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Why is the amplitude simply so without including the $x \dot z$ factor? When you calculate the amplitude of the $|0\rangle^{\otimes n}$ state, you have $z = 0$ (the integer representation of the state you're looking at), so $x \dot z = 0$ for any $x$. Why is the resulting amplitude for the constant case is ±1 and 0 for the balanced case? For the constant ...


Where does that single evaluation of $f(x)$ actually occur? Is it in the construction of $U_f$? $U_f$ is an implementation of $f$ in quantum gates. The evaluation of $f$ occurs in the course of applying the gates making up $U_f$ to the qubits. What is $U_f$ in this case? I realize it depends on $f$, but how can we build it using at most one evaluation of $...

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