1. Why “topological”? — the knot analogy

First, qubits are fragile

A qubit's arrow gets blurred by the slightest disturbance from the surroundings (heat, fluctuating electric and magnetic fields, defects in the material). To prevent this, the mainstream approach today is error correction, in which many qubits together protect one logical qubit (see our explainer on quantum error correction and the surface code). It does, however, need a large number of qubits.

There is another idea: not “fix an error once it happens,” but store the information in a form that errors can hardly touch in the first place. Kitaev proposed that computing with excitations called “anyons” in a two-dimensional quantum system would be fault-tolerant by its physical nature Sourced [Ref. 1]. This is the starting point of topological quantum computing.

An everyday picture: a knot in a rope, and the hole in a donut

Suppose you tie a knot in a rope. Pinching a part of the rope and shaking it, or pulling it a little, does not remove the knot. To undo it, you must move the rope a lot and work on the whole. The knot is not about “one spot” in the rope; it is a property of the whole shape.

Another example is the hole in a donut. Make a donut out of clay and squash it into any shape; as long as you do not tear it or glue parts together, it keeps one hole. The number of holes is a property that does not change under continuous deformation. In mathematics, such properties are called topology.

Storing quantum information like a knot

The idea of topological quantum computing is to store the qubit's information in the “global property” of a material. A small surrounding disturbance is like “pinching one spot of the rope” and barely touches the global property (the information). This way of thinking is called “topological protection.” The review by Nayak and colleagues explains that the error resistance of this approach comes from encoding the quantum state non-locally, which makes it immune to errors caused by local perturbations Sourced [Ref. 3].

2. Anyons and braiding — computing by exchanging particles

An everyday sense: swapping two strands

If you set three strands side by side and keep swapping left and right as time passes, the strands become braided. Think of a braided plait of hair. Which strands you swap, and in what order, changes the braid you end up with.

Exchanging particles is similar. If you draw particle positions with place on the horizontal axis and time on the vertical axis, each particle's path becomes a “strand.” Exchanging particles makes the strands cross.

The difference between three and two dimensions

In the three-dimensional space we live in, if you swap two identical particles and then swap them again, you always return to the start (because the strands can be moved in space to undo the crossing). Electrons and photons behave this way. But in a world confined to a two-dimensional surface, the crossings of strands can stay tangled. The history of the order of exchanges remains as a “tangle.” Particle-like objects (quasiparticles) with this property are called anyons (our explanation; for reviews see [Refs. 3, 4]).

“Non-Abelian” means the order changes the result

Among anyons, non-Abelian anyons are those for which the order of exchanges changes the state of the whole system. As an analogy, “put on socks and then shoes” and “put on shoes and then socks” give different results. This property that order matters can be used for quantum gates.

Computing with braiding and measurement

The review by Nayak and colleagues explains that in topological quantum computing, quantum information is stored in the states of groups of several quasiparticles (topological degeneracy), and the unitary operations needed for quantum gates are carried out by braiding the quasiparticles and then measuring the group state Sourced [Ref. 3]. Kitaev also writes that a measurement can be made by bringing quasiparticles together in pairs (fusion) and observing the result [Ref. 1].

In actual devices, however, designs have been proposed (measurement-only computation) in which, instead of physically moving particles around each other, a sequence of measurements realizes the same operation. Microsoft's future plan (roadmap) also includes a stage that performs single-qubit operations by “measurement-based braiding” (a company plan) Not yet confirmed [Ref. 24].

3. Majorana quasiparticles and parity — storing information at the ends of a nanowire

What a Majorana quasiparticle is

Electrons have “antiparticles” (partners with the opposite sign of electric charge). A Majorana particle is a special kind of particle for which the particle and the antiparticle are the same. The Majorana quasiparticle discussed here is not an elementary particle but a quasiparticle that exists only inside matter, an excitation that is its own antiparticle (as the opening of the paper by Mourik and colleagues puts it, Majorana fermions are particles identical to their own antiparticles, predicted to exist in topological superconductors [Ref. 7]).

In 2010, Lutchyn and colleagues and Oreg and colleagues proposed that if a superconductor is brought into contact with a semiconductor nanowire (with strong spin-orbit coupling) and a magnetic field is applied, the wire enters a topological superconducting state and Majorana quasiparticles appear at its two ends Sourced [Refs. 5, 6, 15]. The root of the idea is the model Kitaev presented in 2001, in which “unpaired Majoranas” appear at the ends of a one-dimensional chain [Ref. 2].

