No-iteration of unknown quantum gates

Understand

We propose a new no-go theorem by proving the impossibility of constructing a deterministic quantum circuit that iterates a unitary oracle by calling it only once.

• Different schemes are provided to bypass this result and to approximately realize the iteration.
• The optimal scheme is also studied.
• An interesting observation is that for large number of iterations, a trivial strategy like using the identity channel has the optimal performance, and preprocessing, postprocessing, or using resources like entanglement does not help at all.