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I've been wondering, are there any known tasks/algorithms that can be performed on 1 quantum device, but also be somehow modified and split between several smaller devices?

The thought behind the idea, is that if creating large quantum computers (meaning computers with large number of qubits to work with) that are also stable and noise-tolerant to some degree is a hard task, maybe we could utilize several smaller devices, which are naturally less prone to noise and perform algorithms that would require a larger device. For instance, instead of using a computer with 10 qubits, we could maybe use 2 computer with 5 to 6 qubits each, or something in that direction.

If there is, by chance, a sub-field in quantum computation that deals with such questions, I'd really like to know about it and explore it more.

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    $\begingroup$ Have you looked at VQEs? This is a major advantage for comp chem $\endgroup$
    – C. Kang
    Sep 13 '20 at 20:22
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If you could completely separate a computation between two different processors, then, in fact, one processor would be enough, and you could run one computation after the other. What you can do is try to rearrange a computation that minimises the number of two-qubit gates acting between two distinct blocks of qubits. Those two-qubit gates probably then need to be replaced by some sort of teleportation operation (or simply moving qubits between the two different devices), so you do need the ability to share entangled states between the two processors, which would be a challenging task, but that's why you try to keep the number to a minimum.

In fact, this is what some practical implementations (specifically, ion traps, see here) have been looking at doing. I don't know if there's been much work to look at optimising specific algorithms - from the theory perspective, we know that it can be done whatever circuit you supply, and circuit optimisations are going to be very specific to a given implementation.

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