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I have added (here) to the Idea-section a paragraph on the example of incremental addition $(-)+n \;\colon\; \mathbb{Z} \xrightarrow{\sim} \mathbb{Z}$
with a pointer to
for how to implement this with just CNOT gates,
and with an image of Leibniz’s mechanical calculator, where the reversal of this operation is obtained by turning the crank the opposite direction.
(Or so it says on Wikipedia. I have not yet found a good published reference on the “stepped reckoner”. )
added pointer to:
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