gate.control()

[ajavadia]

Enhance the Gate class with a method for controlling it.
This should return a new ControlledGate (which derives from Gate).

• Implement ControlledGate class. Existing controlled gates such as CX and CH and CSWAP and CCX should derive from this now. (add ControlledGate class #2862)

After this implementation, the following should work:

# inst is a 2 qubit instruction
# circ is a 5 qubit circuit
circ.append(inst.q_if(), [0, 2, 1])
circ.append(inst.q_if(2), [0, 3, 1, 2])
circ.append(inst.q_if().q_if(), [0, 3, 1, 2])  # should be same as above
circ.draw()  # should clearly show controlled gates

circ.decompose()  # should decompose the controlled gates one level

Follow ups:

• Expose in a nicer user interface.
• Write transpiler passes that efficiently use ControlledGate.

notes:
1- control currently clashes with a property of the instruction. So let's use the q_if method for now, with the goal of eventually moving to control.
2- The decomposition should be shallow, in the sense that the controlled gate provides a definition only in terms of controlling its subcomponents. It will be the job of the unroller to take this definition recursively until the end and implement a circuit over U3 and CX.

[ewinston]

Moving visualization to separate issue, #3223.