[IIAOPSW]

Knotting worldlines of anyons is the basis of topological quantum computing. Yes it can be done in theory, yes there is active research into doing it in practice.

https://en.wikipedia.org/wiki/Topological_quantum_computer

The best research into this right now is being done at Caltech

edit:

ok so tqc is mentioned in the article. my bad. I kind of skimmed the article the first time since I already know about this stuff.

[zmgehlke]

Yes, sponsored by MS at Station Q.

I believe the question there is if non-Abelian braiding statistics can be found to enable universal quantum computation, as Abelian anyons don't enable a univeral quantum computer. (Ideally a 12/5 FQHE, I believe.)

But my reading of the MS paper suggested that they were working with traditional anyons in 2+1D and the question of 3+1D analogs was unresolved. Here Wilzcek seems to suggest that there are no 3+1D analogs.

My question was if the treatment of objects as points, hence having a worldline rather than worldsurface or worldsolid wasn't the cause of that -- you can't knot a line in 4D, but you can knot a surface.

So my question was if the point object model was accurate or a simplification we need to move beyond.

[IIAOPSW]

ah

I'm fairly sure you cannot have a "lineicle" instead of a "particle". I guess maybe you could construct a weird albeit complete set of basis states based on lines through position space. However even if in some crazy interpretation your linicles had the properties of 2+1d anyon's, observing in this wicked basis is likely much harder than just making anyon's.

More simply at the end of the day the experimentalist observes a particle not a string. Thus there is a world line not a world surface.

disclaimer: this is partly my intuition. Maybe your idea has more merit than I give it credit for. My main research is not in anyons

[zmgehlke]

Well, the inspirtation in my mind was the interference from the double slit experiment.

If we think about a particle going from A to B, over t from 0 to 1, then the common interpretation is that it takes all paths and that those paths can interfere with eachother.

If we think about t=0.5, then the "particle" is not in a definite place, but sort of "smeared" out across its possible paths. The thought was if those possible paths, together, could form an embedded sphere in 3+1D, and in some sense could have similar computational knotting behavior. (And moreso that form shells of equal probability in a solid in 3+1+1D, with the extra dimension coming from the probability associated with each point.)

Im not sure how you'd "read" that, though possibly by "weakly" interacting with it in flight or it might contribute to the "random" outcomes of measured values. Since knotting is low-energy in general, we might not notice that behavior under normal conditions because of thermal interference adding a lot of computation in flight, hence making the values seem random. Similarly, heavily controlled experiments likely don't permit enough freedom to be anything but the trivial knot.

I expect that there is a reason that doesn't work, but figuring out where my hunch fails will help learn more about QM.