Initialize with an integer parameter is not compatible with AerSimulator

[Cryoris]

Environment

• Qiskit Terra version: main @ bedecbdce563f4e83acc11c7ec5ca6878a36a4b7
• Python version: 3.10
• Operating system: macOS

What is happening?

As reported in https://quantumcomputing.stackexchange.com/questions/32681/nonsensical-projection-of-initialized-qubits-in-qiskit, using the AerSimulator to run a circuit containing an Initialize instruction with an integer as parameter breaks, due to

Simulation failed and returned the following error message:
ERROR: Failed to load qobj: Invalid qobj "initialize" instruction ("params" is incorrect length).

How can we reproduce the issue?

from qiskit import QuantumCircuit, Aer, transpile

qc = QuantumCircuit(1)
qc(1, [0])  # initialize to integer 1     

backend = Aer.get_backend("aer_simulator")
tqc = transpile(fivequbitcircuit, backend)
job = backend.run(tqc, shots=1000)
result = job.result()

What should happen?

The Initialize instruction should be supported by Aer.

Any suggestions?

Not sure if this is something we should fix on the Terra side, as indeed the .params attribute it a list of length 1, which might be a bit confusing, or if this should be handled in Aer. The cleanest solution might be to convert the integer to a label in Terra's class, as that's already happening under the hood (and that's handled correctly by Aer).

[jakelishman]

Officially this is a problem for Aer to deal with, but Terra really doesn't make it easy to support the Initialize operation for simulators. There's like 3 completely different forms that the params could be, which all have very different semantics.