## Sayonara Majorana?

Many of you have surely already seen the news that the Kouwenhoven group in Delft—which in 2018 published a paper in Nature claiming to have detected Majorana particles, a type of nonabelian anyon—have retracted the paper and apologized for “insufficient scientific rigour.” This work was considered one of the linchpins of Microsoft’s experimental effort toward building topological quantum computers.

Like most quantum computing theorists, I guess, I’m thrilled if Majorana particles can be created using existing technology, I’m sad if they can’t be, but I don’t have any special investment in or knowledge of the topic, beyond what I read in the news or hear from colleagues. Certainly Majorana particles seem neither necessary nor sufficient for building a scalable quantum computer, although they’d be a step forward for the topological approach to QC.

The purpose of this post is to invite informed scientific discussion of the relevant issues—first and foremost so that I can learn something, and second so that my readers can! I’d be especially interested to understand:

1. Weren’t there, like, several other claims to have produced Majoranas? What of those then?
2. If, today, no one has convincingly demonstrated the existence of Majoranas, then do people think it more likely that they were produced but not detected, or that they weren’t even produced?
3. How credible are the explanations as to what went wrong?
4. Are there any broader implications for the prospects of topological QC, or Microsoft’s path to topological QC, or was this just an isolated mistake?

### 39 Responses to “Sayonara Majorana?”

Hi Scott, As you mentioned there are several proposals to produce Majoranas. Original proposal is based on nanowires and that is the approach Microsoft has adopted. There are more than a handful of high profile papers on nanowire approach. The retracted paper was on among them. The main signature of presence of Majoranas in nanowires has been zero bias peak (which is common evidence among all early papers). Sergey Frolov has done a great job analyzing the data of the retracted paper and shown the main claim of the paper that the zero bias peak is quantized to a particular value is invalid. The data is correct (unfirtunately misrepresented) but interpretation is invalid. Personally I do not think all papers with nanowire approach are flawed by this discovery but it is harder to buy the zero bias peak argument if limited data is presented. There are other approaches to find and control Majoranas e.g. in Josephson junctions, topological insulators, atomic chains, special quantum Hall states etc. unfortunately since Microsoft is not investing on those approaches they are only explored within a much smaller group of academics. I personally think Josephson junctions have a good prospect. Majorana field is under funded by federal agencies and now that Microsoft has had a setback, I imagine it will only make it harder to continue for academics.

2. kodlu Says:

At the risk of being somewhat off topic, what do you think of the result by Pan and Zhang which (according to Kalai) spoofs Google’s quantum circuit using GPUs?

According to the Abstract

“Using our method, employing a small computational cluster containing 60 graphical processing units (GPUs), we have generated one million correlated bitstrings with some entries fixed, from the Sycamore circuit with 53 qubits and 20 cycles, with linear cross-entropy benchmark (XEB) fidelity equals 0.739, which is much higher than those in Google’s quantum supremacy experiments.”

3. Scott Says:

kodlu #2: You’ve got to be kidding me. Did you scroll down to the blog post right before this one?

4. oja Says:

I heard rumors (and nothing else!) that there were irregularities with the first Majorana detection paper as well. The group was allegedly reviewing a competing paper and delayed the approval and forced the removal of any mentions of Majorana so that their own Majorana paper would be published first. It seems like a good time to mention that, so that the rumor can be properly debunked.

5. Jelmer Renema Says:

ad 2: an expert panel called in by the TU Delft to investigate said that based on the data that was taken in 2018 but not reported in the paper, the measurements do not support the existence of Majorana’s in this experiment.

ad 3: There is the subject of an ethics investigation at the moment.

6. maline Says:

I’d appreciate if someone would give (or link) a short explanation of why creating Majorana spinors would be so useful for quantum computing.

7. Scott Says:

maline #6: So let me try to do it in 1 paragraph. 🙂

Twenty years ago, Freedman, Kitaev, and Wang made the remarkable discovery that, if you could create suitable non-abelian anyons in a 2-dimensional medium, then you could do a universal quantum computation, just by braiding the anyons around each other in an appropriate pattern, with the braidings (i.e., moving one anyon past another one) roughly corresponding to 2-qubit gates. Better yet, this setup would have a certain degree of quantum fault-tolerance “baked in”: in order to cause an error, you’d need to change the topology of the braiding pattern; a small local change to an anyon’s path would have no effect unless it altered the topology. And thus was born the whole program of topological quantum computing, on which Microsoft (where Freedman works) has bet almost all of its experimental QC effort. The only problem is that, to date, no one knows how to reliably create or detect non-abelian anyons at all, let alone precisely manipulate huge numbers of them! Now, a Majorana fermion turns out not to be a kind of non-abelian anyon that would suffice for universal QC—you’d need more complicated kinds—but at least it’s some non-abelian anyon. And that’s basically the connection.

