agaitaarino
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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 paper, check Figure 3 for experimental fluorescence images of laser-cooled ions in a common confining potential of a linear RF trap, including a single ion, a single line, a zig-zag chain and a three-dimensional construct.

From Figure 3 in the paper above by Schaetz et al: "Structural phase transitions can be induced between one-, two- and three-dimensional crystals, for example by reducing the ratio of radial to axial trapping frequencies." I am sure more recent review papers should exist, but this is the first one I found that was satisfactory. Admittedly, current results are more about direct simulation rather than universal computation, e.g. from figure 13 in the same paper: "Changing the experimental parameters non-adiabatically during a structural phase transition from a linear chain of ions to a zigzag structure, the order within the crystal breaks up in domains, framed by topologically protected defects that are suited to simulate solitons."

On the same topic, and also from 2012, another paper worth checking out would be Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins (arXiv version) (Nature version. You have the experimental picture as Figure 1; it is a Penning trap in this case rather than a Paul trap. Indeed, it is not universal quantum computing but rather the specialized application of quantum simulation, but still it is undeniably experimental progress towards holding ions in place in a 2-D trap and thus advancing towards scalability.

I am myself no expert in traps, but this is what I got on scalability in a recent (2017) conference:

• Experimentalists play around with the potentials and achieve interesting combinations, with central zones that are quasi-crystalline (chains, ladders, ribbons etc) and exotic tips (e.g. ribbons or ladders that finish in a single atom).
• The majority of the popular ions have a configuration of the type [noble-gas]$$s^1$$ (like Ca$$^+$$), preferredly with no nuclear spin but this is for convenience and simplicity. Accessing hyperfine states and/or a more complex spin level structure (like Yb$$^+$$=[Xe]f$$^{14}$$s$$^2$$) opens the door to a richer Hilbert space per ion.
• Collective vibrations are used as the basis of interqubit communication. As in the previous point, the breathing mode is uniquely stable and thus convenient to use, but other vibrations are also accessible and would allow more interesting interqubit communication schemes.
agaitaarino
• 3.5k
• 1
• 9
• 38

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 paper, check Figure 3 for experimental fluorescence images of laser-cooled ions in a common confining potential of a linear RF trap, including a single ion, a single line, a zig-zag chain and a three-dimensional construct.

From Figure 3 in the paper above by Schaetz et al: "Structural phase transitions can be induced between one-, two- and three-dimensional crystals, for example by reducing the ratio of radial to axial trapping frequencies." I am sure more recent review papers should exist, but this is the first one I found that was satisfactory. Admittedly, current results are more about direct simulation rather than universal computation, e.g. from figure 13 in the same paper: "Changing the experimental parameters non-adiabatically during a structural phase transition from a linear chain of ions to a zigzag structure, the order within the crystal breaks up in domains, framed by topologically protected defects that are suited to simulate solitons."

I am myself no expert in traps, but this is what I got on scalability in a recent conference:

• Experimentalists play around with the potentials and achieve interesting combinations, with central zones that are quasi-crystalline (chains, ladders, ribbons etc) and exotic tips (e.g. ribbons or ladders that finish in a single atom).
• The majority of the popular ions have a configuration of the type [noble-gas]$$s^1$$ (like Ca$$^+$$), preferredly with no nuclear spin but this is for convenience and simplicity. Accessing hyperfine states and/or a more complex spin level structure (like Yb$$^+$$=[Xe]f$$^{14}$$s$$^2$$) opens the door to a richer Hilbert space per ion.
• Collective vibrations are used as the basis of interqubit communication. As in the previous point, the breathing mode is uniquely stable and thus convenient to use, but other vibrations are also accessible and would allow more interesting interqubit communication schemes.