When talking about quantum parallelism, in Nielsen and Chuang, it's said that:

it is possible to transform this state into $|x, y \oplus f(x)\rangle$, where $\oplus$ indicates addition modulo 2; the first register is called the ‘data’ register, and the second register the ‘target’ register.

I'm confused about why the first register is called the ‘data’ register and not the ‘control’ register. Is there a difference between a data register and a control register? Is ‘data’ register a standard name in EE or just in QC?

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    $\begingroup$ I've heard the first register called the "upper register" or the "input register"; sorry I don't have a citation for those. But even though the first register "controls" the second register, the first register will have the phase kicked back to it by the second register; in a way the first register is where all the action will be. Remember that measuring the second register is almost always optional after evaluating $f(x).$ $\endgroup$ Commented Sep 23, 2021 at 14:55


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