8. osa lunde Says:

Javid #1: Are we sure nanowires are the only approach MS is pursuing? I’m aware it’s the primary one, but my impression is that they are dabbling from time-to-time in some of the other approaches you’ve mentioned. Admittedly, you would know better than us about that.

There are other claims for observing either Majorana’s or anyonic behavior (if they’re not Majorana’s?). No one seems to be talking about this recently updated paper: https://arxiv.org/abs/1905.10248. Not sure what the implications here mean, or if anyone takes this seriously, but it sounds like we should be cautiously excited, maybe?

As for question #4, it does make me wonder: has anyone ever done a thorough, top to bottom reexamination of the underlying theory of Majorana’s, from the namesake himself through to Freedman/Kitaev/Wang? Is the theory physics here beyond reproach at this point? I find it interesting that so many papers reexamining Majorana claims attributes it to Andreev processes instead – if the mimicry is that good, should the question be re-asked? Do they actually exist?

Microsoft has never been shy about cutting their losses on projects. But, it’s my hope that both they, the government and other academic groups continue this line of research, with the same degree of time/money/effort. Surely, the basic research (just the necessary material research alone) could yield computing benefits beyond just Majoranas? Maybe that could be a selling point. And, quiet as it’s kept, isn’t IBM, Nokia (above), and other companies also researching TQC, but with less fanfare?

If the approach MS is currently taking doesn’t work, then switch approaches? If that ultimately doesn’t pan out, then it seems reasonable and fair to me to move on. Not sure the media and other onlookers will have a mature reaction to something like that. Also, I believe their labs have some experience fabricating other QC platforms. While it might be technically painful, I would think it would be ok to swallow some pride, and (temporarily, maybe) throw their hat into the transmon, gatemon, or other QC platform ring. Just until. But do they need to? Despite the “they’re doomed/ oh so behind” headlines, at what point in QC development does any company or group need to be fearful of everyone else’s progress? 100 qubits? 1000?

I feel like the wounds this paper retraction has opened up go deeper than just questioning Majorana research in this instance, given the personalities involved. Hard questions should be asked. But let’s not throw the baby out with the bathwater, or whatever appropriate cliché makes sense here 🙂

9. Jelmer Renema Says:

@ Osa Lunde #8: unfortunately, it seems that the baby is already being thrown out with the bathwater. Frolov was complaining on twitter that one of his grant applications got turned down with the argument that present methods for detecting Majoranas are ambiguous, while the fact of the matter is that they are not ambiguous (at least that is what he claims), it just happens that the experiment under discussion didn’t detect Majoranas.

10. maline Says:

Scott #7:

So if I get your drift, the word Majorana in these discussions is more of a disclaimer than a selling point! The claim is that anyons of some type were detected, which unfortunately happen to be Majoranas. Is this correct?

One point of confusion for me: how can Majorana “fermions” be anyons? Doesn’t the word fermion imply the ordinary anticommutation relations and statistics?

11. Suomynona Says:

Doug Natelson has some comments on this as well as a link to the official investigative report.

A paper from yesterday on the arXiv poists that the observed zero bias peaks were a result of disorder.

osa #8: There is no reason to suspect that the underlying theory is wrong. Majorana fermions are mathematically allowed to exist based on our understanding of fermions going back almost 100 years. They’re pretty firmly baked into a framework which is extremely well understood. It would actually take a new unknown law of physics to completely outlaw their existence outright.

It’s also perhaps worth noting that the Majoranas of the current discussion are not fundamental particles, but rather quasiparticles, i.e. quantum excitations which behave as Majoranas. The fundamental degrees of freedom in these experiments is only ordinary electrons and atomic nuclei. However, the relevant dynamical degrees of freedom exhibited by the system may be collections of these electrons and/or nuclei which as a collective behave differently. This concept of collective excitations is a fundamental concept in condensed matter physics. An illustrative example is the fractional quantum Hall effect, where the dynamical degrees of freedom can be interpreted as quasi-electrons with fractional values of electric charge, despite the fact that at the fundamental level there are only ordinary electrons (which have integer charge) existing in the material.

