Superconducting Diodes and Quantum Computers

[John Clark]

It had been discovered a few years ago that twisted MoTe2 (Molybdenum Ditelluride) can behave as a one way superconductor, in effect a superconducting diode, but in the December 19, 2025 Proceedings of the National Academy of Sciences theoreticians at MIT have for the first time been able to mathematically explain, with the help of Anyons, how that is possible.

Anyon delocalization transitions out of a disordered fractional quantum anomalous Hall insulator

There are only two types of elementary particles, Fermions and Bosons. but Anyons are 2D quasiparticles with statistical properties between those of  fermions and bosons and electrical charges of 1/3 and 2/3. If you could make a conventional computer out of superconducting diodes it would be incredibly fast and also very energy efficient. But that's not all, it also has Topological Quantum Computer implications.

When you swap two identical Fermions like electrons the quantum wavefunction gets multiplied by -1. When you swap two identical Bosons like photons it gets multiplied by +1, but in both cases if you swap them twice then you’re back to where you started. When it comes to Anyons things are a little more complicated and they come in two types: 

Abelian Anyons: they usually have an electrical charge of 2/3 that of an electron and when you swap them, the wavefunction is multiplied by a complex number, but the order in which the operation is performed still doesn't matter, 2*3=3*2.

Non-Abelian Anyons: they usually have an electrical charge of 1/3 that of an electron and they are the really interesting sort, swapping those particles is like matrix multiplication, A*B≠B*A, and that's why they work so well with quantum logic. If you braid non-Abelian anyons, the order of the braid determines the final state of the computer.

If regular particles are used then the information is stored locally and the slightest perturbation will destroy it, however if Non-Abelian Anyons are used to create a braid then the quantum information is stored non-locally and it will only be destroyed if two identical perturbations hit the two ends of the braids simultaneously, and that is far less likely. This new paper describes a way to engineer Non-Abelian Anyons.

The superconductive state in Molybdenum Ditelluride is caused by Abelian Anyons, however if a precisely controlled amount of impurities are introduced (doped) into the material then tiny swirls of current spontaneously occur, and inside those vortexes are quasiparticles in a "Majorana Zero Mode", and that is another name for Non-Abelian Anyons. And that's just what you need to make a Topological Fault Tolerant Quantum Computer. 

For example, a Logical Qubit is made of 2 electrons and each of the electrons can be thought of as consisting of 2 quasiparticles in a different Majorana Zero Mode, so 4 of them make up a Logical Qubit, M1, M2, M3 and M4. If M1 and M2 are paired in a particular way we will call that quantum state 0.

If the quasiparticles are paired in a different way we will call that quantum state 1.
And we do the same thing for the second electron.

In a conventional computer a NOT gate simply flips a 0 to a 1 and a 1 to a zero, but on a topological computer you perform a NOT-gate by physically swapping the positions of 2 quasiparticles; and because they are Non-Abelian, swapping M1 and M2 and then M2 and M3, gives a different result than swapping M2 and M3, and then M1 and M2. A similar (although a little more complicated) procedure can produce AND-gates and OR-gates. Because of this order dependence, information can be encoded in ways that a conventional computer cannot, encoded in the sequence of swaps. And therefore with this procedure a Turing complete machine is possible.  

The reason this is worth doing is that it makes a quantum machine much more fault tolerant. Suppose you have two strings that have encoded information in this manner and you lie one string over the other or even tie them into a knot, if a random gust of wind jiggles both strings the geometry of the system will change but the topology of it will not unless the jiggle causes the strings to recrosse or untie, but such a complex occurrence is far more unlikely to happen than just a simple jiggle. As long as a random perturbation has not changed which string went around which the quantum information is preserved. 

It's interesting that the breakthrough in Quantum Computers seems to be occurring at about the same time as the breakthrough in AI which, so far at least, involves only conventional computers. I wonder if one is going to help the other and we get a virtuous cycle. 

