I suspect to acheive the 4D needed for construction without undesirable intersection, it will have to be implemented with a dynamic repeating 3D-Volume cycle, essentially rendering the 4D shape in time.
Much like time crystals.
https://en.wikipedia.org/wiki/4D_scanning_transmission_elect...
(Not in the sense that "time" is involved but in the sense that what distinguishes 3D from 4D is almost only software . The same way you can see 4D "all at once" on your 2D screen,but 4tuples coords!= code)
But then again IBM have claimed quantum software=quantum hardware (see above).. they might or might not understand what is or is not needed?
(It's easier if you get one that is not twisted. Something like https://www.sugarrushlane.com/products/filled-red-licorice-s... but with 4 instead of 5 parts. Also imagine each of the 4 parts has a different color. )
Now make a circle with it.
If you don't twist it, you get an horizontal surface that looks like a thick border of a circle, and a vertical surface that looks like the round wall of a cylinder.
If you twist half a turn, when you connect the extremes the top of the + in one extreme is glued to the bottom of the + in the other extreme. Something similar withe the left and right parts of the +. Now you have two overlapped copies of a Möbious strip, each perpendicular to the other.
If you twist a quarter of a turn, when you connect the extremes the top of the + goes to the right, the right to the bottom, the bottom to the left an the left to the top. So you get only one "strip?"