The trick here is to engineer a system where these Majorana degrees of freedom can be manifested. There are many simple models which do, but engineering such systems in real experiments is where the challenge is.

12. Scott Says:

maline #10: No, that’s not right. If Majoranas were really created, that would be super-exciting, and the first-ever examples of non-abelian anyons in the lab. (Of course the kind of anyons that suffice for universal QC would be better still, but no one was claiming that.)

You’re right that “Majorana fermion” is confusing terminology. Someone can correct me if I’m wrong, but I believe the point is that they behave as fermions in 3 dimensions, but display non-abelian statistics in 2 dimensions.

13. Alexander Vlasov Says:

Scott #12: Certainly the terminology is confusing, Majorana fermions vs Majorana modes. There is understanding explanation in “Majorana returns” by Frank Wilchek in Nature Physics, September 2009. It is under paywall, so some citation may be appropriate: “However, in contrast to the algebra associated with the Dirac and Majorana equations, the algebra describing Majorana modes describes the geometry of n Euclidean dimensions in an abstract mode space, rather than the paltry 3+1 dimensions of spacetime.” In fact, the the n-dimensional Euclidean space theme here is also related with matchgates, that may be more known to computer scientists due to Valiant works.

14. Vampyricon Says:

Scott #7,

What would make a “suitable” anyon?

15. Scott Says:

Vampyricon #14: One example is what are called “Fibonacci anyons.” See here for more.

16. Jonah Says:

As a condensed matter experimentalist, let me venture forth two pennies. In my time, cherry-picking of data is not widespread but not unheard of. I hope that this paper will motivate more soul-searching in the community about how seriously we treat our data. We are far from the high energy approach of rigorous statistics, blind tests and so on, often because our goal in the lab is to eliminate statistical error in favor of clear-cut data. In a sense it’s a luxury of the field, but it hides the arguably deeper problem of competing models and explanations. Specifically as concerns the Majorana track, this points to the need for alternative probes. As far as I understand, the theory has come to a solid understanding that a few alternatives besides Majorana modes can explain these zero-bias peaks. What’s needed is a new probe that is sensitive to the underlying topological properties in some sense, as opposed to the electrical transport properties, which can be mimicked by other, less exotic creatures.

17. fred Says:

Scott #15

The opening of that paper really reads like typical Quantum Supremacist pamphlet.
I.e. overselling QC as much as possible while leaving out all the caveats, potentially confusing a non-specialist.

“While classical computers perform Boolean operations on a register of bits, quantum computers perform unitary operations on an exponentially large vector space, typically composed from many quantum bits, or qubits. Using this exponentially large computation space, it is possible, at least in principle, for quantum computers to efficiently solve classically difficult problems such as prime factorisation of large numbers (Shor, 1994) or the simulation of complex quantum systems”

“Another example of a classically hard algorithm, which can benefit from quantum computation, is the determination of the Jones polynomial of knots. The Jones polynomial is a knot invariant with connections to topological quantum field theory and other knot-like systems. It is also, in general, exponentially difficult to compute by classical means. However, a quantum algorithm developed by Aharonov, Jones and Landau (AJL) can be used to efficiently estimate the value of the Jones polynomial at the roots of unity, by first reducing the problem to finding the diagonal elements of the product of certain matrices. “

Is Jones polynomial one of those problems we can genuinely call “exponentially difficult” without being NP-complete?

18. fred Says:

“the simulation of complex quantum systems”

Realizing logical qubits is in itself the simulation of a complex quantum system.
So once the first logical qubits are realized, the goal will be met, no?

19. Scott Says:

fred #17:

The opening of that paper really reads like typical Quantum Supremacist pamphlet.
I.e. overselling QC as much as possible while leaving out all the caveats, potentially confusing a non-specialist.

I sometimes get the impression that such text is copied and pasted from one QC paper to the next, and recommend scrolling past it till you reach the meat. 🙂

Is Jones polynomial one of those problems we can genuinely call “exponentially difficult” without being NP-complete?

It depends on the desired accuracy. Calculating the Jones polynomial exactly (or multiplicatively approximating it) is known to be #P-complete, which is “even harder” than NP-complete. Additively approximating the Jones polynomial at a root of unity was shown by Aharonov, Jones, and Landau to be BQP-complete—thus, almost certainly exponentially hard for classical computers in the worst case, but almost certainly not NP-hard.