 John K Clark    See what's on my new list at  Extropolis

c[]

[Brent Meeker]

Doesn't that give different results whether they are Abelian or not.

m1, m2, m3 -> m2,m1,m3 -> m3,m1,m2
m1, m2, m3 -> m1,m3,m2 -> m2,m3,m1

Brent

[John Clark]

On Tue, Jan 20, 2026 at 4:02 PM Brent Meeker <meeke...@gmail.com> wrote:

> Doesn't that give different results whether they are Abelian or not.
m1, m2, m3 -> m2,m1,m3 -> m3,m1,m2
m1, m2, m3 -> m1,m3,m2 -> m2,m3,m1

 

If the interactions with the following particles are Abelian then the final result of

{ [(M1*M2)*M3]*(M2*M1)*M3*] }*(M3*M1)*M2

would be identical to the final result of the following reactions 

{ [(M1*M2)*M3]*(M1*M3)*M2*] }*(M2*M3)*M1 

But if you do the same thing with particles that are NOT Abelian then those two results would NOT be the same. 

 John K Clark    See what's on my new list at  Extropolis

eh7

[Henrik Ohrstrom]

Also, is he as confused about the qualities of the lands as Erik the Red? Now he is about to anex Island instead, or is it also?

/Henrik 

[Brent Meeker]

OK, I see my mistake.  I was looking at whether the swapping was order independent.

But your post, "and because they are Non-Abelian, swapping M1 and M2 and then M2 and M3, gives a different result than swapping M2 and M3, and then M1 and M2."  is unnecessarily complicated.  Swapping M1 and M2 gives a different results if they are non-Abelian.

Brent

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[John Clark]

On Wed, Jan 21, 2026 at 9:35 PM Brent Meeker <meeke...@gmail.com> wrote:

> OK, I see my mistake.  I was looking at whether the swapping was order independent.

But your post, "and because they are Non-Abelian, swapping M1 and M2 and then M2 and M3, gives a different result than swapping M2 and M3, and then M1 and M2."  is unnecessarily complicated.  Swapping M1 and M2 gives a different results if they are non-Abelian.

I used that as an example because not only does it demonstrate how exotic  non-Abelian particles can encode information in ways that regular everyday Abelian particles cannot,  it also shows how that information can be used to perform calculations that Abelian particles cannot. 

 John K Clark    See what's on my new list at  Extropolis

6hu

eh7

[Brent Meeker]

On 1/22/2026 3:46 AM, John Clark wrote:

On Wed, Jan 21, 2026 at 9:35 PM Brent Meeker <meeke...@gmail.com> wrote:

> OK, I see my mistake.  I was looking at whether the swapping was order independent.

But your post, "and because they are Non-Abelian, swapping M1 and M2 and then M2 and M3, gives a different result than swapping M2 and M3, and then M1 and M2."  is unnecessarily complicated.  Swapping M1 and M2 gives a different results if they are non-Abelian.

I used that as an example because not only does it demonstrate how exotic  non-Abelian particles can encode information in ways that regular everyday Abelian particles cannot,  

Yes, M1*M2 is a different bit than M2*M1.

Brent

it also shows how that information can be used to perform calculations that Abelian particles cannot. 

 John K Clark    See what's on my new list at  Extropolis

6hu

eh7

Brent

On 1/21/2026 5:16 AM, John Clark wrote:

On Tue, Jan 20, 2026 at 4:02 PM Brent Meeker <meeke...@gmail.com> wrote:

> Doesn't that give different results whether they are Abelian or not.
m1, m2, m3 -> m2,m1,m3 -> m3,m1,m2
m1, m2, m3 -> m1,m3,m2 -> m2,m3,m1

 

If the interactions with the following particles are Abelian then the final result of

{ [(M1*M2)*M3]*(M2*M1)*M3*] }*(M3*M1)*M2

would be identical to the final result of the following reactions 

{ [(M1*M2)*M3]*(M1*M3)*M2*] }*(M2*M3)*M1 

But if you do the same thing with particles that are NOT Abelian then those two results would NOT be the same. 

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