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For questions regarding complexity analysis of quantum algorithms and comparisons with complexities of classical algorithms.
5
votes
Accepted
If sampling the output of $U_1U_2$ is easy, is sampling the output of $(U_1U_2)^\dagger$ als...
We know that
$$\begin{eqnarray} P_{(U_1U_2)^{\dagger}}(y\ \vert\ x) &=& \left\vert\langle y\vert(U_1U_2)^{\dagger}\vert x\rangle\right\vert^2 = \left\vert\left(\langle x\vert U_1U_2\vert y\rangle\righ …