I am struggling with how to go about applying the outline of controlled operations in N&C Quantum Computation and Quantum Information (pg 177-185, 10th ed) to construct a generalized-control-U gate.
The question I am trying to solve is how to compute the square root of a quantum circuit, where in the question it mentions using a clever trick involving phase estimation algorithm to do this efficiently. Specifically, the part I am confused with is where it is asking to construct a 2-qubit controlled-U operation using 3n 3-qubit gates, where n is an arbitrary number.
For the longest time, I assumed that this controlled-U gate was a single-qubit U gate with two control gates. But I am unsure if this is the case, rather U might be an n-qubit gate with 2 control-qubits.
Long story short, I am very confused on how to interpret the question and how to go about solving it, if anyone has seen something similar to this or can shed some light, I would be very grateful. Let me know if my question requires more details.