How should multi-controlled gates be added?

[Cryoris]

Multi-controlled gates are currently partially objects (MCX MCU1) and partially functions monkey-patched to the circuit (mcr*). Some, as the MCX, moved to the circuit library as Gate objects. In principle library objects can be added to the circuit using compose, but all multi-controlled gates right now are accessible as circuit methods.

This raises two questions:

1. Which multi-controlled gates should have their proper class?
2. How should they be added to circuits?

Possible solution:

1. The ones where we know of multiple implementations, such as MCX, or where more efficient implementations that the standard control mechanism are known.

2. Two options:
   a. Don't allow circuit methods:

   circuit.append(RXGate(0.2).control(5), [0, 1, 2, 3, 4, 5])
   circuit.compose(MCX(5))

   Advantage: Less circuit methods
   Problem: Verbose and need to import each gate to control

   b. Allow the controlled circuit methods to accept lists of qubits:

   circuit.crx(0.2, [0, 1, 2, 3, 4], 5)  # goes and does RXGate(0.2).control(5)
   circuit.cx([0, 1, 2, 3, 4], 5)  # goes and does MCX(5)

   maybe the cx is still qualified to have mcx to also allow arguments such as mode.
   Advantage: easy adding of multi-controlled gates, no additional methods
   Problem: circuit.cx([0,1], 2) currently means apply two CX gates.

   c. Keep mcrx as circuit method and

   circuit.mcrx(0.2, [0, 1, 2, 3, 4], 5)  # goes and does RXGate(0.2).control(5)
   circuit.mcx([0, 1, 2, 3, 4], 5)  # goes and does MCX(5)

   Advantage: easy adding of multi-controlled gates,
   But: additional methods

Personally I'd prefer 2b, since it gives us the power of multi-controlled gates with an intuitive and somewhat expected syntax and I'm not aware of a use-case for the current interpretation where cx([0, 1], 2) constructs two CX gates. Also adding special variants of a gate can be done using a mode flag which is a little more convenient than importing the gate and appending it, i.e.
circuit.cx(..., mode='v-chain') over from ... import MCXVChain; circuit.append(MCXVChain(), ...).

Are there opinions that the multi-controlled gates should only be library objects and not offer circuit methods? (@ajavadia @jaygambetta)

[nonhermitian]

I'm not aware of a use-case for the current interpretation where cx([0, 1], 2) constructs two CX gates

This is actually quite nice to have, and saves writing a for-loop just to add gates where you know they are going to go. Useful for cluster states, GHZ states etc.

[ajavadia]

@nonhermitian you are right but I think an internal poll indicated that most people expected this to create a multi-controlled gate.