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In trapped ion quantum computers, especially in systems with multiple traps, you may need at some point to perform a "chain reordering", in which you change an ion's position within the ion chain like in the figure below (source):

This is basically a SWAP between two qubits, you can either do it by applying a SWAP gate or by physically rotating the ions. Of course, both methods have time and reliability overheads but, is there (currently) a consensus of which one is generally better than the other?.

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  • $\begingroup$ When you talk about "physically rotating the ions", do you mean physically switching the position of two ions (as compared to just swapping the state, leaving the ions in the same position)? My impression as a non-specialist is that the physical switch is more problematic, but have no evidence for this. $\endgroup$ – DaftWullie Jan 26 at 13:54
  • $\begingroup$ Yes, that's what I mean, as shown in the figure, under "Option 2". Apparently, it can be done with not much of a problem. $\endgroup$ – alexvilloria26 Jan 26 at 13:58
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Prelim: I am no expert on implementation techniques or the frontier of what gate technology is being used in current renditions of Trapped Ion QC.

The Molmer-Sorensen gate is generally what is used in Hot Trapped Ion QC since it does not require the phonon mode of the Ion trap to be in the ground state; this gate forms a universal set of gates.

The gate operates by 'physically rotating the Qubits' (loosely), and through those operations applied at different times we can trivially obtain the SWAP and also C-NOT, C-Z, etc. So it's not a question of 'either rotate the bits or apply the SWAP gate', since the rotation is itself the SWAP gate.

Now if we are using other types of gates, like the Cirac-Zoller gate; then yes we would have to apply the gate in different ways to obtain the SWAP operation (Cirac-Zoller is just a C-NOT so this is quite trivial), and if we only have access to the Cirac-Zoller gate then there is no way to 'rotate' the Qubit. It is all a question of what tools are available for the technology you are working with.

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  • $\begingroup$ Thank you for your answer, I've changed the question as I think it wasn't clear enough. $\endgroup$ – alexvilloria26 Jan 26 at 13:47

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