One qubit from two ends — the tally-stick analogy

Suppose there is one Majorana quasiparticle at each end of a wire. These two together form one ordinary electron state. That state has two possibilities, “one electron present” or “absent,” called parity (whether the number of electrons is even or odd). These two possibilities are used as the qubit's 0 and 1.

Think of a tally stick. Split one stick in two and put each half at opposite ends. Examining only one half tells you nothing about the content of the whole stick. You can only tell whether it is the original stick by putting the two halves together. For Majorana quasiparticles too, examining only one end does not reveal the parity (the information). The information spans the two ends, and a local disturbance can touch only one end. This is the source of the protection.

Limits of the analogy: halves of a tally stick become two separate objects once split. The two Majoranas are the two ends of a single quantum state that cannot be divided, not detachable parts. Also, if an electron from outside enters at one end, the parity changes (this is quasiparticle “poisoning”; Chapter 5).

Does a longer wire reduce errors exponentially? — our calculation

Kitaev wrote that a one-dimensional system of length L has two ground states of different parity whose energy difference becomes smaller in proportion to exp(−L/ℓ₀) Sourced [Ref. 2] (ℓ₀ is a length set by the material). The smaller the energy difference between these two states, the harder it is to tell them apart, so the parity information becomes more robust against disturbance. Kitaev adds that such a system can be used as a qubit and is intrinsically immune to decoherence [Ref. 2].

Let us check the meaning of this formula with numbers. The exponential e^−L/ℓ₀, where L/ℓ₀ is how many times longer the wire is than the characteristic length, shrinks quickly as follows (the simplest estimate, ignoring the prefactor).

Calculation: e^−x (Our calculation). The “35” is an example using values from the company's preprint (wire length 3.5 µm; minimum coherence length expected for a clean system about 100 nm), the ratio 3.5 µm / 100 nm = 35 [Ref. 27]. In real devices, however, disorder and finite temperature mean this simple formula does not hold exactly.

How is parity read out?

Parity is whether the electron number is even or odd, and it is hard to learn by measuring the charge at one spot (the QuTech work confirms that the two parity states of a minimal chain are charge-neutral and cannot be told apart by a measurement that does not couple the two modes [Ref. 36]). So a semiconductor quantum dot is connected to the wire, and the fact that the quantum capacitance of the dot (the tiny electrical-capacitance response to electrons coming and going) changes slightly with parity is used for readout. Microsoft's 2025 Nature paper reported a single-shot interferometric measurement of parity using this method in an InAs and Al device. It writes that the capacitance change of the quantum dot is up to about 1 fF, the measurement's signal-to-noise ratio is 1 in 3.6 µs, and the dwell time in the two states exceeded 1 millisecond at an in-plane field of about 2 tesla Sourced [Ref. 18]. The same paper itself states that the measurements can be interpreted in terms of both topologically trivial and non-trivial origins [Ref. 18].

4. Materials — nanowires, superconductors and the interface

What this approach needs from materials

Translated into materials terms, what the proposals of Lutchyn and colleagues and Oreg and colleagues require is as follows Sourced [Refs. 5, 6, 15].

• Semiconductor: strong coupling between the direction of an electron's spin and its direction of motion (spin-orbit interaction), a large response to a magnetic field (a large g-factor), and low disorder (defects and impurities). InAs and InSb are used
• Superconductor: a large superconducting gap (the energy needed to break an electron pair) and tolerance of magnetic fields. Al, NbTiN, Pb and others are used
• Interface: the boundary between semiconductor and superconductor should be uniform at the atomic level and induce a “hard gap” (no extra states inside the gap) in the semiconductor
• Magnetic field: a field of several hundred millitesla up to about 2 tesla is applied (it depends on the device)

Why a “hard gap” is needed

Chang and colleagues write that earlier devices, in which a superconductor contacts a semiconductor, show a continuum of states inside the gap through which current flows (a soft gap), and that this nullifies topological protection Sourced [Ref. 8]. If there are many extra states inside the gap, the premise that “the gap protects it” fails. Chang and colleagues reported a hard gap in epitaxial (crystal-aligned) InAs and Al nanowires [Ref. 8]. Krogstrup and colleagues grew InAs/Al by molecular beam epitaxy, stated that an atomically uniform interface is the key to the quality of the induced gap, and wrote that the method “seems to solve the soft-gap problem” [Ref. 9]. The soft-gap problem itself is discussed in the paper of Takei and colleagues [Ref. 10].

