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In simpler terms your question is: if noise/decoherence keeps entering the computation, how can a big computation possibly survive? The key concept you're missing is quantum error correction, which can pump noise/decoherence back out of the system. Of particular practical interest is the surface code.

Ion trap quantum computers hold ions in empty space using electric not magnetic fields. That is impossible using static fields (Earnshaw's theorem) so an alternating field is used. The effect is that charged particles such as ions seek a field minimum; this type of ion trap is also called a quadrupole trap because the simplest (lowest order) field having a ...

$\require{\mhchem}$ There are almost too many ion species to list that have been used in ion trap based quantum computing or related experiments. The usual choice is one that is, when singly ionized, hydrogen-like which has convenient consequences for their laser spectroscopy: Then a strong, typically $20$ MHz wide transition lies in the UV or blue end of ...

You may want to check out this Schaetz et al, Reports on Progress in Physics of 2012 "Experimental quantum simulations of many-body physics with trapped ions" (alternate link in semanticscholar). In sum: yes, the arrangement of the ions is one key limitation to scalability, but no, configurations are not currently limited to a single line of atoms. On that ...

While I’m not an experimentalist, and have not studied these systems in any great depth, my (crude) understanding is the following: In ion traps you (more or less) have to trap the ions in lines. However, this isn’t a limitation in terms of the ease of communication because what you’re probably thinking about is when a linear system has nearest neighbour ...

The ion states are the different energy states of the ion. These different energy states can be denoted with the total spin of the ion and the phonon levels of the ion. If we look at a Helium atom which has two electrons the total spin can be S = 0 if the electrons are in the following spin state: $$ \frac{1}{\sqrt{2}}(\uparrow \downarrow-\downarrow \...