20. jm Says:

Scott #12 and maline #10: As Alexander Vlasov #13 mentions, a better name for the phenomenon being sought in topological quantum wires is Majorana zeromodes. This means that there are some hermitian operators $$\gamma_i$$ acting on the Hilbert space, commuting with the Hamiltonian, and satisfying $$\{\gamma_i, \gamma_j\} = 2\delta_{ij}, i = 1.. N$$.
(Such modes arise localized at the ends of topological wires and are interesting because the smallest Hilbert space representing this algebra is $$2^{N/2}$$-dimensional. This means that the Hilbert space does not factorize into a separate factor for each localized mode, and this nonlocality offers some protection to the quantum information stored there. In other contexts, e.g. the Moore-Read quantum Hall state, such modes can be localized on mobile particles; such a particle is then a non-abelian anyon, not a fermion.)

A Majorana fermion in any dimension, in contrast, is an ordinary particle with Fermi statistics. It arises as a quantum of excitation of a Majorana spinor field. This is a real spinor representation of the Lorentz group.

These two very different concepts share Majorana’s name only because they both involve anticommuting objects satisfying a reality condition.

21. Scott Says:

jm #20: OK, thanks very much! I just changed “Majorana fermions” to “Majorana particles” in the post.

22. fred Says:

Scott #19

Reading the paper, it occurs to me that not only is building an actual QC way harder than building a classical computer, but the level of knowledge and specialization required to work on this is also way beyond what used to be the standard in classical electronics.
QC will be experimental physics for a long time before it becomes engineering.

Back in the early 90s in Europe in polytechnic school (electro-mechanical engineering degree), in a few years they could train someone to really understand well all aspects of the topic, both theoretically but also very hands-on with a ton of practical lab work (semi-conductor, the transistor, logic gates, general circuit layout, programming (assembly, pascal, fortran, c), analog electronics with E-M theory, wave guides, radio signals, control theory, error correction, the distribution of electrical energy, sampling theory, etc). With as much coverage on the mechanical side too. We were kept busy at school from 8am till 8pm, 5 days a week (it was tough, to the point that we all still have nightmares about it, 30 years later).
But after graduation we could be hired and hit the ground running in almost any area (personally I immediately ended up working in software engineering anyway, which was my favorite “hobby” since I was a kid).
But last time I checked my university website, most of that very wide and practical training is now gone, replaced with a handful of way more exotic and specialized topics (like opto-electronics).

Makes me wonder how the workforce for all that “classical” electronics stuff is being replaced.
Probably all that knowledge has been displaced to Asia, or companies that still work on this have to train their junior engineers themselves.

23. Scott Says:

fred #22: Indeed, no one said this was going to be easy!

24. botnet-client Says:

@ Jonah:

I’ve become suspicious of highly precise investigations into particle physics that simultaneously not rule out or prove the existance of quantum foam.

25. Matthias Troyer Says:

Scott, let me share my perspective and provide some more information. Over the last year, as the scientific community found problems with the TU Delft paper, a thorough re-analysis was done. A new paper based on that has been posted by the authors in arXiv:2101.11456 . Details of the changes are explained in this repository, including an independent review by a committee of experts. The latter is a good summary of what went wrong and a cautionary tale for everyone.

Regarding the implications, let me make two comments. First, this has been an experiment about a specific device choice and materials and fabrication process. There are indeed other papers showing zero bias peaks and other indirect evidence. The field has also moved significantly beyond what we all understood four years ago. Already back then, and even more so now, it has become clear to experts that local measurements, including of the conductance plateaus, would not be sufficient proof of Majorana quasiparticles but that additional experiments would be needed.

The Microsoft effort has never been based on that paper. There has been significant progress on theory and detailed numerical device modeling that makes us confident that we can fabricate topological qubits based on Majoranas. There has also been significant progress in fabrication and experiments, far beyond what was possible several years ago. I and my colleagues are thus confident in the potential of this approach.

Those interested in recent progress can listen to talks of our team at next week’s March Meeting. In particular, Leo Kouwenhoven will give an invited talk on Majorana qubits (abstract) and Roman Lutchyn on Topological superconductivity in superconductor–semiconductor heterostructures (abstract).

26. Inna Vishik Says:

This is a bit outside my field, but I want to comment on your first and fourth question, by pointing out that there are many materials platforms where Majoranas have been predicted to be realizeable. This includes magnetic nanowires on a superconductor (which is qualitatively similar to the approach in the retracted paper), a superconducting or proximitized superconducting topological insulator, ferromagnetic superconductors, px+ipy superconductors, twisted bilayer magic angle graphene, iron-based superconductors (here I’m dubious), and quantum spin liquids. Within most of these categories is a large number of compounds or heterostructures. While most won’t pan out, it is premature to rule out topological quantum computing based on the present retraction, though it may still be in the realm of fundamental materials physics (my field) rather than actual qubits.