Material combinations and reports so far

The table is our own organization (Our calculation). It does not argue which combination is “right” or better.

5. Looking at the numbers — gaps, temperature and parity lifetime (our calculation)

Is the gap large enough compared with temperature?

The “topological gap” of a topological superconductor (the energy wall that protects the information) must be sufficiently larger than the thermal jitter. How easily heat lifts an excitation over this wall is roughly proportional to exp(−Δ/k_BT) (our explanation; a general estimate at thermal equilibrium). As in our explainer on silicon spin qubits, let us convert energy to temperature (1 µeV corresponds to about 11.6 mK).

Calculation: Δ/k_B (k_B = 86.17 µeV/K) and exp(−Δ/k_BT) (Our calculation). The temperature of 20 mK is an example of a refrigerator's operating temperature, not the actual temperature of each device. The gap values are those reported by the topological gap protocol (TGP), whose validity is disputed (Chapter 6).

Parity lifetime — longer is better, but what was measured?

The parity lifetime is the typical time until parity flips. To use parity as a qubit, this lifetime must be far longer than the operation time (about a microsecond). The figure below places reported values on a logarithmic scale.

Let us sort out what the numbers mean. The Z parity lifetime shows how long the parity itself is kept, and is reported as 12.4 ms for the Al-based tetron and about 20 s for the Pb-based preprint (company claims) Sourced [Refs. 25, 27]. 20 s / 12.4 ms is about 1,600 times, and 20 s / 1 µs (the operation-time guide) is about 2 × 10⁷ times Our calculation.

To work as a qubit, however, an X measurement (parity inside the wire) is also needed. In the X loop of the same Al-based tetron, the parity flips quickly, in 14.5 µs, and the estimated measurement assignment errors are reported as 16% for X and 0.5% for Z Sourced [Ref. 25]. The ratio of the Z and X lifetimes is 12.4 ms / 14.5 µs = about 855 Our calculation. What the 2026 preprint shows is a Z measurement; an X measurement could not be found in the preprint's text (our reading). So “the parity lifetime became 1000 times longer” is not the same as “the time a qubit can be used became 1000 times longer.”

6. Claims and disputes — what is confirmed, what is disputed, what is not confirmed

This chapter organizes the course of the experiments in topological quantum computing by setting official documents, papers, critical papers and replies side by side. It does not settle on either conclusion, and separates “what can be confirmed,” “points where interpretation is disputed” and “points not confirmed.” The check date is 16 October 2026.

