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Suppose we have two quantum circuits, the first computes (or at least approximates) the classical $\sqrt{\cdot}$ function $$S|x\rangle|0\rangle=|x\rangle |\sqrt{x}\rangle,$$ while the second circuit $A$ computes (again could probably just approximate) the $\arccos(\cdot)$ function $$A|x\rangle|0\rangle=|x\rangle |\arccos(x)\rangle.$$ Lastly, suppose we have ...


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