Universal construction of controlled-unitary gates using dynamical decoupling and the quantum Zeno effect

We present two new algorithms that universally construct a quantum circuit approximating a controlled-U(t) up to a global phase factor of U(t), denoted by ΛθU(t), where U(t) = e−iHt is the unitary evolution operator of an unknown Hamiltonian H of the system, and is given as a black box with tunable parameter t. We show that it is possible to approximately construct ΛθU(t) with arbitrarily high accuracy. This algorithm is based on the dynamical decoupling effect [1]. If another black box consisting of a time-inverted version of U(t), namely U(−t), is also available we can implement ΛθU(t) exactly with arbitrarily high success probability. This algorithm is based on the quantum Zeno effect.