shouldn't single-qubit initialization decomposition result in single-qubit instructions?

[1ucian0]

Not sure if an issue, so tagging as question for now. If I'm saying nonsense, an explanation would be enough to close this issue (even if I don't understand it).

When creating an initializer with single-qubit states, I would expect that the decomposition turns into single qubits gates/instructions. In this case¹ I want to initialize two qubits in |1>:

from qiskit.extensions.quantum_initializer.initializer import Initialize
initialize = Initialize([ 0, 0, 0, 1])

The result of decomposing it, I think, should be something along these lines:

initialize.definition.draw()

          ┌───┐
q_0: ─|0>─┤ X ├
          ├───┤
q_1: ─|0>─┤ X ├
          └───┘

However, it results in a circuit with CNOTs:

from qiskit import transpile
transpile(initialize.definition, basis_gates=['u3', 'cx', 'reset'], optimization_level=0).draw()

          ┌──────────────┐┌───┐┌───────────────┐┌───┐
q_0: ─|0>─┤ U3(pi/2,0,0) ├┤ X ├┤ U3(-pi/2,0,0) ├┤ X ├
          └┬────────────┬┘└─┬─┘└───────────────┘└─┬─┘
q_1: ─|0>──┤ U3(pi,0,0) ├───■─────────────────────■──
           └────────────┘                            

I understand that synthesis is something hard you want to keep general and probably we dont want to handle too many "special cases" (or do we?). To this end, would it help to support something likeInitialize('11') (a la Statevector.from_label)?

In summary,

• should we "aid" Initialize to decompose into single-qubit instructions when possible?
  • If No,
    • should Initialize synthesis be smarter and minimize/avoid multi-qubit gates when possible?
    • should the transpiler do the leg work here?
  • If Yes,
    • should we support something like Initialize('11'), Initialize('+l'), and the other labels from Statevector.from_label?
    • should we keep the labels when a Statevector is created from labels and allow Initialize(Statevector.from_label('11'))²?

Footnotes: ¹ This issue is inspired by a question in stack exchange ² Supporting Statevector as Initializeparameter seems intuitive to me in any case. Currently an unexpected .data needs to be added Initialize(Statevector.from_label('11').data)

[1ucian0]

From some in-webex discussions, it seem the way to go will be Initialize('11'). Implemented in #5229