Timeline

1. What can be confirmed

• Theoretical proposals: the proposals of Kitaev (2001, 2003) and of Lutchyn et al. and Oreg et al. (2010) exist as peer-reviewed papers Sourced [Refs. 1, 2, 5, 6].
• The 2012 observation: Mourik and colleagues observed states pinned at zero voltage in InSb nanowires in fields of about 100 mT, and wrote that this supports the Majorana hypothesis Sourced [Ref. 7].
• Retraction of the 2018 paper: Zhang and colleagues reported in 2018 a plateau of quantized conductance at 2e²/h [Ref. 13]. The retraction notice of March 2021 (by the authors) says that other researchers pointed out inconsistencies between the raw data made available to them and the published figures. When the authors re-analysed, they found that in some figures corrections for charge jumps had not been stated in the paper, that a figure axis was mislabelled, and that after recalibration the plateau values shifted by 8% (upward from 2e²/h), with points outside the two-sigma error bars. They wrote that they could no longer claim to have observed quantized Majorana conductance Sourced [Ref. 14].
• The 2023 paper (Microsoft): reported that devices passed the “topological gap protocol (TGP).” The paper writes that the results are consistent with the observation of topological superconductivity and Majorana zero modes, that the maximum topological gaps reported are 20 to 60 µeV, and that this is a prerequisite for experiments on fusion and braiding of Majorana zero modes Sourced [Ref. 17]. In other words, fusion and braiding were future experiments at the time of that paper.
• The February 2025 paper (Microsoft, Nature): reported a single-shot interferometric measurement of parity in an InAs and Al device. The paper states that the measurement can be interpreted in terms of both topological and non-topological origins, and that the device is compatible with future tests of fusion rules Sourced [Ref. 18].
• The Nature editorial note: at the start of the peer review file, the editorial team writes that after the second round of review it sought additional input from two reviewers to establish technical correctness, and then proceeded to publication. It specifically notes that the results of the paper do not represent evidence for the presence of Majorana zero modes in the reported devices, and that the paper was published for introducing a device architecture that might enable fusion experiments using future Majorana zero modes Sourced [Ref. 19].
• The company's announcement: in its announcement of 19 February 2025, Microsoft called Majorana 1 the “world's first quantum chip” built on a new “Topological Core” architecture, said eight topological qubits had been placed on the chip, and described the Nature paper as “peer-reviewed confirmation” that Majorana particles were created and measured with microwaves (company claims) [Ref. 28]. The strength of the wording differs from that of the editorial note for the same paper (above).
• DARPA's evaluation: on 6 February 2025, DARPA announced that it had selected Microsoft and PsiQuantum for the final phase (validation and co-design) of the US2QC program. It says its evaluation team had worked with both companies since early 2023 and that more than 50 experts examined their technical approaches, prototype plans and long-term plans. Microsoft's approach is described as a “compact superconducting topological qubit architecture” [Ref. 31]. The announcement of 7 October 2026 says Microsoft and PsiQuantum are already in the final stage (Stage C) [Ref. 32]. This is a stage that verifies whether a design can be built as designed and operated as intended; it is not a certification that topological qubits exist (our explanation; DARPA states that QBI is not a competition between companies and does not pick winners and losers [Ref. 32]).
• The July 2025 preprint (X and Z parity): in a tetron with two nanowires and four Majorana zero modes (when tuned into the topological phase), the time scales of the X and Z parity measurements were estimated at τ_X = 14.5 µs and τ_Z = 12.4 ms, with measurement assignment errors of 16% for X and 0.5% for Z. This paper was accepted by Physical Review A on 1 October 2026 (the version of record has not been confirmed) Sourced [Refs. 25, 26].
• The June 2026 preprint (Microsoft): in an InAs-Pb tetron whose superconductor was changed to Pb, a Z parity switching time of about 20 seconds was reported (not peer-reviewed). The paper gives the top-quintile gap reported by the TGP as about 70 µeV for the Pb-based devices (about 30 µeV for Al-based) (company claims) Sourced [Ref. 27]. Microsoft announced this as “Majorana 2” and stated an aim of a practical quantum computer by 2029 (a company target) Not yet confirmed [Ref. 29].

2. Points where interpretation is disputed (both sides side by side)

The table is our own organization (Our calculation). Refs. 39 to 41 are news reports (used as pointers to primary information); the primary sources are Refs. 17 to 23 and 27. This article does not rule on which side is right.

3. Points not confirmed

• Demonstration of braiding and fusion: the authors' own papers call this a “future experiment” [Refs. 17, 18]. Within this survey, we could not confirm a peer-reviewed paper that demonstrated braiding or fusion with topological qubits.
• Performance as a qubit: coherent operation and fidelity measured by benchmarking could not be confirmed. Microsoft's plan (roadmap) places this in future stages (a company plan; Not yet confirmed) [Ref. 24].
• Reproduction by third parties: within this survey, we could not confirm a paper in which a laboratory other than Microsoft's independently reproduced the results of Microsoft's devices.
• The results of DARPA's independent evaluation: we could not confirm that they have been published. Microsoft says that in September 2026 it handed a topological system to DARPA for independent testing (a company claim) [Ref. 30].

7. Other routes — chains built from quantum dots, and reproduction on quantum computers

Microsoft's approach is not the only route in topological quantum computing. Here we look at three other routes.

The table is our own organization (Our calculation). It does not rank the routes.

8. What we could not confirm, and a summary

What we could not confirm

• Microsoft's formal reply to Legg's February 2025 critique (of the 2023 PRB paper): we could not confirm one within this survey.
• The full text of the Matters Arising of 24 June 2026: on Nature's pages we could check the abstract of the critique (Legg) and the opening of the reply (Microsoft Quantum). The full texts require a subscription, so we did not check them.
• The additional data said to have been shown at the American Physical Society meeting in March 2025: the report (APS Physics magazine) says they would be presented there, but we could not confirm what they were [Ref. 39].
• The peer-review status of the June 2026 preprint, and the total number of qubits in Majorana 2: not confirmed (Microsoft's blog shows a figure of a four-qubit array, but we could not confirm a total chip count) [Ref. 29].
• Independent reproduction of the devices by laboratories other than Microsoft's: not confirmed.
• The results of DARPA's evaluation: we could not confirm published results.
• The present state of experiments on the fractional quantum Hall state (ν = 5/2): we stayed with the statement of a 2008 review and did not check the current state.
• Standards or specifications specific to topological quantum computing: not confirmed (Chapter 9).