27. Scott Says:

Matthias #25: Thank you for sharing your perspective!

[In case “full disclosure” is relevant to my other readers: Matthias is now part (a big part) of the Microsoft QC effort. Before he joined Microsoft he was also a leader in evaluating and in some cases debunking D-Wave’s claims; I’ve admired his work on that issue and others.]

28. fred Says:

Scott #23

it was also the general observation that, as technology moves forward (driven by growth), complexity usually tends to keep ramping up, and people become more and more specialized and no one is even able to master all the moving parts of any sub-system within a system (things sometimes do get simpler, but it’s rare).

When it’s about the LHC having many bugs, or physics papers with 12 co-authors having math mistakes, it doesn’t really have much of an impact on society.
But when it’s about practical things like the Boeing 737 Max (where the good practice of the past have been lost between generations of engineers), nuclear power plants, the power grid, automated trading systems, every day cars (which can no longer be diagnosed/fixed without a specialized computer and downloading a system update), or simply trying to forward emails… that’s an entirely different ball game.

There is a deep hidden cost to the never ending drive for more control (aka progress).

29. Scott Says:

fred #28: And yet for all that, we do have technologies that didn’t exist when I was younger, such as the phone on which I’m writing this. And airplanes steadily continued to get safer, until they’re now unbelievably, ridiculously safe by historical standards — do you have any idea what level of risk people would just accept as normal in the 1930s? — which is what made the fatal incompetence in the Boeing 737 Max stand out at all. Sometimes complicated engineering processes, specialization, and modularity actually work!

30. Jelmer Renema Says:

@ Fred 28: I think the countervailing effect to increasing complexity is that as a discipline gets more mature, the knowledge involved moves from academia to structures more suitable to the kind of long-term effort that is required to come to an actual working technology, e.g. companies and government research labs. With quantum, we’re right in the middle of that process at the moment. Many national quantum technologies programs envision a key role for these long-term actors.

Consider that one of the key motivations for Martinis move to Google was that his systems had become sufficiently complex that it took the full length of a PhD to learn how to fabricate one.

31. fred Says:

Scott #29

Moore’s law (exponential improvement) has mitigated a lot of the downsides. The vast majority of coders don’t have to worry about software optimization (the type that was done in the 80s).

Aviation is quite a matured industry (it goes beyond just technology, with decades of well established procedures), so there’s that. But I was surprised that serious engine failures don’t see that rare (but since there’s redundancy, it’s often not a major issue)

32. fred Says:

Forgot to mention that deep learning is an example of major “simplification” breakthrough – it’s relatively easy to learn and to apply, with results far beyond anything that could only be achieved previously by very specialized experts.

33. asdf Says:

Coincidentially I just came across this interesting biographical article about Ettore Majorana:

https://nautil.us/issue/13/symmetry/the-disappearing-physicist-and-his-elusive-particle

I had read the Wikipedia article about him some time earlier. He was an “out there” theorist in the 1920s-30s who disappeared at sea in 1938 under mysterious circumstances. Quite a story.

34. Steven Evans Says:

Scott Says:
Comment #315 March 14th, 2021 at 1:33 pm

Cheers for the comment on the S word. I’ll have a think about what you’ve written, and what people like Sabine Hossenfelder have written and see if I can get a better feel for it. Thanks for the interesting post.

35. fred Says:

Not about Majorana particles, but Skyrmions (which are also vortices that can be in superposition)

https://www.quantamagazine.org/graphenes-new-twist-reveals-superconductivitys-secrets-20210316/

36. John Baez Says:

It’s not really surprising that a physicist who invented a particle that is its own antiparticle would “mysteriously disappear”.

37. Scott Says:

Inna Vishik #26: Thanks so much!

38. Alexander Vlasov Says:

John Baez #36: They also may suddenly “mysteriously appear” sometimes, e.g., operators $$\phi_j, \pi_j$$ in section about Spin(10) of your paper with John Huerta about algebras of GUT are formally coincide with thing they have called “Majorana modes/fermions”.

39. fred Says:

A interesting article that’s related

https://www.quantamagazine.org/like-magic-physicists-conjure-curious-quasiparticles-20210324/

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