with quantum dots", Phys. Rev. A 57, 120–126 (1998), DOI 10.1103/PhysRevA.57.120 — doi.org/10.1103/PhysRevA.57.120
2. Kane B. E. "A silicon-based nuclear spin quantum computer", Nature 393, 133–137 (1998), DOI 10.1038/30156 — doi.org/10.1038/30156
3. Burkard G., Ladd T. D., Pan A., Nichol J. M., Petta J. R. "Semiconductor spin qubits", Rev. Mod. Phys. 95, 025003 (2023), DOI 10.1103/RevModPhys.95.025003 (arXiv:2112.08863) — doi.org/10.1103/RevModPhys.95.025003
4. NIST "CODATA Fundamental Physical Constants" (electron gyromagnetic ratio, Boltzmann constant, Planck constant, lattice parameter of silicon) — physics.nist.gov/cuu/Constants/
5. NIST "Atomic Weights and Isotopic Compositions for Silicon" — physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=Si
6. Tyryshkin A. M. et al. "Electron spin coherence exceeding seconds in high-purity silicon", Nature Materials 11, 143–147 (2012), DOI 10.1038/nmat3182 — doi.org/10.1038/nmat3182
7. Muhonen J. T. et al. "Storing quantum information for 30 seconds in a nanoelectronic device", Nature Nanotechnology 9, 986–991 (2014), DOI 10.1038/nnano.2014.211 — doi.org/10.1038/nnano.2014.211
8. Dwyer K. J. et al. "Enriching 28Si beyond 99.9998 % for semiconductor quantum computing", J. Phys. D: Appl. Phys. 47, 345105 (2014), DOI 10.1088/0022-3727/47/34/345105 — doi.org/10.1088/0022-3727/47/34/345105
9. Tang K. et al. "Targeted enrichment of 28Si thin films for quantum computing", J. Phys. Commun. 4, 035006 (2020), DOI 10.1088/2399-6528/ab7b33 — doi.org/10.1088/2399-6528/ab7b33
10. Mazzocchi V. et al. "99.992% 28Si CVD-grown epilayer on 300 mm substrates for large scale integration of silicon spin qubits", J. Cryst. Growth 509, 1–7 (2019), DOI 10.1016/j.jcrysgro.2018.12.010 — doi.org/10.1016/j.jcrysgro.2018.12.010
11. Itoh K. M., Watanabe H. "Isotope engineering of silicon and diamond for quantum computing and sensing applications", MRS Commun. 4, 143–157 (2014), DOI 10.1557/mrc.2014.32 — doi.org/10.1557/mrc.2014.32
12. Yoneda J. et al. "A quantum-dot spin qubit with coherence limited by charge noise and fidelity higher than 99.9%", Nature Nanotechnology 13, 102–106 (2018), DOI 10.1038/s41565-017-0014-x — doi.org/10.1038/s41565-017-0014-x
13. Noiri A. et al. "Fast universal quantum gate above the fault-tolerance threshold in silicon", Nature 601, 338–342 (2022), DOI 10.1038/s41586-021-04182-y — doi.org/10.1038/s41586-021-04182-y
14. Xue X. et al. "Quantum logic with spin qubits crossing the surface code threshold", Nature 601, 343–347 (2022), DOI 10.1038/s41586-021-04273-w — doi.org/10.1038/s41586-021-04273-w
15. Mills A. R. et al. "Two-qubit silicon quantum processor with operation fidelity exceeding 99%", Science Advances 8, eabn5130 (2022), DOI 10.1126/sciadv.abn5130 — doi.org/10.1126/sciadv.abn5130
16. Takeda K. et al. "Quantum error correction with silicon spin qubits", Nature 608, 682–686 (2022), DOI 10.1038/s41586-022-04986-6 — doi.org/10.1038/s41586-022-04986-6
17. Philips S. G. J. et al. "Universal control of a six-qubit quantum processor in silicon", Nature 609, 919–924 (2022), DOI 10.1038/s41586-022-05117-x — doi.org/10.1038/s41586-022-05117-x
18. Mądzik M. T. et al. "Precision tomography of a three-qubit donor quantum processor in silicon", Nature 601, 348–353 (2022), DOI 10.1038/s41586-021-04292-7 — doi.org/10.1038/s41586-021-04292-7
19. Steinacker P. et al. "A 300 mm foundry silicon spin qubit unit cell exceeding 99 % fidelity in all operations", arXiv:2410.15590 (second version, October 2024) — arxiv.org/abs/2410.15590
20. Steinacker P., Dumoulin Stuyck N. et al. "Industry-compatible silicon spin-qubit unit cells exceeding 99% fidelity", Nature 646, 81–87 (2025), DOI 10.1038/s41586-025-09531-9 — doi.org/10.1038/s41586-025-09531-9
21. Nickl A. et al. "Eight-Qubit Operation of a 300 mm SiMOS Foundry-Fabricated Device", arXiv:2512.10174 (December 2025, preprint) — arxiv.org/abs/2512.10174
22. Neyens S. F. et al. "Probing single electrons across 300-mm spin qubit wafers", Nature 629, 80–85 (2024), DOI 10.1038/s41586-024-07275-6 — doi.org/10.1038/s41586-024-07275-6
23. Petit L. et al. "Universal quantum logic in hot silicon qubits", Nature 580, 355–359 (2020), DOI 10.1038/s41586-020-2170-7 — doi.org/10.1038/s41586-020-2170-7
24. Yang C. H. et al. "Operation of a silicon quantum processor unit cell above one kelvin", Nature 580, 350–354 (2020), DOI 10.1038/s41586-020-2171-6 — doi.org/10.1038/s41586-020-2171-6