9. How to read evaluations and standards

The progress of topological quantum computing is measured with staged “yardsticks”: electrical tests that show a topological phase, quality of parity measurement, parity lifetime, operation and performance as a qubit, and demonstration of braiding and fusion (Fig. 8). The “gate fidelity” and “coherence time” used for ordinary qubits have not yet been measured for topological qubits. In addition, independent third-party evaluation, and the peer review, critique and retraction of papers, serve in practice as yardsticks. On the standards side, terminology standards are taking shape, but we could not confirm any evaluation standard specific to topological quantum computing (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)

• What is “how many qubits” counting? Distinguish whether a claim such as “eight qubits were placed” is a design number or a number whose operation as qubits has been confirmed. The numbers in this article are all numbers of physical devices or design numbers, not logical qubits
• Separate the measured fact from the interpretation: “parity could be measured” and “it has a topological origin” are different claims. There are cases where a paper itself states both interpretations
• A company announcement, a peer-reviewed paper and an editorial note are different things: a press release can be stronger than the paper. Check the peer review file and editorial notes too. A preprint is not peer-reviewed
• Plans and achievements are different: targets such as a practical quantum computer by 2029 are Not yet confirmed. Progress through DARPA's stages is progress in design verification, not a certification that qubits exist

10. Glossary

11. References (primary sources)

1. Kitaev A. Yu. "Fault-tolerant quantum computation by anyons", Annals of Physics 303, 2–30 (2003), DOI 10.1016/S0003-4916(02)00018-0 (arXiv:quant-ph/9707021) — doi.org/10.1016/S0003-4916(02)00018-0
2. Kitaev A. "Unpaired Majorana fermions in quantum wires", Physics-Uspekhi 44, 131–136 (2001), DOI 10.1070/1063-7869/44/10S/S29 — doi.org/10.1070/1063-7869/44/10S/S29
3. Nayak C., Simon S. H., Stern A., Freedman M., Das Sarma S. "Non-Abelian anyons and topological quantum computation", Rev. Mod. Phys. 80, 1083–1159 (2008), DOI 10.1103/RevModPhys.80.1083 — doi.org/10.1103/RevModPhys.80.1083
4. Das Sarma S., Freedman M., Nayak C. "Majorana zero modes and topological quantum computation", npj Quantum Information 1, 15001 (2015), DOI 10.1038/npjqi.2015.1 — doi.org/10.1038/npjqi.2015.1
5. Lutchyn R. M., Sau J. D., Das Sarma S. "Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures", Phys. Rev. Lett. 105, 077001 (2010), DOI 10.1103/PhysRevLett.105.077001 — doi.org/10.1103/PhysRevLett.105.077001
6. Oreg Y., Refael G., von Oppen F. "Helical Liquids and Majorana Bound States in Quantum Wires", Phys. Rev. Lett. 105, 177002 (2010), DOI 10.1103/PhysRevLett.105.177002 — doi.org/10.1103/PhysRevLett.105.177002
7. Mourik V. et al. "Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices", Science 336, 1003–1007 (2012), DOI 10.1126/science.1222360 — doi.org/10.1126/science.1222360
8. Chang W. et al. "Hard gap in epitaxial semiconductor–superconductor nanowires", Nature Nanotechnology 10, 232–236 (2015), DOI 10.1038/nnano.2014.306 — doi.org/10.1038/nnano.2014.306
9. Krogstrup P. et al. "Epitaxy of semiconductor–superconductor nanowires", Nature Materials 14, 400–406 (2015), DOI 10.1038/nmat4176 — doi.org/10.1038/nmat4176
10. Takei S., Fregoso B. M., Hui H.-Y., Lobos A. M., Das Sarma S. "Soft Superconducting Gap in Semiconductor Majorana Nanowires", Phys. Rev. Lett. 110, 186803 (2013), DOI 10.1103/PhysRevLett.110.186803 — doi.org/10.1103/PhysRevLett.110.186803
11. Shabani J. et al. "Two-dimensional epitaxial superconductor-semiconductor heterostructures: A platform for topological superconducting networks", Phys. Rev. B 93, 155402 (2016), DOI 10.1103/PhysRevB.93.155402 — doi.org/10.1103/PhysRevB.93.155402
