Consistent naming of controlled gates

As discussed with @ewinston, the names of the controlled gates are inconsistent. For instance, the controlled version of HGate is called CHGate but YGate becomes CyGate. This applies to many others too. We should name them all consistently.

Possible choices would be:

1. Only the first letter of the gate name is upper case, i.e.

YGate CyGate RyGate CryGate U3Gate Cu3Gate

1. The gate names are full uppercase, i.e.

YGate CYGate RYGate CRYGate U3Gate CU3Gate

1. The control gates only prepend a C, the gate name is kept, i.e.

YGate CYGate RyGate CRyGate U3Gate CU3Gate

Currently the rotations are called RXGate, thus 2. and 3. might be the same. Most rotation gates follow 1., which I personally think looks most aesthetic and fits also with the named gates as Fredkin or Toffoli. However, I think writing all in uppercase is probably the least error-prone method.

What are the thoughts on this?

[ajavadia]

I would also like to see a gate namespace that has aliases for the lower case circuit extensions to the gate objects. Eg something like gates.cx => CXGate. Here you could also add additional aliases if desired, eg gates.ccx, gates.toffoli => CCXGate

Yes please I have been wanting to move these gates out of qiskit.extensions for 2 years. Moving them to qiskit.circuit.gates sounds good, and exposing a qiskit.gates namespace so that one can do:

from qiskit import gates
circuit.append(gates.cx, [0, 1])

@Cryoris can you start with the gate name standardization/deprecations first and then we do this in steps? Seems everyone is good with uppercase. IGate and qc.i seem fine to me.

[Cryoris]

Achieved via #3695 🚀