Eigenphase Hadamard-test probability
= Eigenphase Hadamard-test probability
If $U|\psi\rangle=e^{2\pi i\theta}|\psi\rangle$, the ordinary Hadamard test returns ancilla zero with probability
$$
p_0=\frac{1+\cos(2\pi\theta)}2=\cos^2(\pi\theta).
$$
= Eigenphase Hadamard-test probability
If $U|\psi\rangle=e^{2\pi i\theta}|\psi\rangle$, the ordinary Hadamard test returns ancilla zero with probability
$$
p_0=\frac{1+\cos(2\pi\theta)}2=\cos^2(\pi\theta).
$$