12. Pauka S. J. et al. "Repairing the surface of InAs-based topological heterostructures", J. Appl. Phys. 128, 114301 (2020), DOI 10.1063/5.0014361 — doi.org/10.1063/5.0014361
13. Zhang H. et al. "Quantized Majorana conductance", Nature 556, 74–79 (2018) (retracted), DOI 10.1038/nature26142 — doi.org/10.1038/nature26142
14. Zhang H. et al. "Retraction Note: Quantized Majorana conductance", Nature 591, E30 (2021) (8 March 2021), DOI 10.1038/s41586-021-03373-x — doi.org/10.1038/s41586-021-03373-x
15. Frolov S. M., Manfra M. J., Sau J. D. "Topological superconductivity in hybrid devices", Nature Physics 16, 718–724 (2020), DOI 10.1038/s41567-020-0925-6 — doi.org/10.1038/s41567-020-0925-6
16. Pikulin D. I. et al. "Protocol to identify a topological superconducting phase in a three-terminal device", arXiv:2103.12217 (2021) — arxiv.org/abs/2103.12217
17. Aghaee M. et al. (Microsoft Azure Quantum) "InAs-Al hybrid devices passing the topological gap protocol", Phys. Rev. B 107, 245423 (2023), DOI 10.1103/PhysRevB.107.245423 — doi.org/10.1103/PhysRevB.107.245423
18. Microsoft Azure Quantum "Interferometric single-shot parity measurement in InAs–Al hybrid devices", Nature 638, 651–655 (2025) (19 February 2025), DOI 10.1038/s41586-024-08445-2 — doi.org/10.1038/s41586-024-08445-2
19. Nature Peer Review File of the paper above (the editorial note is at its start) — media.springernature.com/…/41586_2024_8445_MOESM2_ESM.pdf
20. Legg H. F. "Comment on 'InAs-Al hybrid devices passing the topological gap protocol', Microsoft Quantum, Phys. Rev. B 107, 245423 (2023)", arXiv:2502.19560 (February 2025) — arxiv.org/abs/2502.19560
21. Legg H. F. "Comment on 'Interferometric single-shot parity measurement in InAs-Al hybrid devices', Microsoft Quantum, Nature 638, 651-655 (2025)", arXiv:2503.08944 (March 2025) — arxiv.org/abs/2503.08944
22. Legg H. F. "On the robustness of topological gap detection via transport", Nature 654, E22–E26 (2026) (Matters Arising, 24 June 2026), DOI 10.1038/s41586-026-10567-8 — doi.org/10.1038/s41586-026-10567-8
23. Microsoft Quantum "Reply to: On the robustness of topological gap detection via transport", Nature 654, E27–E28 (2026) (reply to the Matters Arising, 24 June 2026), DOI 10.1038/s41586-026-10568-7 — doi.org/10.1038/s41586-026-10568-7
24. Aasen D. et al. (Microsoft Quantum) "Roadmap to fault tolerant quantum computation using topological qubit arrays", arXiv:2502.12252 (February 2025, a company plan) — arxiv.org/abs/2502.12252
25. Aghaee M. et al. (Microsoft Quantum) "Distinct Lifetimes for X and Z Loop Measurements in a Majorana Tetron Device", arXiv:2507.08795 (July 2025) — arxiv.org/abs/2507.08795
26. Physical Review A "Distinct lifetimes for X and Z loop measurements in a Majorana tetron device" (accepted paper, accepted 1 October 2026), DOI 10.1103/cx4w-lxx1 — journals.aps.org/pra/accepted/10.1103/cx4w-lxx1
27. Microsoft Quantum "20 Second Parity Lifetime in an InAs–Pb Tetron Device", arXiv:2606.03884 (June 2026, preprint, not peer-reviewed) — arxiv.org/abs/2606.03884
28. Microsoft "Microsoft's Majorana 1 chip carves new path for quantum computing" (19 February 2025, company announcement) — news.microsoft.com/source/features/innovation/microsofts-majorana-1-chip-carves-new-path-for-quantum-computing/
29. Microsoft Quantum Blog on “Majorana 2” (June 2026, company announcement) — quantum.microsoft.com/en-us/insights/blogs/majorana-2-scalable-quantum-processor
30. Microsoft Quantum Blog on the quantum research center in Maryland (22 September 2026, company announcement) — quantum.microsoft.com/en-us/insights/blogs/microsoft-quantum-research-center-maryland
31. DARPA "DARPA selects two discrete utility-scale quantum computing approaches for evaluation" (6 February 2025) — darpa.mil/news/2025/quantum-computing-approaches
