(AE/MC) Controlled Circuits in Braket

[probvar]

To implement AE/MC, we need to implement a controlled-A operation, where A is a potentially complicated quantum circuit. Currently, I am unaware of a circ.controlled() operation like there is in qiskit and cirq. If it exists, it is quite hidden and wasn't used by the braket grover's or qpe braket example notebooks.

There are two potential paths I've thought of to implement this:

1. Following the method outlined in the braket qpe notebook, which creates the general controlled operation by transforming the sequence of gates to be controlled into a unitary matrix. Tom suggested that may not work on hardware, and likely believes that this would not work.
2. Duplicating in braket the qiskit or cirq functions used to for creating general controlled gates/circuits. This function is primarily defined in qiskit here

After discussing this with Tom, we are putting this issue on the back burner, and will hope to be able to address it either with Braket's continued development or with more time to be able to implement these complicated methods. We found out from Sashwat, who is interning with QSecure, that Braket will be potentially adding this feature "soon," so we might be able to address this once Braket adds this feature. (We talked with Sashwat around July 21st, 2021)