25. Camenzind L. C. et al. "A hole spin qubit in a fin field-effect transistor above 4 kelvin", Nature Electronics 5, 178–183 (2022), DOI 10.1038/s41928-022-00722-0 — doi.org/10.1038/s41928-022-00722-0
26. Intel "Intel's New Chip to Advance Silicon Spin Qubit Research for Quantum Computing" (Tunnel Falls, 15 June 2023, Intel newsroom) — intel.com/…/quantum-computing-chip-to-advance-research.html
27. Elzerman J. M. et al. "Single-shot read-out of an individual electron spin in a quantum dot", Nature 430, 431–435 (2004), DOI 10.1038/nature02693 — doi.org/10.1038/nature02693
28. Paquelet Wuetz B. et al. "Atomic fluctuations lifting the energy degeneracy in Si/SiGe quantum dots", Nature Communications 13, 7730 (2022), DOI 10.1038/s41467-022-35458-0 — doi.org/10.1038/s41467-022-35458-0
29. Hendrickx N. W. et al. "A four-qubit germanium quantum processor", Nature 591, 580–585 (2021), DOI 10.1038/s41586-021-03332-6 — doi.org/10.1038/s41586-021-03332-6
30. Xue X. et al. "CMOS-based cryogenic control of silicon quantum circuits", Nature 593, 205–210 (2021), DOI 10.1038/s41586-021-03469-4 — doi.org/10.1038/s41586-021-03469-4
31. Vandersypen L. M. K. et al. "Interfacing spin qubits in quantum dots and donors—hot, dense, and coherent", npj Quantum Information 3, 34 (2017), DOI 10.1038/s41534-017-0038-y — doi.org/10.1038/s41534-017-0038-y
32. Zwanenburg F. A. et al. "Silicon quantum electronics", Rev. Mod. Phys. 85, 961–1019 (2013), DOI 10.1103/RevModPhys.85.961 — doi.org/10.1103/RevModPhys.85.961
33. Knill E. et al. "Randomized benchmarking of quantum gates", Phys. Rev. A 77, 012307 (2008), DOI 10.1103/PhysRevA.77.012307 — doi.org/10.1103/PhysRevA.77.012307
34. Magesan E., Gambetta J. M., Emerson J. "Scalable and Robust Randomized Benchmarking of Quantum Processes", Phys. Rev. Lett. 106, 180504 (2011), DOI 10.1103/PhysRevLett.106.180504 — doi.org/10.1103/PhysRevLett.106.180504
35. Nielsen E. et al. "Gate Set Tomography", Quantum 5, 557 (2021), DOI 10.22331/q-2021-10-05-557 — doi.org/10.22331/q-2021-10-05-557
36. Fowler A. G., Mariantoni M., Martinis J. M., Cleland A. N. "Surface codes: Towards practical large-scale quantum computation", Phys. Rev. A 86, 032324 (2012), DOI 10.1103/PhysRevA.86.032324 — doi.org/10.1103/PhysRevA.86.032324
37. DiVincenzo D. P. "The Physical Implementation of Quantum Computation", Fortschr. Phys. 48, 771–783 (2000), arXiv:quant-ph/0002077 — arxiv.org/abs/quant-ph/0002077
38. ISO/IEC "ISO/IEC 4879:2024 Information technology — Quantum computing — Vocabulary" (ISO page) — committee.iso.org/standard/80432.html
39. ISO/IEC "IEC/ISO JTC 3 Quantum technologies" (committee page) — committee.iso.org/committee/10138914.html
40. IEEE SA "IEEE Draft Standard for Quantum Technologies Definitions" (P7130, Active PAR) — standards.ieee.org/ieee/7130/10680/
41. Takeda K. et al. "A fault-tolerant addressable spin qubit in a natural silicon quantum dot", Science Advances 2, e1600694 (2016), DOI 10.1126/sciadv.1600694 — doi.org/10.1126/sciadv.1600694
42. Diraq / imec "Imec technology lights the path to utility scale for Diraq's quantum chips" (company announcement, September 2025) — diraq.com/newsdesk/imec-technology-lights-the-path-to-utility-scale-for-diraqs-quantum-chips
43. The Quantum Insider "Diraq Demonstrates Scaled Foundry-Fabricated Silicon-Based Qubit Array Made at imec" (9 July 2026; an article reporting a company announcement, used only as a pointer to primary information) — thequantuminsider.com/2026/07/09/diraq-demonstrates-scaled-foundry-fabricated-silicon-based-qubit-array-made-at-imec/
44. DARPA "Four more teams enter Quantum Benchmarking Initiative's final stage" (7 October 2026) — darpa.mil/news/2026/four-more-teams-enter-quantum-benchmarking-initiative-final-stage

14. Claim-to-source audit

Last updated: 16 October 2026. Sources are mainly primary (peer-reviewed papers, arXiv papers, NIST physical constants and isotope compositions, ISO and IEEE pages); company announcements are marked as company claims. The quantum-dot size (20 x 20 x 5 nm) is a made-up value for the calculation. We could not confirm, and therefore do not state, the full text of the Nature version of Steinacker et al., the journal for the eight-qubit paper, Intel's status from 2024 onward, or standards specific to silicon spin qubits. All figures are explanatory concept drawings or drawings including our calculations; Figs. 1 and 8 are ImageGen-generated conceptual illustrations.