32. 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
33. Dvir T. et al. "Realization of a minimal Kitaev chain in coupled quantum dots", Nature 614, 445–450 (2023), DOI 10.1038/s41586-022-05585-1 — doi.org/10.1038/s41586-022-05585-1
34. ten Haaf S. L. D. et al. "A two-site Kitaev chain in a two-dimensional electron gas", Nature 630, 329–334 (2024), DOI 10.1038/s41586-024-07434-9 — doi.org/10.1038/s41586-024-07434-9
35. Bordin A. et al. "Enhanced Majorana stability in a three-site Kitaev chain", Nature Nanotechnology 20, 726–731 (2025), DOI 10.1038/s41565-025-01894-4 — doi.org/10.1038/s41565-025-01894-4
36. van Loo N. et al. "Single-shot parity readout of a minimal Kitaev chain", Nature 650, 334–339 (2026) (11 February 2026), DOI 10.1038/s41586-025-09927-7 — doi.org/10.1038/s41586-025-09927-7
37. Google Quantum AI and Collaborators (Andersen T. I. et al.) "Non-Abelian braiding of graph vertices in a superconducting processor", Nature 618, 264–269 (2023), DOI 10.1038/s41586-023-05954-4 — doi.org/10.1038/s41586-023-05954-4
38. Iqbal M. et al. "Non-Abelian topological order and anyons on a trapped-ion processor", Nature 626, 505–511 (2024), DOI 10.1038/s41586-023-06934-4 — doi.org/10.1038/s41586-023-06934-4
39. Ball P. "Experts Weigh in on Microsoft's Topological Qubit Claim", Physics 18, 57 (10 March 2025; an explanatory article by the APS; a news report) — physics.aps.org/articles/v18/57
40. Science News "Microsoft's quantum chip got an upgrade. Critics are still skeptical" (June 2026; a news report) — sciencenews.org/article/microsoft-quantum-chip-upgrade-majorana
41. Scientific American "Top quantum computer expert claims Microsoft's 'topological qubit' doesn't hold up" (24 June 2026; a news report) — scientificamerican.com/article/top-quantum-computer-expert-claims-microsofts-topological-qubit-doesnt-hold-up/
42. ISO/IEC "ISO/IEC 4879:2024 Information technology — Quantum computing — Vocabulary" (ISO page) — committee.iso.org/standard/80432.html
43. ISO/IEC "IEC/ISO JTC 3 Quantum technologies" (committee page) — committee.iso.org/committee/10138914.html
44. IEEE SA "IEEE Draft Standard for Quantum Technologies Definitions" (P7130, Active PAR) — standards.ieee.org/ieee/7130/10680/
45. Liu C.-X., Sau J. D., Stanescu T. D., Das Sarma S. "Andreev bound states versus Majorana bound states in quantum dot-nanowire-superconductor hybrid structures: Trivial versus topological zero-bias conductance peaks", Phys. Rev. B 96, 075161 (2017), DOI 10.1103/PhysRevB.96.075161 — doi.org/10.1103/PhysRevB.96.075161
46. Das A. et al. "Zero-bias peaks and splitting in an Al–InAs nanowire topological superconductor as a signature of Majorana fermions", Nature Physics 8, 887–895 (2012), DOI 10.1038/nphys2479 — doi.org/10.1038/nphys2479

12. Claim-to-source audit

Last updated: 16 October 2026. Sources are mainly primary (original theory papers, peer-reviewed experimental papers, the retraction notice, the Nature editorial note and peer review file, critical papers and replies, and official DARPA, ISO and IEEE pages); company announcements and preprints are marked as company claims, and news reports are used only as pointers to primary information. This article does not rule on which company's or researcher's claim is right; it separates what can be confirmed, what is disputed in interpretation, and what is not confirmed. We could not confirm, and therefore do not state, Microsoft's formal reply to Legg's February 2025 critique, the full text of the Matters Arising, the peer-review status of the June 2026 preprint, independent reproduction, the results of DARPA's evaluation, or standards specific to topological quantum computing. All figures are explanatory concept drawings or drawings including our calculation; Figs. 1 and 9 are ImageGen-generated conceptual illustrations.