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On 1993, Seth Lloyd published in Science a proposal for A Potentially Realizable Quantum Computer. In a nutshell, this consists in a long chain of weakly coupled qubits which are operated with (almost) no need for the operator to differentially address the different memory positions (i.e. no spatial addressing is required), and at the same time it does not require every qubit to present a different energy. Instead, all qubits are equivalent, with the exceptions of

  • the two extremes of the chain are distinguishable from the bulk (and this feature is used to introduce new information) and
  • a qubit is sensitive to its immediate neighbours, so at any given time you effect the same simultaneous operation on all qubits with certain surroundings, while leaving those with differing ones unperturbed (this feature allows operating in a manner of cellular automata)

My question is: have few-qubit versions of Lloyd's proposal been proposed, or implemented? (If yes: under what architecture(s), and if not, what would be required to do it?)

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This sort of architecture has certainly been studied more, often under the banner of "Global Control", significantly reducing some of the requirements (in particular, only requiring an ABABAB... repeating structure instead of ABCABC...). I am not aware of any of these ideas having been implemented. I assume this is partly because there are large overheads in the length of time required to implement something, which makes it more difficult to fit inside the decoherence time of a system.

I was involved in some studies at some point, detailing how you can make larger versions fault tolerant, but also suggesting implementations in optical lattices (here and here). These were at least partly motivated by this experimental paper. At a similar time, Zoller was also looking at this idea.

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